análisis numérico de las tensiones y deformaciones en un

Trabajo de Fin de Grado

Grado en Ingeniería de Tecnologías Industriales

Análisis numérico de las tensiones y deformaciones en un implante dental

MEMORIA

Autor: Maria Sarrá Paloma y Anna Serra Cantarell Director: Miquel Ferrer Ballester Convocatoria: Enero 2017

Escola Tècnica Superior d’Enginyeria Industrial de Barcelona

Análisis numérico de las tensiones y deformaciones en un implante dental Pág. 1

Resumen

EnelpresenteTrabajodefindeGradoseexponeelanálisisnuméricodelastensionesydeformacionesdeunimplantedental.Elobjetivoprincipaldeesteestudioescomprobarla influencia del cambio de material de la corona del diente en la distribución detensionesinternasydeformaciones.Deestemodo,sesigueelanálisisempezadoporunalumnodelauniversidad,querealizóunestudiosimilaraéste[1].Secompararánlosresultados obtenidos entre distintos trabajos publicados para comprobar si lasconclusionessiguensiendoválidas.

Despuésdellevaracabounarecopilacióndeinformaciónsobrelosimplantesdentales,suscomponentes,propiedadesyotrascaracterísticas,elprocesoquesehaseguidoeneste estudio consta de dos partes diferenciadas. En primer lugar, se ha definido lageometría del implante. Se han hecho los cambios pertinentes y se ha construido elensamblajede laspiezasque lo constituyen.En segundo lugar, sehan llevadoa cabodistintassimulacioneshaciendomodificacionesenlascondicionesdecontornoysehahecho un estudio de los resultados. Se ha analizado la tensión transmitida a cadacomponentedelimplantedentalyaltejidoóseoenelqueseimplanta.Tambiénsehaestudiadoladeformacióntotaldelapieza.

EnlaprimeraetapadelanálisissehautilizadoelprogramainformáticoSolidworks,unsoftware CAD para el modelado de piezas 3D, que permite dibujar piezas 3D degeometrías complejas y hacer el ensamblaje posterior.Despuésde la obtenciónde lageometríasehaprocedidoalasegundafasedelestudio,paralacualsehautilizadoelprograma informático ANSYS Workbench, software que trabaja con el método deelementos finitos. A través de este programa se ha realizado un análisis estáticocompuestode4casosqueseexpondránmásadelante.Paracadacasosehanestudiadolosefectosquetienelaaplicacióndeunafuerzapuntualounapresiónsobreelimplantedentalyeltejidoóseoenelqueseintegra,ysehaanalizadocómovaríaesteefectoenfuncióndelmaterialdelacoronadelimplante.

Una vez obtenidos los resultados, se ha llevado a cabo un estudio de los mismosaplicando los conocimientos obtenidos en el Grado en Tecnologías Industriales de laETSEIB, extrayendo una serie de conclusiones que se irán exponiendo a lo largo deltrabajo.

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Índice

RESUMEN ____________________________________________________ 1

ÍNDICE _______________________________________________________ 3

1. GLOSARIO _________________________________________________ 5

2. PREFACIO _________________________________________________ 6

3. INTRODUCCIÓN _____________________________________________ 7

4. ELIMPLANTEDENTAL _________________________________________ 84.1. Definición ........................................................................................................... 84.2. Clasificación ........................................................................................................ 9

4.2.1. Enfuncióndelposicionamientodelimplante ............................................................. 94.2.2. Enfuncióndelnúmerodefasesnecesariasparaimplantarlo ..................................... 114.2.3. Enfuncióndelelementooconjuntoaimplantar ...................................................... 12

4.3. Partes ............................................................................................................... 13

5. GEOMETRÍA _______________________________________________ 14

6. MÉTODODEELEMENTOSFINITOS _______________________________ 236.1. Modelodelosmateriales .................................................................................. 23

6.1.1. Implanteypilar ...................................................................................................... 246.1.2. Tejidoóseo ............................................................................................................ 246.1.3. Corona ................................................................................................................... 26

6.1.3.1. Capainterior ............................................................................................. 26

6.1.3.2. Capaexterior ............................................................................................ 276.1.4. Tablaresumendemateriales .................................................................................. 28

6.2. Mallado ............................................................................................................ 286.3. Condicionesdecontorno ................................................................................... 316.4. Idealizaciones ................................................................................................... 32

6.4.1. Geometría ............................................................................................................. 326.4.2. Propiedadesdelosmateriales ................................................................................. 326.4.3. Interfazhueso-implante .......................................................................................... 336.4.4. Condicionesdecontorno ........................................................................................ 33

7. ANÁLISISDELOSRESULTADOS _________________________________ 34

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7.1. Estudioestático ................................................................................................ 347.1.1. CasoA:Fuerzapuntualenelcentrodelimplante ...................................................... 36

7.1.1.1. CoronaMET .............................................................................................. 37

7.1.1.2. CoronaMCER ............................................................................................ 38

7.1.1.3. CoronaMCOM .......................................................................................... 39

7.1.1.4. CoronaFCOM ............................................................................................ 407.1.2. CasoB:Excentricidaddelpuntodeaplicacióndelafuerza ......................................... 42

7.1.2.1. CoronaMET .............................................................................................. 43

7.1.2.2. CoronaMCER ............................................................................................ 44

7.1.2.3. CoronaMCOM .......................................................................................... 45

7.1.2.4. CoronaFCOM ............................................................................................ 467.1.3. CasoC:Sustitucióndelafuerzapuntualporunapresión ........................................... 47

7.1.3.1. CoronaMET .............................................................................................. 48

7.1.3.2. CoronaMCER ............................................................................................ 49

7.1.3.3. CoronaMCOM .......................................................................................... 50

7.1.3.4. CoronaFCOM ............................................................................................ 517.1.4. CasoD:Fuerzapuntualoblicua ................................................................................ 52

7.1.4.1. CoronaMET .............................................................................................. 537.2. Análisis detalladode las deformaciones conel cambiodeposicióndeuna fuerza

puntual ............................................................................................................ 547.2.1. CoronaMET ........................................................................................................... 55

8. CONCLUSIONES ____________________________________________ 57

9. AGRADECIMIENTOS _________________________________________ 63

10. BIBLIOGRAFIA ____________________________________________ 64

11. ANEXOS _________________________________________________ 66


1. Glosario

MET: Corona dematerialmetálico Cr-CO (SP2HeraeniumPwHeraeus Kulzer GmbH,Hanau,Alemanya).

MCER:Coronadematerialmetal-cerámicoVita3DMaster(Vita,Alemanya).

FCOM:Coronadematerialfibradecarbono-compositeBioCarbonBridge(MicroMèdica,Itàlia),BioXFill(MicroMèdicaItàlia).

MCOM:Coronadematerialmetal-compositeCr-Co(LaserPFM,Renishaw,RegneUnit)iBioXFill(MicroMèdica,Itàlia).

σ1:Estadoprincipalmáximodetensión.

σ2:Estadoprincipalmediodetensión.

σ3:Estadoprincipalmínimodetensión.

σVM:TensiónequivalentedeVonMises.

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2. Prefacio

LamotivaciónparalarealizacióndeesteproyectohasidoprincipalmenteelinterésqueambasteníamosenaplicaryadquirirnuevosconocimientosdelaasignaturaResistenciadeMateriales. A lo largo del grado, coincidimos en que las asignaturas que nos hanatraído son las relacionadas con el comportamiento de los materiales, por lo quedecidimosllevaracaboelproyectoenestedepartamento.

Sobrelaeleccióndeltemaconcretodelproyecto,elhechodequefuerauntemaactualyalaordendeldíafueunodelosfactoresquemásinfluyó.Laimplantologíaesunapartede la ciencia médico dental que ha conseguido grandes avances durante la últimadécada, gracias al desarrollo de las tecnologías y a los conocimientos adquiridos delfuncionamientocelulardelostejidos.

Además,existenestadísticasqueafirmanqueel69%delapoblaciónadultahaperdidopor lomenosundientede formapermanente [2],por loque,ademásdeserun temaactual,tambiénesunabuenaopcióndenegocio.


3. Introducción

La utilización de implantes dentales se ha vuelto un recurso habitual en nuestrasociedad.Estetratamiento,quepermitereponerlosdientesperdidos,espocoagresivoy, además, es una solución duradera y permanente. Es por esto que existenmuchosestudiosquetienencomoobjetivomejoraryoptimizarestetipodeprótesis.

El objetivo principal del proyecto es estudiar el comportamiento de la prótesiscambiandoelmaterialdelacoronaylageometríadelapieza.Deestemodo,sepretendeseguirelanálisisempezadoporunalumnodeestauniversidadquededicósuTrabajodefindeMáster(2016)alcálculodetensionesinternasydeformacionesprovocadasporuna carga estática. En este proyecto, respecto al anterior, se ha añadido una capametálicaenelimplante,sehanintroducidocorreccionesenlageometríayfinalmentesehanplanteadonuevoscasosaestudiar.

Elmétododeelementosfinitosescomúnmenteutilizadoparallevaracaboestudiosdeeste tipo,puestoqueayudaapredecir losefectosde las tensionesenel implanteyelhuesoenelqueseintegra.Estemétodoconsisteenladivisióndeunsistemacontinuoen subdominios o elementos, unidos entre sí a través de puntos situados en suscontornos (nodos), cuyo comportamiento se rige por un conjunto de ecuacionesdiferenciales.Graciasalastecnologíasactualessepuedereproducirlageometríadeunimplante y realizar simulaciones que permiten obtener resultadosmuy cercanos a larealidad. Sin embargo, existen algunos factores que pueden alterar los resultadosobtenidos,yaseanlascondicionesdecontornoolaspropiedadesdelosmateriales.Porlo tanto, se intentará hacer un estudio lo más preciso posible que se asemeje a losresultadosobtenidosexperimentalmente.

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4. Elimplantedental

4.1. Definición

El implantedental(Fig.1)esunapiezahechadematerialbiológicamente inertecuya funciónes tantoestéticacomofuncional.Enelámbitoestético,suprincipalfunciónesquesu apariencia sea lomás natural y semejante a un dienteverdaderoposible,mientrasque,enelámbitofuncional,suprincipal utilidad es cumplir con las funciones propias deun diente. Esta pieza se inserta en el hueso alveolar,reemplazandodeestaformalaraízdeldiente.Enelhuesoenelqueseintegraelimplantesedistinguendostiposdetejido óseo, el trabecular y el cortical, con distintaspropiedades[4].Elhuesotrabecularsecaracterizaporseruntejidoesponjoso,mientrasqueelhuesocorticalesdensoycompacto.

Laestabilidaddelimplanteysucomportamientocomounsólidoempotradoperfectoseconsigue gracias al proceso de osteointegración. Laosteointegración(Fig.2)eslaunióndirecta,estructuraly funcional, sin tejido periodontal alrededor delimplante dental y el hueso alveolar; es decir, el huesoqueseadhierealasuperficiedelimplante.Esteprocesobiológicotieneuníndicedeéxitodel97,5%[5].

Latransferenciadecargaen la interfazhueso-implantedependedevarios factores:eltipo de carga, las propiedades del implante y la corona, la geometría de la unidadprotésica,lanaturalezadelainterfazhueso-implante,ylacalidadycantidaddeltejidoóseoquerodeaalimplante.Deentreestosfactores,lageometríadelimplantedentalsepuedemodificarfácilmenteenlaetapadediseño.Lacalidadycantidaddetejidoóseo,tantocorticalcomotrabecular,debeserasistidoclínicamenteysehadetenerencuentaenlaselecciónelimplante[6].

Elanálisisdelatransferenciadecargaenunimplantedentalesprimordial,yaquetantoelhuesocomolaunidadprotésicaestánconstantementesometidosaesfuerzos.Sedebellegar a un equilibrio tal que se evite la fatiga delmaterial del implante y su posible

Fig1.Implantedental

Fig2.Implanteosteointegrado


fractura por sobreesfuerzo, pero teniendo en cuenta que, a su vez, un esfuerzodemasiado bajo puede dar lugar a atrofia por desuso y, en consecuencia, la posiblepérdidadelhueso.

4.2. Clasificación

Existen diferentes clasificaciones de los implantes dentales en función del criterio declasificación utilizado. A continuación, se exponen tres tipos de clasificaciones: enfuncióndel posicionamientodel implante, en funcióndel númerode fases necesariasparaimplantarloyenfuncióndelelementooconjuntoaimplantar.

4.2.1. Enfuncióndelposicionamientodelimplante

Segúnestecriteriodeclasificación,seconsiderandostiposdeimplantesdentales[7]:

• Endo-óseos

• Subperiósticos(yuxta-óseos)

Los implantes dentalesendoóseos son aquellos que van colocados dentro del huesomaxilar.Estetipodeimplantessonlosmásutilizadosenlaactualidaddebidoasugranefectividad.Sefabricancontitaniopuroparagarantizarsucompatibilidadysumétododeinserciónbasadoenlaosteointegración,siendounaintervenciónquirúrgicabastantesencillayquenosueletenercomplicaciones.Dehecho, lasestadísticas indicanquesetratadeunodelosprocesosoralesconmayorprobabilidaddeéxito;concretamente,un98%decasosfavorables[8].

Después del proceso quirúrgico, se precisa que el tornillo se integre en el hueso(procesodeosteointegración),paralocualserequiereuntiempode,aproximadamente,4meses.Actualmenteseda laopciónalpacientedeque,duranteesteperiodo,recibaunaprótesisprovisional,porcuestionestantoestéticascomofuncionales.Unavezsehacompletadoelprocesodeosteointegración,seprocedealacolocacióndeloselementosrestantes.

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Dentro de los implantes dentales endoóseos se distinguen varias formas de implante[9][10]:

Cilíndricos

Estetipodeimplante,talycomosunombreindica,tieneformadecilindroeincluyeunaseriedeperforacionesparaqueelhuesosepuedadesarrollarensuinteriory,deestamanera,quedeintegradoysefijeporretenciónmecánica.Esunprocesolento,yaquelaintegracióndelhuesoenelinteriordelcilindrorequieretiempo,y,porestemotivo,estetipo de implantes no son muy utilizados en la actualidad. Pueden ser de superficieroscada,conelobjetivodeaumentarlasuperficiedecontactoentrehuesoyimplante.

Roscados(Fig.3)

Sonlosmáscomuneshoyendíadebidoasuestabilidadyalaposibilidaddecolocarsetanto en un diente como en variosdientes consecutivos. Consiste en untornillo fabricado de titanio, metalcompatible con la biología del tejidoóseo que se integra muy bien en elmismo. Este tornillo, a partir de unprocesoquirúrgicobastantesencillo,se

implantaenelhuesomandibular.

Laminados

Este tipode implantedental no está recomendadopor los dentistas si la pérdidadeldienteestotal,pero,engeneral,dabuenosresultadossiseutilizaparalasustitucióndeun incisivo central en el nivel del maxilar superior, especialmente si el huesomandibular es ancho y profundo. La principal ventaja del implante dental endoóseolaminadoesque sepuede realizarenunaúnica intervención. Sinembargo, al ser tanlimitadoelabanicodecasosenquesepuedeutilizarsinriesgodedesprendimiento,estetipodeimplantenoesmuycomúnhoyendía.

Fig3.Implanteendoóseoroscado


Otro tipo de implante dental en función de su posicionamiento es el implante dentalsubperiósticooyuxtaóseo.Consisteenunmarcodemetalquesecolocaenelhuesomandibularjustodebajodeltejidogingival.Al ircolocadojustodebajodeltejidodelaencía,estetipodeimplantetienelaformadelaorilladelhuesoconelobjetivodequepuedafijarsecorrectamente.Constadeunosdispositivosconformadesillademontarquesecolocansobrelacrestaóseaentreelperiostioyelhuesoalveolar[10].

Estetipodeimplantesseutilizaprincipalmenteenpacientesnoaptosparautilizarunimplanteendoóseo,yaqueelhuesomandibulartienequetenerunaalturamínima.

4.2.2. Enfuncióndelnúmerodefasesnecesariasparaimplantarlo

Siguiendoestecriterio,elconjuntodeimplantesdentalessepuededividirendostipos[11]:

• Decargainmediata

• Endosfases

El implantedentaldecargainmediata, talycomosunombreindica,esaquelqueserealizaenunaúnicafase.Enestetipodeimplantedental,seevitaunasegundafaseconel objetivo de no abrir la encía, colocando el implante y la corona en una únicaintervención.Noobstante,esteprocedimientonoesposiblesincontarconunaseriedecondicionescomolacalidadycantidaddelhuesoalveolar.

Elimplantedentalendosfases,porotrolado,requierededosetapasparallevaracabolaimplantacióndelaunidadprotésica.Enlaprimerafasesellevaacabolainsercióndelimplantey,despuésdeunperiodonecesarioparagarantizarlaintegracióndelimplanteconelhueso(3-4mesesenlamandíbulainferiory5-6mesesparaelmaxilarsuperior),seprocedealasegundafase.Enlasegundaetapadelproceso,seatornillaelpilarsobrelapartesuperiordelimplanteysecementalacoronasobreél.

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4.2.3. Enfuncióndelelementooconjuntoaimplantar

Segúnestaclasificación,seobtienentrestiposdeimplante[12]:

• Unúnicodiente

• Unpuente

• Unaarcadaentera

Talycomolosnombresindican,estaclasificaciónhacereferenciaalelementoasustituirenlabocadelpaciente.

Enel casodeunúnicodiente (Fig.4),hayuna coronaparaunsoloimplante.Funcionacomoundientenatural,sinapoyarseendientesadyacentes.

Unpuente(Fig.5)esunacomposicióndecoronasdentalesunidasentresíycementadasavariosimplantes.

Finalmente, también se puede realizar unasustitución de todo el conjunto de dientes. En estecaso, se trataría de un implante dental del tipo

arcadaentera(Fig.6).Estetipodeimplantedentalconsiste en la sujeción de una reproducción del

conjuntodedientesdelmaxilarsuperioroinferioratravésdevariosimplantes.

Fig4.Implantedeunúnicodiente

Fig5.Puente

Fig6.Arcadaentera


4.3. Partes

Elimplantedentalestácompuestodetrespartesprincipales(Fig.7):

• Lacorona

• Elpilar

• Elimplante

La corona es la parte que reproduce el aspecto de un diente natural. Esta pieza estáformadaporunacapainteriorquepuedeserdefibraodemetal,ylaparteexteriorquereproduce la forma del diente natural, que puede ser demetal, demetal-cerámico ometal-composite.Paralacapainterior,seutilizametalofibradecarbono(enfuncióndelmaterialqueseutiliceparalacapaexteriordelacorona)conunageometríadiferenteencadacaso.

Elpilareslapiezaquehacedeuniónentrelacoronayelimplantey,generalmente,vaunido al implante a través de un tornillo. Se pueden encontrar pilares de diferentesdiseños y longitudes en funciónde suuso. Si el implantedental sustituye a unúnicodiente, sedebedisponerdeun sistemaantirrotaciónpara impedir elmovimientodelpilarylacoronasobreelimplante.

Porúltimo,elimplanteeslapiezaqueseinsertaenelhuesodelamandíbulayconsisteenuntornilloqueharálafunciónderaíz.

Porúltimo,elimplanteeslapiezaqueseinsertaenelhuesodelamandíbulayconsisteenuntornilloqueharálafunciónderaíz.

Fig7.Partesdelimplantedental

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5. Geometría

Sehacontactadoconelestudiantequerealizóelproyectoelcuatrimestreanteriorparaque nos enviase las piezas escaneadas del implante en formato IGES, para poderlasmanipularatravésdelprogramainformáticoSolidworks,softwareCAD,paramodeladomecánicoen3D.Acontinuaciónsemuestranlaspiezasqueleentrególaempresaqueseencargódehacerelescaneado3D(Fig.8):

En este proyecto se realiza la geometría con dos posibles casos. Se ha añadido alconjuntouncomponentequeconsisteenunacapasituadaenel interiorde lacorona,quepuedeserdemetalodefibradecarbonoy,enfuncióndeesto,tendráunageometríauotra, lascualesseexplicaránenesteapartado.Dependiendodelageometríadeestacapa,evidentementevaríalageometríadelacoronaensuinterior,porloquetambiénsehantenidoquerealizarcorreccionesenesteaspecto.Parafacilitarlanomenclatura,lageometríaconunacapainteriordemetalsereferenciaráconelnúmero1ylageometríaconcapadefibradecarbonoconelnúmero2.

Elpilar es lapieza en laque sehan tenidoquehacermásmodificaciones.Enprimerlugar,sehacambiadolapartesuperiorparaquetuvieraformacilíndrica.Comoesunapiezaescaneada,enSolidworkssevecomounúnicosólidoy,porlotanto,noexisteunhistorial de operaciones que se pudieran modificar, sino que hay que crear nuevasoperaciones. Sehaextruidouncorteparaeliminar laparte superiordelpilary sehacreado un plano en la nueva superficie para poder generar un cilindro con lasdimensionesadecuadas.

Fig8.Piezasobtenidasdelescaneado3D


Otramodificaciónquesehallevadoacaboenelpilarhasidolageneraciónmanualdelarosca.Estepasohasidoposterioralensamblaje,yaquesehaobservadoquefallabaalimportarelsólidoalprogramadeelementosfinitos.Alimportarlageometríadelapiezaensamblada,elprogramadaproblemasenlazonaroscadadelpilar:seobservaunafaltade material en algunas zonas. Se ha atribuído la causa del error al hecho de que elroscado pueda presentar irregularidades por haber sido obtenida a través de unescaneado3D.

Fig 10. Comparativa geometría pilarinicialvs.pilarmodificado

Fig 9. Pieza importada a ANSYSWorkbenchconfaltadematerial

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Parasolucionarestacuestión,sehadecididorealizarlasmedidaspertinentesygenerarla rosca manualmente a partir de Solidworks, asegurando de esta forma su totalregularidad.Elprocedimientoquesehaseguidohasido,enprimerlugar,laextrusióndeun cono con las dimensiones adecuadas para su posterior roscado (Fig. 11).Seguidamente,sehaextruidouncilindroenlaparteinferiordelconoyselehaasignadoelredondeopertinente(Fig.12).

Se ha definido un croquis formado por una hélice, también con forma cónica, queenvuelveelconopreviamenteextruido.Acontinuación,seharealizadootrocroquisenel extremo de la hélice (Fig. 13), formado por un triángulo que define la forma delroscado,enelquesehancopiadolasdimensionesobtenidasdelescaneado.Finalmente,se ha copiado la parte superior del pilar, ya que en ésta ya se habían realizado lasmodificaciones pertinentes, y se ha copiado en la parte superior del cono roscado,asignando las relaciones de posición convenientes. Finalmente, se ha utilizado laherramientaCombinardeSolidworksy,dentrodeésta,laopciónAgregarparaformarunúnicosólidoapartirdelasdospiezas.

Fig11.Vistadetallezonainferiordelpilarmodificado

Fig12.Vistapilarmodificado

Fig13.Croquisrevolucionadoparagenerarlarosca


También se ha redondeado la arista de la base superior del cilindro del pilar con unradiode0,2mmparaevitarquesegenerentensionesenloscantosvivosencontactoconlacorona.

Respecto a la capa interior de la corona, tal y como se ha mencionado, hay dosmateriales posibles, cada cual con una geometría diferente. Para el caso 1, la capainteriordelacoronaestáhechademetal,ytienelaformadelcilindrodelpilarconunespesor de 0,5mm. En el caso 2, la capa interior tiene forma similar a la del dientenaturalperoenescalareducida.SehamodeladoamboscasosapartirdeSolidworks.

El modelado de la capa metálica mencionada essencillo (Fig. 14). Se puede llevar a cabo de variasmaneras;finalmente,sehaoptadoporlaextrusióndeun cilindro de diámetro exterior de medidascoincidentes coneldiámetro interiordelhuecode lacorona, y, posteriormente, se ha añadido una ‘tapa’circularaestecilindro.

También se han redondeado en este caso las aristas encontacto con la zona exterior de la corona y con el pilar(con un radio de 0,2mm) para evitar la concentración detensionesenlaszonasquesehaconsideradonecesario.

Elmodeladodelacapainteriordefibradecarbonohasidoun poco más elaborado. En un principio, lo que se hahechoha sido reescalar lapieza ‘corona’delproyectodereferencia con las dimensiones adecuadas. Sin embargo,enestageometríaseproducenvérticesycantosvivosquegeneraríanzonascríticasdetensionescuandoseaplicaraunacargaenlassimulaciones,ynoseadecuaalarealidad.Parasolucionarestetema,sehadecididoreproducirenuncroquislaformaaproximadade un diente, y se ha revolucionado dicho croquis entorno a un eje de revolución.Tambiénsehanredondeadolasaristasquesehaconsideradooportunoparaevitarlageneracióndetensionesenloscantosvivos.

Respecto a la corona, se han tenido que realizar modificaciones en su interior paraadaptarloa lacapamencionadaanteriormente,quesehaañadidoen lageometríade

Fig11.Capainteriormetálica

Fig 12. Capa interior de fibra decarbono

Pág. 18 Memoria

este proyecto. Para este caso, también existen dos geometrías, ya que depende de lacapainteriorqueseutilice.

Para realizar la geometría correspondiente a la corona concapa interior de fibra de carbono (con forma de diente), elprocedimiento utilizado ha sido insertar el archivo deSolidworksdelacapainteriorenelde lacorona.Apartirdelas relaciones de posición adecuadas, se ha fijado la capainteriorenlaposiciónenlaqueiráenelensamblaje.Después,se ha utilizado la herramienta Combinar del programaseleccionandolaopciónEliminar,utilizandocomosólidobaselacoronaycomosólido‘tijera’lacapainterior.Deestaforma,lo que se consigue es copiar la forma de la capa interior en la corona, eliminando elmaterialquesobradelsólidoprincipal(corona).

Enelcasodelacoronaconcapainteriormetálica, lamodificación que se ha llevado a cabo ha sido elaumento del hueco interior. Concretamente, se haaumentadoeldiámetroenunvalorde1mm,esdecir,elgrosordelacoronasehareducidoen0,5mm.Estamodificaciónesnecesariapara laposterior insercióndelacapametálicaenelinteriordelacorona.

Sehaintentadomodificarelescaneado,pero,comohapasadocon la pieza anterior, Solidworks la muestra como un únicosólido.Pararealizarlamodificación,sehaprocedidoarealizaruncroquisconeldiámetroadecuadosobrelasuperficielímitedel agujero cilíndrico de la corona, y, seguidamente, se haextruido dicho croquis. Se ha llevado a cabo el mismoprocedimientoenelpilar,pero,enlugardeextruirunsólido,loque se ha hecho ha sido extruir un corte de las mismasdimensiones. En este caso, también se ha realizado unredondeode0,2mmen laaristaencontactocon lacapa interiormetálica,parapoderensamblaryevitarpicosdetensionesencantosvivos.

Fig13.Coronaparageometría2

Fig14.Croquisparaaumentodiámetrointeriordelacorona

Fig15.Coronaparageometría1


Por último, la última pieza que faltapormodelareslaqueharálafunciónde encía. Tal y como se ha explicadoanteriormente, el tejido óseo estáformado por dos tipos de tejido, elcorticalyel trabecular.Estehechoseha querido reflejar en la geometríapara obtener unos resultados lomásverosímiles posible. Se ha decididoque la pieza que hace la función dehuesoconsistaenunbloquerectangularenelquevaenroscadoel implante.Estebloque,posteriormente,sehadivididoenunbloque interior correspondiente al tejido óseo trabecular y una capa exteriorcorrespondiente al cortical. Para ello, se ha extruido un rectángulo de las medidasadecuadas.Sehadecididoutilizarlasmismasmedidasqueenelproyectodereferencia,generandounbloquerectangularde30mmdelargo,14mmdeanchoy20mmdealto.Posteriormente, se ha insertado la pieza del pilar roscado en el mismo archivo deSolidworksquecontieneelbloquey,medianterelacionesdeposición,sehafijadoelpilarenelmismositiodondesecolocaráposteriormenteenelensamblaje(insertadoenelbloqueensupuntomedio).Acontinuación,sehautilizadolaherramientadeSolidworksCombinar, yautilizadapreviamente, seleccionando la opciónEliminar y estableciendocomosólidoprincipalelbloque.Deestaforma,seeliminaelmaterialquesesolapaentredos sólidos, consiguiendo de esta forma calcar la parte inferior del pilar (la que vainsertadaenelbloque)enelbloqueyasegurandodeestaformaelensamblajedeestosdossólidossinpresenciadeinterferencias.

Una vez obtenido el bloque que hace la función de hueso, se ha procedido a sumodificaciónatravésdelaextrusióndediversoscortesparaobtenerlasdospiezasqueformaneltejidotrabecularyelcortical,ysehanunidoensamblándolasparaformarelconjuntoóseo.

Fig16.Bloquetejidoóseoroscado

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Despuésderealizar lasmodificacionesmencionadas,al realizarelensamblaje1sehaobservado que, aún habiendo realizado dichos cambios, algunas piezas siguen sinencajar.

Es por ello que se ha tenido que realizar unaúltimamodificación,queconsiste,porunlado,enla extrusión de un corte en la base del cilindrodelpilar,reduciendodeestaformalaalturadela“zona inclinada” del pilar y aumentando, encambio,laalturadelcilindro.Deestaforma,sehaconseguido evitar su interferencia con la capametálicadelinteriordelacorona.Tambiénsehatenido que rellenar el vacío que se había

generadoentrelacoronayelpilarjustoenlazonainferiordelacapametálica.Estepasose ha llevado a cabo a través de la revolución de un croquis con las dimensionesadecuadasalrededordelejedelpilar.

Finalmente, despuésde todas las correcciones explicadas con el findeque laspiezasensamblenysugeometríasealomáscercanaposiblealarealidad,sehaprocedidoalensamblajedelasdosposiblesgeometrías.Enprimerlugar,lageometría1(compuestaporlacoronacorrespondientealacapainteriormetálica,lacapametálica,elpilaryelbloque formado por los dos componentes correspondientes a los tejidos óseos) y,posteriormente, la geometría 2 (compuesta por la corona correspondiente a la capainteriordefibradecarbono,lacapadefibradecarbono,elpilaryelbloqueformadoporlos dos componentes correspondientes a los tejidos óseos). Se han impuesto las

Fig17.Conjuntotejidoóseo(corticalytrabecular)

Fig18.Ensamblajeconinterferencias


relacionesdeposiciónnecesariasparaensamblarlosconjuntosysehaobservadoque,en ambos casos, tanto la corona como su capa interior tienen permitida la rotaciónalrededordelcilindrodelpilar.Paraevitarestarotación,sehautilizadolaherramientadeSolidworksBloquearRotación.Además,paraasegurarelcorrectoensamblajedelaspiezas,sehacomprobadoquenohayinterferenciaentreellasatravésdelaherramientaCalcularInterferenciasdeSolidworks.

A continuación, se ilustra el resultado de los ensamblajes para las dos posiblesgeometrías:

Fig19.Ensamblajeparageometría1

Fig20.Ensamblajeparageometría2

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Una vez obtenidos los tres archivos de ensamblaje, se han guardado los archivos enformato IGES para que sean compatibles con el programa que se utilizaráposteriormenteparalasimulación.

Fig21.Vistafrontaldelensamblaje


6. Métododeelementosfinitos

Elusodelmétododeloselementosfinitosparalaresolucióndeproblemasingenieriles,físicos,etc.haaumentadodeformaexponencialalolargodelosúltimosañosdebidoaldesarrollodelastecnologíasyalosavancesinformáticos.Estemétodopermiteresolvercasos que, con los procedimientosmatemáticos convencionales, eranmuy difíciles o,incluso, imposibles de resolver. Se tenía que optar entonces por la realización deprototiposysuposteriorensayo,yseibanhaciendomejorasdeformaiterativa.

Se han desarrollado diversos programas informáticos que trabajan con elmétodo deelementosfinitos,que,agrossomodo,consisteenconvertirunsistemacontinuoenunnúmero finito de elementos conectados entre sí a través de puntos situados en suscontornos, que reciben el nombre de nodos, cuyo comportamiento se rige por unconjuntodeecuacionesdiferenciales.

Enesteproyecto,elsoftwaredeelementosfinitosconelquesehatrabajadoesANSYSWorkbench. En un principio, se pensaba utilizar ANSYS Mechanical, ya que es elprograma que se ha utilizado en el grado y del que se tenía más conocimiento. Sinembargo,lalicenciadeANSYSparaestudianteseslimitadaydiomuchosproblemasalahoradeimportarlageometría,yaqueelnúmerode“keypoints”onodoserademasiadoelevado.Parasolucionarestacuestión,sehadescargadootraversióndelprogramamáscompletayconcapacidadsuficiente.

6.1. Modelodelosmateriales

Las propiedades de los materiales tienen una influencia directa en el cálculo detensiones internas. Enprimer lugar, hayquedefinir si losmateriales son isótropos opresentanalgúntipodeanisotropía.

Un material isótropo tiene unas propiedades mecánicas que no varían con lasdirecciones. Sabiendo que estos materiales no son perfectamente isótropos, se hadecididoaplicarestaidealizaciónporquefacilitaeltrabajo.Además,sehaconsideradoquetodoslosmaterialestienenuncomportamientoelásticolineal.

Así pues, para llevar a cabo la simulación, sólo se necesitan conocer los siguientes

Pág. 24 Memoria

parámetros:elmódulodeYoung,ladensidadycoeficientedePoisson.

Sedeberíanobtenerlaspropiedadesmecánicasdecadamaterialdeformaexperimental,haciendolosensayospertinentes.Sinembargo,sehasupuestoqueobtenerlosdeformabibliográficanotendráunefectoconsiderableenlosresultadosfinales.

En lasimulaciónconANSYS, sedefinen losmaterialesde laspartesqueseexponenacontinuación

• Implanteypilar• Tejidoóseo• Corona• Recubrimientometálico

6.1.1. Implanteypilar

El implante y el pilar objetos de estudio están fabricados de una aleación de titanio,concretamenteTi-6Al-4V.

El titanio es un elemento que, generalmente, se utiliza para fabricar prótesis yherramientasquirúrgicas.Setratadeunbiomaterial.Esdecir,noestóxicoynoproduceunareacciónderechazoenlossereshumanos.Además,eltitanioaumentalaadhesióndelimplantealhuesoyfavorecelaosteointegracion.EsunmaterialconunmódulodeYoung parecido al del tejido óseo. Se trata de una característica fundamental, puestoque,sielimplantetuvieseunmóduloelásticomuchomásalto,absorberíatodalacarga.Enestecaso,eltejidoóseopodríadeshacerseydejaríadesujetarelimplante.

Se tomarán como datos losmismos que utilizó el estudiante que realizó el proyectoanteriormente.

6.1.2. Tejidoóseo

Sedecidequématerialsevaaelegirparaquesimuleelhuesohumano.Enunprincipio,se optó por la resina epoxi. Se trata de una buena opción, puesto que presentacaracterísticasmecánicassimilares.Sinembargo,sehizounabúsquedadeinformación


para encontrar algunos datos que fuesen más precisos. Una publicación sobre laaplicación de elementos finitos para el cálculo de tensiones internas en un implantedefinelosmaterialesdelhueso.Altratarsedeunanálisismáscompleto,sediferencianlosdostiposdetejidoquesujetanlaprótesis:eltejidotrabecularyelcortical,siendoelprimeroelqueseencuentraenelinterioryelsegundoenelexterior.

Enprimerlugar,sehaceunarecopilacióndelaspropiedadesmecánicasdelostejidosutilizadasporvariosestudios(Tabla6-1).

Material Móduloelástico(MPa) MódulodePoisson

TejidoCortical 2727 0,3

10000 0,3

13400 0,3

15000 0,3

TejidoTrabecular 150 0,3

250 0,3

500 0,3

1370 0,31

Tabla6-1.Propiedadesmecánicasdelostejidosutilizadasenestudiosdeimplantesdentales

Fig 22. Representación del tejido cortical y trabecular.Obtenidode[3]

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Comosepuedecomprobar,sehanencontradodatosquedifierenbastanteentresí.Sedecidetomarlosvaloresquesemuestranacontinuación(Tabla6-2)ysecomparanconlascaracterísticasdelaresinaepoxi.

LaresinaepoxitieneunMódulodeYoungde3GPayuncoeficientedePoissionde0,3.Suconstantedeelasticidadestáentrelasdelosdostejidos.Podríahacerselasimulaciónconestematerialynoseríaunamalaopción.Sinembargo,paraaportarunosdatosmáspróximosalarealidadyparaestudiarbienlastensionesgeneradasenelhueso,sehandecididosimularlosdostiposdetejido.

6.1.3. Corona

Elmaterialdelacorona,enestecasoconcretodeestudio,esdegranimportancia,yaquelo que se quiere analizar es su influencia en la distribución de tensiones ydeformaciones. La corona está compuesta, tal y como se ha explicado, por una capainterioryunaexterior,cadaunacondistintasopcionesdematerial.

6.1.3.1. Capainterior

Lasdosopcionesposiblesdematerialparalacapainteriordelacoronasonmetalofibradecarbono.Enelcasodelmetal,elmaterialmásusadoparaestecomponenteesunaaleación de cromo y cobalto (CoCr). Se caracteriza por su biocompatibilidad, su

MódulodeYoung CoeficientedePoisson

Tejidocortical E=15000MPa ν=0,3

Tejidotrabecular E=500MPa ν=0.3

Resinaepoxi E=3000MPa ν=0.3

Tabla6-2.Comparativadelosmaterialesposiblesparaeltejidoóseo


resistenciaaldesgasteyalacorrosión,ysuspropiedadesmecánicasadecuadasparalaaplicaciónespecífica[13].

La fibra de carbono se lleva utilizando en odontología más de 15 años [14]. Es unmaterial sumamente ligero, resistente, flexible y biocompatible, y, generalmente, seutilizamezcladaconpolímerostermoestables,siendo laresinaepoxi lamás frecuente[15].Laresinaepoxiaportaalmaterialpropiedadescomoaltaresistenciaalaflexión,compresiónyaislamientotérmico[16].

6.1.3.2. Capaexterior

Respectoalmaterialdelacapaexteriordelacorona,varíaenfuncióndelmaterialconelquesehayafabricadolacapainterior.Paralacapainteriordemetalaleado(CoCr),lasopcionesposiblessonmetal,metal-cerámicoymetal-composite.Porotrolado,silacapainterioresdefibradecarbono,lacapaexterioresdefibradecarbono-composite.

Deentretodaslasposibilidades,losmaterialesescogidosenesteproyectoparalacapaexteriordelacoronahansidolosutilizadosenelproyectodereferencia,conelobjetivode que este factor no afecte a la hora de comparar los resultados obtenidos. Dichosmaterialesseexponenacontinuación:

• Lacoronametálicade compuestoCr-Co (SP2HeraeniumPwHeraeusKulzerGmbH, Hanau, Alemania) [17], formado por cobalto, cromo, molibdeno itungsteno(MET).

• La corona de metal-cerámica está fabricada con el compuesto Cr-Co(LaserPFM, Renishaw, Reino Unido) y la cerámica Vita 3D Master (Vita,Alemania)(MCER)[18].

• La corona de metal-composite está formada por el compuesto Cr-Co(LaserPFM, Renishaw, Reino Unido) y el composite BioXFill (MicroMèdica,Itàlia)(MCOM)[19].

• Lacoronadefibradecarbono-compositeestáfabricadaconBioCarbonBridge(MicroMédica,Italia)ycompositeBioXFill(MicroMèdica,Itàlia)(FCOM)[19].

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6.1.4. Tablaresumendemateriales

6.2. Mallado

Unavezsehaimportadolageometría,sedebeprocederalmalladodeésta,esdecir,aladivisión del dominio en subdominios o elementos. El mallado es, pues, un procesonecesario para el posterior análisis por elementos finitos.ANSYS es una herramientamuypotenteenloquealmalladoserefiere,unaventajaatenerencuenta,yaque,alserunageometríacompleja,elmalladotieneunagranimportanciaalahoradeobtenerlosresultados.

Un factorrelevantecuandosemallaunapiezaesel tipodeelementoescogido.Existeunagranvariedaddetiposdeelementocondistintasformas.

Pordefecto,eltipodeelementoqueutilizaelprogramaANSYSWorkbenchenloscasostridimensionaleseselelementoSOLID187,debidoalafacilidadquepresentaalahora

MódulodeYoung(MPa) CoeficientedePoisson Densidad(g/cm3)

MET 208000 0,310 8,90

MCER 69000 0,280 2,50

MCOM 22000 0,300 8,30

FCOM 300000 0,300 1,40

CoCr 200000 0,300 8,50

FibradeCarbono 350000 0,300 1,80

Ti-6-Al-4VELI 113800 0,342 4,43

TejidoCortical 15000 0,300 1,79

TejidoTrabecular 500 0,300 0,45

Resinaepoxi 3000 0,300 1,20

Tabla6-3.Resumendelosmaterialesutilizadosenlassimulaciones


de mallar geometrías complejas en tres dimensiones. Este tipo de elemento secaracteriza por las propiedades de plasticidad, hiperelasticidad, creep, rigidez,desviaciónygrancapacidaddedeformación.Tambiéntienelacapacidaddeformulaciónmixta para simulaciones de deformaciones de materiales elastoplásticos casiincompresibles y materiales hiperelásticos totalmente incompresibles. El elementoSOLID187 está definidopor 10nodos y cada unode ellos tiene 3 grados de libertad:translacionesenlasdireccionesnodalesx,y,z.

La fichadelelementoSOLID187,paramás información,seencuentraadjuntadaen losanexosdelproyecto(Anexo3).

Elsiguientepasoaseguirparacompletarelmalladodelapiezaesdefinirlamalla.Unabuena opción a la hora de mallar es utilizar una malla variable, es decir, utilizarelementos de distinto tamaño según la zona que se estémallando. En las zonasmáscríticas, por ejemplo, se utilizarían elementos de menor tamaño para obtener unosresultadosmásprecisos,mientrasqueenotraszonassepodríanutilizarelementosmásgrandes.

Unnúmeroelevadodeelementosproporcionaunosresultadoscercanosa larealidad;cuantomayor sea el númeromás se asemejan. No obstante, cuantosmás elementos,tambiénesmayoreltiempodecálculoycomputación.Porlotanto,loidealseríallegaraunpuntodeequilibrioenquelosresultadosnosealejenenexcesodelarealidadyeltiempodecomputaciónseaaceptable.Paraconseguirlo,unabuenatécnicaesrealizarunanálisisdesensibilidaddelmallado.Dependiendodecómosemalla, losresultadospueden variar, ya que cada celda es un sistema de X ecuaciones con X incógnitas.Cuantasmásceldas,menoslargaeslainterpolaciónentreceldaycelda,conlocualmásprecisosson losresultados.La ideaesponermásceldasen laszonascríticasodondehayamásgradienteenlaspropiedades.Elanálisisdesensibilidaddemalladoconsiste

Fig23.GeometríaelementodeltipoSOLID187

Pág. 30 Memoria

enprobardiferentesmallados,cadacualmásfinoqueelanterior,ycomprobarcómosellegaaunpuntoenelquelosresultadosnovaríanentreunmalladoyotro.Cuandosellegaaestepuntosesabequesehallegadoaunmalladodecalidadbastantebuena.

Sehallevadoacaboelprocedimientoexplicado,probandoenprimerlugarunmalladoderelevancia60,despuésunoderelevancia100y,finalmente,unmalladoderelevancia100 refinando las zonas más críticas. Se ha observado que los resultados variabanmucho al cambiar la relevancia de 60 a 100. Sin embargo, la diferencia entre losresultados obtenidos con el mallado de relevancia 100 y el refinado era pocosignificativa, y, teniendo en cuenta que el tiempo de computación para obtener losresultados con el mallado refinado era excesivo, se decidió que la mejor opción erarealizarelmalladoderelevancia100sinelrefinado.

Fig24.Malladoconrelevancia100


6.3. Condicionesdecontorno

Antes de analizar cualquier sistema, se deben fijar las condiciones de contornocorrespondientes,esdecir,aquellasvariablesconocidasquecondicionanelcambiodelsistema,comopuedenserfuerzas,desplazamientos,temperatura,etc.

Talycomosehaexplicadoanteriormente,atravésdelmétododeloselementosfinitosse divide el dominio a estudiar en subdominios o elementos. Estos elementos estánunidosensucontornoatravésdelosnodos,sobrelosquesematerializanlasincógnitasdelproblema.

Enelcasoaestudiar,lascondicionesdecontornoquedebenimponersesonlafijacióndelabasedelbloquequerepresentaaltejidoóseo,imponiendodesplazamientonuloentoda la superficie inferiordelbloque.Para imponeresta condición, seha impedidoeldesplazamientoenladirecciónyentodalasuperficieinferiordelbloque,alavezqueseha impuesto desplazamiento nulo en la dirección z en dos de los vértices de dichasuperficie,y,finalmente,tambiénsehaimpedidoeldesplazamientoenladirecciónxenunodeesosvértices(Fig.28).

Fig25.Desplazamientosnopermitidos

Pág. 32 Memoria

Lacondicióndecontornodelnodesplazamientode labasese imponepara todos loscasosqueseexpondránacontinuación.Seimpondráotracondicióndecontornoque,enelanálisisestático,seráunafuerzaounapresión,enfuncióndelcasoaestudiar.

Unavezimpuestaslascondicionesdecontorno,sepuedeprocederalasimulación.

6.4. Idealizaciones

Sehanllevadoacabounaseriedeidealizacionesdeformaconscientequefacilitanlassimulacionesyqueseexponenacontinuación.

6.4.1. Geometría

La geometría de la corona es demasiado compleja para crearla con el programaSolidWorks. Es por esto que se obtuvo haciendo un escaneado de la pieza. Se puedesuponerqueestapartedel implanteesunaréplicabastanteexactade larealidad.Sinembargo, el resto de la prótesis se ha dibujado con SolidWorks. Puede ser que hayaligerasvariacionesrespectoalasmedidasrealesyqueestopuedegenerarresultadosunpocodistintos.

Por otro lado, el tejido óseo se ha aproximado a un prisma. Obviamente, no es lageometríarealdelhueso,peroesdifícilgenerarunvolumenmásparecido.

6.4.2. Propiedadesdelosmateriales

Se han hecho una serie de aproximaciones en relación a las propiedades de losmateriales:

Enprimerlugar,sehaconsideradoquelosmaterialessonisótropos,aunquenoloseancompletamente. También se ha considerado que tienen un comportamiento elásticolineal.Deestemodoquedabanbiendefinidossólocondosconstanteselásticas.

Ensegundolugar,nosehanhecholosensayospertinentesparaobtenerunosdatosmás


precisosdelaspropiedadesmecánicasdelosmaterialesdebidoaquenosedisponíadelosrecursosnecesarios.

Finalmente,sehaconsideradoqueeltejidoóseoesparecidoalaresinaepoxi.Unadelasprincipales dificultades de los proyectos que intentan simular el comportamientomecánico del implante es hacer una buena aproximación del hueso. A pesar de quequedafueradelabastodeestetrabajo,somosconscientesdequeeltejidoóseonotienelas propiedades especificadas en este proyecto. Se ha intentado mejorar este puntosimulando los dos tejidos óseos (trabecular y cortical) y aplicando las propiedadesmecánicas que aparecían en un estudio sobre implantes dentales. Aún así, el tejidocorticalenningúncasopuedeconsiderarsequeseaunmaterialisótropo.Quedaabiertaestalíneadeestudioparaseguirmejorandolaprecisióndelosresultadosexpuestos.

6.4.3. Interfazhueso-implante

Se ha considerado una osteointegración perfecta entre el implante y el hueso. Estoquiere decir que el hueso se integra en todas las ranuras del implante colocado. Sinembargo,estonoesloqueocurreenloscasosclínicos.Engeneral,elpacienteconunaciertaedadtieneriesgodepadecerosteoporosis,unapatologíaquesecaracterizaporlapérdidademasaósea,dificultandosucorrectaimplantación.

Además,dependiendodelazonadondesecoloquelaprótesis,habráunmayoromenorgradodeosteointegración.Finalmente, labuenaregeneracióndel tejidoóseo tambiéndepende de la calidad del hueso de cada paciente. La edad, el sexo o fumar puedencomplicarelprocesodeintegración.

6.4.4. Condicionesdecontorno

El caso base que se ha estudiado ha sido con la aplicación de una fuerza estática yvertical.Esteanálisispuedeserútilparacompararlastensionesquesegeneranconlosdistintostiposdecorona.Sinembargo,sisepretendieseanalizaruncasocrítico,noseríaunabuenaopciónporquelaprótesissufremásconcargasoblicuas.Además,estetipodeesfuerzoeselquerecibeenelprocesodemasticación.

Pág. 34 Memoria

7. Análisisdelosresultados

7.1. Estudioestático

Elestudioestáticoconsisteenelanálisisdetensionesydeformacionesquesedanenelimplantedentalenfuncióndelmaterialdelqueestéfabricadalacorona.Pararealizaresteestudio,elprocedimientoaseguirhasido ladivisióndeésteendiferentescasos,realizando para cada uno de ellos la simulación con los 4 posibles materiales de lacorona.

Loscasosquesehanestudiadosonlosmismosqueanalizóelestudiantequerealizóelproyectoquesehatomadocomoreferencia.Sinembargo,sehanllevadoacaboalgunascorrecciones que se ha considerado mejorarían el modelo. En primer lugar, en elproyectodereferenciasepresentabauncasoenelqueelbloquequehacefuncióndetejidoóseoestabadivididoendostejidos,eltrabecularyelcortical.Enesteestudio,paraobtenerunosresultadoslomáscercanosalarealidadposibles,setendráencuentaladivisión del bloque en dos tejidos para todos los casos de estudio. También se hanmodificado algunos de los casos a analizar, y se han suprimido aquellos que seconsiderabaoportunopordistintosmotivos.Enelproyectodereferenciaseanalizabauncasoqueconsistíaenestudiarcómovariabaladistribucióndetensionesalmodificareltamañodelbloquequehacíalafuncióndehueso.Sinembargo,enelpresentetrabajonosehaestudiadodichocaso.Esporelloqueenesteproyectonosehatenidoencuentaestecasodeestudio.Enelproyectodereferenciatambiénseestudiabalavariacióndelas tensiones y deformaciones cuando se cambiaba el implante de posición en lasuperficiedelbloque.Elestudiantequerealizóelproyectoconcluyóqueestehechonoimplicaba una variación en la distribución de tensiones y deformaciones, por lo quetambiénsehadecididosuprimirelcaso.

Asípues, loscasosquesehanconsideradode interésparaesteproyectohansido lossiguientes:

• CasoA:Fuerzapuntualenelcentrodelacorona• CasoB:Excentricidaddelpuntodeaplicacióndelafuerza• CasoC:Sustitucióndelafuerzapuntualporunapresión• CasoD:Fuerzaoblicuaenelcentrodelacorona


Paravisualizarlosresultadossehaoptadoporhaceruncortedesecciónenlamitaddelapiezatalycomosemuestraacontinuación(Fig.29).Deestaforma,sevemásclaraladistribucióndetensionesylasdeformaciones.

Paraelestudiodeloscasosexpuestos,seexaminarándosvaloresencadaunodeellos:latensióndeVonMisesyladeformaciónunitaria.

LatensióndeVonMisesesunindicadorqueseutilizaparadeterminarelfalloelásticode materiales dúctiles. Sin embargo, en este estudio se emplea para hacer unacomparaciónconceptualdelastensionesinternasdecadapieza.Nosebuscaencontrarla zonade ruptura.Esporestoqueseempleaestamagnitud,apesardequealgunaspiezasnosondúctiles.

Fig26.Cortedesección

Pág. 36 Memoria

7.1.1. CasoA:Fuerzapuntualenelcentrodelimplante

ElcasoAconsisteenelanálisisestáticodelastensionesydeformacionesenelimplantedentalcuandoseaplicaunafuerzapuntualde300Nenunpuntosituadoenelcentrodela corona. Este caso será el que se tome como base o referencia en los siguientesapartadosparacompararlosresultadosobtenidos.


7.1.1.1. CoronaMET

MET

Implante+corona Implante Tejido

TensióndeVonMises TensióndeVonMises TensióndeVonMises

Deformaciónunitaria Deformaciónunitaria Deformaciónunitaria

Tabla7-1.Resultadosdelcaso:Fuerzapuntualenelcentrodelacorona(MET)

Pág. 38 Memoria

7.1.1.2. CoronaMCER

MCER




Tabla7-2.Resultadosdelcaso:Fuerzapuntualenelcentrodelacorona(MCER)


7.1.1.3. CoronaMCOM

MCOM




Tabla7-3.Resultadosdelcaso:Fuerzapuntualenelcentrodelacorona(MCOM)

Pág. 40 Memoria

7.1.1.4. CoronaFCOM

FCOM




Tabla7-4.Resultadosdelcaso:Fuerzapuntualenelcentrodelacorona(FCOM)


Los resultados obtenidos indican un pico de tensión en el punto de aplicación de lafuerza,talycomoseesperaba,yaquerepresentaunasingularidadnuméricaalestarseaplicandounafuerzaenunpuntodeáreacero.Cuandoquierenconocerselastensionesde las zonas cercanas al punto de aplicación, se comprueba que éstas se disparan.Existenmétodosparaeliminarelvalorsingular,talescomoaplicarunapresiónenunasuperficie en lugar de una fuerza o eliminar los elementos en los que se dispara latensión.Sinembargo,nohasidonecesario realizarestosprocedimientos,yaqueestasingularidad numérica no afecta en granmedida al análisis. Esto es debido a que elprincipalfactordeinterésesladistribucióndetensionesquellegaalimplanteynotantolatensióngeneradaenlacorona,y,portanto,unavezsehanreescaladolosvaloresdetensiones,sepuedenobservarlas tensionesydeformacionessintenerencuentaestevalorsingular.

Sehaceunacomparaciónde losresultadosobtenidoscon losdelproyectodemáster.Hayvariacionespocorelevantes,quepuedenserdebidasalanuevacapametálicadelageometría o a la posición de la fuerza. Aún así, se llega a la misma conclusión: losmaterialesnoafectandemanerasignificativaalosesfuerzosgeneradosenelimplantenieneltejidoóseo.

En referencia a la deformación unitaria, se comprueba que dependiendo del tipo decorona,seobtienenresultadosbastantedistintos.Estopuedeexplicarseapartirdelaspropiedadesmecánicasdecadamaterial:cuantomásrígidoes,menoresladeformaciónqueexperimenta.

Pág. 42 Memoria

7.1.2. CasoB:Excentricidaddelpuntodeaplicacióndelafuerza

Enesteapartado, sehaobservadoelefectoque tieneelposicionamientode la fuerzasobre la distribución de tensiones y deformaciones en el implante. Para ello, se haposicionadolafuerzaenunpuntodescentradodelacorona.LafuerzaaplicadahasidolamismaqueenelcasoA(300N),para,deestaforma,podercompararlosresultadosyobservar la variación de la distribución de tensiones cuando se cambia el punto deaplicacióndelafuerza.

Al aplicar la fuerza sobreunpuntodeáreanula, comoenel casoanterior, sedaunasingularidadnumérica,que,talycomosehaexplicado,consisteenlatendenciadelosvaloresdelastensionesainfinitoenelpuntodeaplicacióndelafuerza.Sinembargo,enestecaso,tampocoafectaanuestroestudio;sisemodificalaescalasepuedenobservarlastensionessintenerencuentaelvalorsingular.


7.1.2.1. CoronaMET

MET




Tabla7-5.Resultadosdelcaso:Excentricidaddelpuntodeaplicacióndelafuerza(MET)

Pág. 44 Memoria

7.1.2.2. CoronaMCER

MCER




Tabla7-6.Resultadosdelcaso:Excentricidaddelpuntodeaplicacióndelafuerza(MCER)


7.1.2.3. CoronaMCOM

MCOM




Tabla7-7.Resultadosdelcaso:Excentricidaddelpuntodeaplicacióndelafuerza(MCOM)

Pág. 46 Memoria

7.1.2.4. CoronaFCOM

En los resultados obtenidos se observa que tanto las tensiones como lasdeformacioneseneltejidoóseopermanecenprácticamenteigualesalcambiarelmaterialdelacorona.Enelimplantelasvariacionessonmássignificativas,

FCOM




Tabla7-8.Resultadosdelcaso:Excentricidaddelpuntodeaplicacióndelafuerza(FCOM)


perosiguensinserrelevantes.Elcasode lacoronametálica(MET)eselquemásdifiererespectoalosdemásresultadosenelimplante.Como pasa cuando se aplica una fuerza centrada, los resultados de lasdeformacionesenlacoronasonmuydistintosalcambiardematerial.

7.1.3. CasoC:Sustitucióndelafuerzapuntualporunapresión

Porúltimo,sehaaplicadounapresiónsobreunasuperficiecentradadel implante.Deestamanera,noexistesingularidadnumérica.

Para poder comparar los resultados obtenidos con el caso base, se debe aplicar unapresión equivalente a la división del valor de fuerza asignado en los apartadosanteriores(300N)entrelasuperficieescogidaparaejercerlapresión.Sehaelegidounasuperficiequerodeeelpuntodeaplicaciónutilizadoenelcasodereferencia.

𝑃 = !!= !"" !

!,!"!"# !!! = 175,743 𝑀𝑃𝑎

Fig27.Zonadeaplicacióndelapresión

Pág. 48 Memoria

7.1.3.1. CoronaMET

MET




Tabla7-9.Resultadosdelcaso:Sustitucióndelafuerzapuntualporunapresión(MET)


7.1.3.2. CoronaMCER

MCER




Tabla7-10.Resultadosdelcaso:Sustitucióndelafuerzapuntualporunapresión(MCER)

Pág. 50 Memoria

7.1.3.3. CoronaMCOM

MCOM




Tabla7-11.Resultadosdelcaso:Sustitucióndeunafuerzapuntualporunapresión(MCOM)


7.1.3.4. CoronaFCOM

FCOM




Tabla7-12.Resultadosdelcaso:Sustitucióndeunafuerzaporunapresión(FCOM)

Pág. 52 Memoria

7.1.4. CasoD:Fuerzapuntualoblicua

Seharealizadoelestudiodeunúltimocaso;estavez,únicamenteconlacoronadeMET,conelobjetivodeobservarlosefectosquetienelaaplicacióndeunafuerzanoverticalen el centrode la corona. Se sabeque al aplicaruna fuerzaoblicua seobtienenunastensionesmayoresquecuandoseaplicaunacargavertical[5].

Inicialmente,sehaprobadoaplicarunafuerzademódulo300N,igualquelaaplicadaenlos otros casos, pero inclinada respecto al eje vertical. Para ello, se ha utilizado unafuerza de componentes Fx=-100N, Fy=-280N y Fz=0. Sin embargo, la inclinación erademasiadograndeyproducíadeformacionesexcesivamenteelevadas.

Sehaidoreduciendoelgradodeinclinaciónhastaobtenerunosresultadosrazonables,que se ha conseguido con una inclinación de aproximadamente 2° (fuerza decomponentesFx=-5N,Fy=-150NyFz=0).

Fig28.Piezadeformadaconfuerzaoblicuaaescalareal


7.1.4.1. CoronaMET

Se comprueba, pues, que las tensiones y las deformaciones aumentan de formasignificativaalañadirunamínimahorizontalidadalafuerzaaplicada.Apesardequeelmódulodelafuerzaeslamitaddelaejercidaenelcasodereferencia,ladeformacióneneltejidoóseosedispara.

MET

Implante+corona Tejido

TensióndeVonMises TensióndeVonMises

Deformaciónunitaria Deformaciónunitaria

Tabla7-13.Resultadosdelcaso:Fuerzapuntualoblicua(MET)

Pág. 54 Memoria

7.2. Análisisdetalladodelasdeformacionesconelcambiodeposición

deunafuerzapuntual

Enel casoB, sehananalizado las variaciones en las tensionesydeformacionesde lapieza generadas por el descentramiento de la fuerza puntual. En este análisis, se haqueridoestudiarenprofundidadelefectoquetieneelcambiodeposicióndeunafuerzapuntualsobrelasdeformacionesdelapieza.Sehaelegidolacoronademetalparallevaracabolassimulaciones.

Seharealizadounbarridoaplicandolafuerzapuntual(de300N,comoenelcasobase)en8nodosdiferentes,adiferentesdistanciaselunodelotro,perotodasrondandolos0,5mm. Además, se ha buscado que los nodos en los que se ha aplicado la fuerzaestuvieranlomásalineadosposible.

Lasdeformacionesdeinterésparaestecasosonlasverticalesenlazonadeltejidoóseo,especialmenteenlazonadedebajodelapuntadelimplante.

Acontinuaciónsepresentanlasdistancias(enmm)entrecadapardenodosestudiado:

1à2 0,35254mm 5à6 0,60033mm

2à3 0,35527mm 6à7 0,54496mm

3à4 0,41038mm 7à8 0,33399mm

4à5 0,6718mm

Tabla7-14.Distanciasentrelosnodosutilizadosenelanálisis

Fig29.Nodosutilizadosenelanálisis

87

654321


7.2.1. CoronaMET

Nodo1 Nodo2 Nodo3 Nodo4

Nodo5 Nodo6 Nodo7 Nodo8

Tabla7-15.Resultadosdelcaso:Análisisdetalladodelosefectosdelcambiodeposicióndeunafuerza

Se observa que las variaciones en las deformaciones del tejido cuando se cambia elpuntodeaplicacióndelafuerzasonmínimas.

Pararealizarunestudiocuantitativodelosresultados,sellevaacabolaseleccióndeunnodo(elmismoparatodaslassimulaciones)ysemideladeformaciónquesufreencadacaso.Acontinuaciónserealizaungráficoparailustrarlavariacióndeladeformacióndedichonodo,situadoenlazonadeinterés(debajodelapuntadelimplante),enfuncióndeldescentramientodelafuerzaejercida.

Tabla7-16.Deformacióndelosnodosenfuncióndelaexcentricidad

Nodo1 Nodo2 Nodo3 Nodo4 Nodo5 Nodo6 Nodo7 Nodo8

Eyy -0,0093679 -0,0095173 -0,0096445 -0,0097521 -0,0099957 -0,010163 -0,010402 -0,010559

e[mm] 0 0,35254 0,70781 1,11819 1,78999 2,39032 2,93528 3,26927

Pág. 56 Memoria

Gráfico1.Deformaciónverticalenfuncióndelaexcentricidaddelafuerza

Enelgráficoseobservaqueladeformaciónenladirecciónyaumentaenvalorabsolutoamedidaquesealejaelpuntodeaplicacióndelafuerzadelcentro.


8. Conclusiones

ANÁLISISDELOSRESULTADOSCASOESTÁTICO:

Acabadoelestudioestático,sepuedeconcluirlosiguiente:

-Enprimerlugar,secompruebaqueseacumulamástensióneneltejidocorticalqueenel trabecular. En cambio, las deformaciones son mucho más grandes en el tejidotrabecular.Escomprensible,puestoqueelmódulodeYoungdelprimertejidoesmuchomayoryesmásresistentealadeformación.

-Enelimplante,lospuntoscontensiónmáselevadaseencuentranentodosloscasosdeestudioenlapartesuperiordelapiezaqueestáencontactoconeltejidocortical.Comolacargaestáaplicadasobrelacoronay lastensionessevantransfiriendoatravésdelimplante,lazonasuperiordelimplanteeslaprimeraenrecibirestastensiones.Esporestoqueelpuntodemáximatensióndelimplanteseencuentraenlapartemencionada.

- Se observa que el material del que está hecho la corona no tiene una influenciarelevante en el cálculo de tensiones en el implante y en el tejido. Esto refuerza laconclusión a la que llegó el alumno del Trabajo de Fin deMáster al que nos hemosreferido a lo largo del presente trabajo. Así pues, a pesar de que los valores de lastensionesydeformacionessondistintos,lanuevacapametálicaylosdostejidosóseosnorepresentanungrancambioenesteanálisis.

Fig30.Distribucióndetensionesenelimplante

Pág. 58 Memoria

MET MCOM MCER FCOM

Tabla8-1.Comparativadelastensionesenelimplanteparaelcaso:Fuerzapuntualenelcentrodelacorona

-Lasdeformacionesenlacoronavaríanconsiderablementeenfuncióndelmaterialdeestapieza.EstoesdebidoaquelasdeformacionesdependendelmódulodeYoung.Porlo tanto, al cambiar de material (y consecuentemente de módulo de Young), secompruebaque sedanvariaciones significativas en cualquierade los cuatro casosdeestudio.

Enlatablasiguienteseilustraestehechoapartirdelcasodefuerzaestáticaenelcentrodelacorona:

MET MCOM MCER FCOM

Tabla8-2.Comparativade tensionesenel implantedentalparaelcaso:Fuerzapuntualenelcentrode lacorona

-Comoseesperaba,laaplicacióndeunapresiónenlugardeunafuerzapuntualeliminalasingularidadnuméricaysuavizaelpicode tensiónydeformaciónde lacorona.Sinembargo,losresultadosnocambiantantoenlaszonasalejadasdelpuntodeaplicación.


A continuación se presenta un resumen de los resultados obtenidos en el caso de lafuerzapuntualylapresión,ambosparaelcasodelacoronadeMET.

FuerzapuntualMET:

Implante+corona Implante

TensióndeVonMises DeformaciónUnitaria TensióndeVonMises DeformaciónUnitaria

Tabla8-3.Tensionesydeformacionesenelcaso:Fuerzapuntualenelcentrodelacorona(MET)

PresiónMET:

Implante+corona Implante


Tabla8-4.Tensionesydeformacionesparaelcaso:Sustitucióndelafuerzapuntualporunapresión(MET)

Comoseobserva,porejemplo,enelcasodelMET,latensiónmáximadelconjuntodelimplante dental, que se encuentra en la corona, se ve reducido cuando se cambia lafuerzapuntualaplicadaporunapresión.Lasvariacionesenladeformaciónenlacoronatambién son significativas (en este caso pasan de 0,04 a 0,01mm). Sin embargo, seobservaque,alalejarnosdelazonadeaplicacióndelacarga,tantolastensionescomo

Pág. 60 Memoria

lasdeformacionessonmuysimilares,aúncambiandolafuerzaaplicadaporunapresión.

- Se observa también que se cumple el principio de Saint Venant, según el cual lastensionesy,consecuentemente, lasdeformaciones(cuandoseconservalahipótesisdeHooke) enuna zonaalejadade lospuntosde aplicacióndeuna fuerza tienenvaloresmuy similares. Se observa que en el punto de aplicación de la carga, la corona, lastensionesvaríanmucho,mientrasquecuandonosalejamos,porejemploenlazonadelimplante,pasanasermuysemejantes.

- La aplicación de una fuerza oblicua representa el caso más crítico de los estudiosrealizadosconunacargaestática.Eselqueseasemejamásalarealidad.Lastensionesgeneradas sonmuchomayores en todos los casos. También aumenta la deformaciónunitaria.

MET

Fuerzapuntualcentrada Fuerzaoblicua


Tabla8-5.Comparativadelastensionesydeformacionesentrefuerzapuntualcentradayfuerzaoblicua


- La cantidad y la calidad del hueso que envuelve el implante genera variacionesimportantesenelcálculodetensionesydeformaciones.SehamodificadoelmódulodeYoungde losdos tejidosy sehanobtenidovaloresbastantedispares. Comoya sehacomentadoenelproyecto,laspropiedadesmecánicasdeestostejidostienenunagranvariabilidad.Sonestructurascomplejasysuscaracterísticasdependendecadapaciente.

Se ha comprobado cómo variaban las tensiones y las deformaciones cambiando laspropiedadesdelostejidos.Acontinuación,seilustranlosresultadosdelasimulación;seha tomado comobase el caso de aplicación de una fuerza puntual en el centro de lacorona de MET y, a partir de éste, se han modificado los módulos de Young de losmaterialesquehacenlafuncióndetejidoóseo.

CasobaseEcortical=2727MPaEtrabecular=150MPa

TensióndeVonMises Deformaciónunitaria TensióndeVonMises Deformaciónunitaria

TensióndeVonMises Deformaciónunitaria TensióndeVonMises Deformaciónunitaria

Tabla8-6.Comparativadelastensionesydeformacionesentreencasobaseycasocondiferentetejidoóseo

Se observa que en el implante, tanto las tensiones como las deformaciones, sonmuysimilares,apesardelavariacióndelaspropiedadesdeltejidoóseo.Estosedebeaqueelimplanterecibelastensionesantesqueeltejidoy,porlotanto,lasmodificacionesenlas

Pág. 62 Memoria

propiedades del tejido no afectan de forma significativa al implante. Sin embargo, alanalizarlastensionesydeformacioneseneltejidoóseo,seobservaque,alcambiarlaspropiedades de éste, las diferencias entre las tensiones y las deformaciones sonsignificativas.

Aquí pot anar el títol del vostre PFC Pág. 63

9. Agradecimientos

Por último, queremos agradecer a todas las personas que han hecho posible larealizacióndeesteproyecto.

Enprimer lugar,alprofesorMiquelFerrer, tutordeestetrabajo,porsucomprensión,dedicaciónyconsejos.

También queremos agradecer a nuestras familias su apoyo incondicional, tanto en elproyectocomoalolargodetodoelgrado,porsusánimosypaciencia.

Una mención especial a Beatriz Rodríguez-Sánchez, profesora de la universidadRijksuniversiteit Groningen(RUG), por la facilitación de publicaciones a las que noteníamosaccesoyquehansidodegranayudaalolargodeltrabajo.

Finalmente,queremosagradeceralprofesoradodelaescuelayaquesinsudedicaciónno se hubieran adquirido los conocimientos quehanpermitido la realizaciónde esteproyecto.

Pág. 64 Memoria

10. Bibliografia

[1] SergioArmijo,TrabajodeFindeGradoenETSEIB:“Estudi3Dd’unimplantdental”,2016.

[2] ImplantesDentales.(2017).IMPLANTESDENTALESHQ.Retrieved17January2017,fromhttp://www.implantesdentaleshq.com/

[3] Kayabaşı, O., Yüzbasıoğlu, E., &Erzincanlı, F. (2006). Static,dynamicandfatiguebehaviors of dental implant usingfinite elementmethod.Advances In Engineering Software,37(10), 649-658.http://dx.doi.org/10.1016/j.advengsoft.2006.02.004

[4] VanegasA.,J.,LandinezP,N.,&Garzón-Alvarado,D.(2017).Generalidadesdelainterfasehueso-implantedental.Scielo.sld.cu.Retrieved16January2017,fromhttp://scielo.sld.cu/scielo.php?script=sci_arttext&pid=S0864-03002009000300011

[5] Ferrús,D.,&Bratos,C.(2017).¿Quéeslaosteointegracióndelosimplantesdentales?.ClínicaDentalFerrus&Bratos.Retrieved16January2017,fromhttp://www.clinicaferrusbratos.com/implantes-dentales/implante-osteointegrado/

[6] Geng,J.,Tan,K.,&Liu,G.(2001).“Applicationoffiniteelementanalysisinimplantdentistry:Areviewoftheliterature.TheJournalOfProstheticDentistry”,85(6),585-598.http://dx.doi.org/10.1067/mpr.2001.115251

[7] TiposdeImplantesDentales.(2017).IMPLANTESDENTALESHQ.Retrieved16January2017,fromhttp://www.implantesdentaleshq.com/tipos-de-implantes-dentales/

[8] Alsadeg,Ruaa."DentalImplants-SuccessVsFailureRate".JournalofDentalHealth,OralDisorders&Therapy4.2(2016):n.pag.Web.

[9] "ImplantesEndo-Óseos".Propdental.N.p.,2017.Web.9Jan.2017.

[10] Implantesdentales:tiposyprecios.(2017).ClínicaDentalMadridNavarro.Retrieved10January2017,fromhttp://www.dentalnavarro.com/articulos-implantes-dentales/implantes-dentales-tipos-y-precios

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[11] IMPLANTESDENTALES:Tipos,VentajasYRiesgos,ProcesoDeColacacion.(2017).Traveltodentist.com.Retrieved16January2017,fromhttp://traveltodentist.com/es/servicios/implantologia/implantes-dentales/

[12] IMPLANTESDENTALES.(2017).ClínicaHigueras.Retrieved13January2017,fromhttp://www.clinicadentalhigueras.com/implantes-dentales/

[13] “Aleacionesimplantables”.Odontologia-online.com.Retrieved16January2017,fromhttp://www.odontologia-online.com/publicaciones/materiales-dentales/185-aleaciones-implantables.html

[14] FredrikssonM,AstbackJ.Aretrospectivestudyof236patientswithteethrestoredbycarbonfiberreinforcedepoxyresinposts.JournalofProst.Dent.1998.Vol80(2),151-157.

[15] DonnetJB,RebouillatS..”CarbonFibers:thirdEdition,revisedandexpanded”.MarcelDekkerAG.1998

[16] DíazLópezC.,DíazLópezL.,BouFernándezA.,BouSeverínJ.L.,DíazGonzálezJ.L.,(2016),“ESTRUCTURASDEFIBRADECARBONO,NUEVASOPCIONESENLAPRÓTESISODONTOLÓGICA”

[17] Heraeus-Kulzer,“HeraeniumPWuserinstructions”:http://heraeuskulzer.com/media/webmedia_local/international/pdf/Legierungstabelle_GB.pdf

[18] Vita3DMaster,VitaAlemanya,“Vita3DToothGuide”:https://www.vitazahnfabrik.com/es/VITA-Toothguide-3D-MASTER-26233,27568.html

[19] MicroMedicaCatálogo2014–Arrobadental:http://arrobadental.com/pdf/2014-micro-medica.pdf

[20] Fawzi,Sahar."TheEffectOfDentalImplantDesignOnBoneInducedStressDistributionAndImplantDisplacement".InternationalJournalofComputerApplications74.17(2013):15-21.Web

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11. Anexos


11.1Anexo(1)

Static, dynamic and fatigue behaviors of dental implant usingfinite element method

Oguz Kayabas�ı a,*, Emir Yuzbasıoglu b, Fehmi Erzincanlı a

a Department of Design and Manufacturing Engineering, Gebze Institute of Technology, PK 141, Cavırova, Gebze, Turkeyb Department of Prosthodontics, Faculty of Dentistry, Ondokuz Mayıs University, 55139 Kurupelit, Samsun, Turkey

Received 7 March 2005; received in revised form 10 February 2006; accepted 10 February 2006Available online 2 May 2006

Abstract

In evaluation of the long-term success of a dental implant, the reliability and the stability of the implant–abutment and implant boneinterface plays a great role. In general, the success of the treatment depends on many factors affecting the bone–implant, implant–abut-ment and abutment–prosthesis interfaces. In the literature, many researcher are investigated static loading effects on the implant howeverdynamic loading and fatigue effects has not investigated formally. In this study, static dynamic and fatigue behaviors of the implant areinvestigated. Dynamic loads in 5 min applied on occlusal surface. Fatigue life the implant calculated based on Goodman, Soderberg,Gerber and mean-stress fatigue.� 2006 Elsevier Ltd. All rights reserved.

Keywords: Finite element analysis; Dental implant; Fatigue; Abutment

1. Introduction

Since dental implants were introduced for rehabilitationof the completely edentulous patients in the late 1960s [1,2]an awareness and subsequent demand for this form of ther-apy has increased. The use of implants have revolutionizeddental treatment modalities and provided excellent long-term results [3,4].

In evaluation of the long-term success of a dentalimplant, the reliability and the stability of the implant–abutment and implant bone interface plays a great role.In general, the success of the treatment depends on manyfactors affecting the bone–implant, implant–abutmentand abutment–prosthesis interfaces [5].

Analyzing force transfer at the bone–implant interface isan essential step in the overall analysis of loading, whichdetermines the success or failure of an implant. It has longbeen recognized that both implant and bone should be

stressed within a certain range for physiologic homeostasis.Overload can cause bone resorption or fatigue failure ofthe implant, whereas underloading of the bone may leadto disuse atrophy and subsequent bone loss [6,7]. Prostheticcomponents are subjected to a complex pattern of horizon-tal and vertical force combinations [8]. Yet all force com-ponents do not have the same impact with respect tomaterial resistance and incidence of failure. Force vectorsthat are directed along the main axis of the implant arecompressive in nature and remain well below the material’sresistance in compression [9].

A key factor for the success or failure of a dentalimplant is the manner in which stresses are transferred tothe surrounding bone [10]. The FEA allows researchersto predict stress distribution in the contact area of implantswith cortical bone and around the apex of implants in tra-becular bone.

Three-dimensional (3-D) finite element analysis (FEA)has been widely used for the quantitative evaluation ofstresses on the implant and its surrounding bone [11,12].Therefore, FEA was selected for use in this study to exam-ine the effect of the static and dynamic loads on the stress

0965-9978/$ - see front matter � 2006 Elsevier Ltd. All rights reserved.doi:10.1016/j.advengsoft.2006.02.004

* Corresponding author. Tel./fax: +90 262 653 84 97.E-mail addresses: [email protected] (O. Kayabas�ı), yuzbasi@omu.

edu.tr (E. Yuzbasıoglu).

www.elsevier.com/locate/advengsoft

Advances in Engineering Software 37 (2006) 649–658

mailto:[email protected]

mailto:yuzbasi@omu. edu.tr

mailto:yuzbasi@omu. edu.tr

distribution for an implant-supported fixed partial dentureand supporting bone tissue and fatigue behavior of theimplant complex. The purpose of this study was to deter-mine the optimal life time for an Osseo integrated implantby computational methods.

In the literature, many researcher are investigatedstatic loading effects on the implant however dynamicloading and fatigue effects has not investigated formally.In this study, static dynamic and fatigue behaviors of theimplant are investigated. Dynamic loads in 5 min appliedon occlusal surface. Fatigue life the implant calculatedbased on Goodman, Soderberg, Gerber and mean-stressfatigue.

2. CAD and finite elements modeling

2.1. CAD modeling

A 3-D model of a mandibular section of bone with miss-ing second premolar and its superstructures were used inthis study. A mandibular bone model was selected, simulat-ing A-2 type bone, according to the classification system ofLekholm and Zarb [13]. Trabecular bone was modeled as asolid structure in cortical bone [14–16]. A bone block,24.2 mm high and 16.3 mm wide, representing the sectionof the mandible in the second premolar region, was mod-eled. It consisted of a spongy center surrounded by 2 mmof cortical bone. A model of Ø 4.1 mm · 12 mm ITIsolid-screw implant (ITI; Instut Straumann AG, Walden-burg, Switzerland) and a 6�, solid abutment (ITI; InstutStraumann AG, Waldenburg, Switzerland) 4 mm in heightwas selected for this study. Cobalt–chromium (Wiron 99;Bego, Bremen, Germany) was used as crown frameworkmaterial [17] and feldsphatic porcelain was used for theocclusal surface [18]. Porcelain and metal thickness usedin this study were 1.5–0.5 mm, respectively. Cement thick-ness layer was 60 lm thickness modeled [19]. The implantwas positioned in a modeled cortical and trabecular boneblock. The implant and its superstructure were modeled

using CAD software Pro/Engineer 2001. The model isshown in Fig. 1.

2.2. Finite element analysis

2.2.1. Finite element modelingFinite element model required in FE analysis is created

by discrediting the geometric (i.e. CAD) model shown inFig. 2 into smaller and simpler elements. Mesh densitygradually coarsening from loading surfaces which is poten-tial impact region to, the bone and from contact surface toouter surface. The FEM model consists of total 298.070four-node tetrahedron elements; 44.127 elements forimplant, 13.534 elements for abutment, 4.987 elementsfor metal framework, 9.902 element for feldsphatic porce-lain, 60.762 element for bone, 19.658 element for gingiva.Tetrahedron elements in implant, abutment, metal frame-work, feldsphatic porcelain, bone and gingiva correspondto SOLID45 type elements in ANSYS element library witheach node having three degree of freedom. The finite ele-ment models are shown Fig. 2. The physical interactionsat implant–bone, implant–abutment, abutment–adhesivecement, adhesive cement–metal framework interfaces dur-ing loading are taken into account through bonded sur-face-to-surface contact features of ANSYS.

In this work Ti–6Al–4V for implant fixture and abut-ment, cobalt–chromium alloy for metal framework, felds-phatic porcelain for occlusal material are used in thefinite element analyses. Behaviors of these materials arerepresented with linear isotropic material models. Mechan-ical properties of materials used in this study are shown inTable 1.

To account for the effect of the bone behavior on theimplant accurately, inner and outer sides of the bone (cor-tical bone and cancellous bone) are modeled with differentmaterial properties. Inner side of the bone (cortical bone) isrepresented with transversely isotropic material model(Ex = Ey = 11.5 GPa, Ez = 17 GPa; Gxy = 3.6 GPa, Gxz =Gyz = 3.3 GPa; mxy = 0.51, mxz = myz = 0.31 GPa). Outer

Fig. 1. 3D solid model of implant, abutment, metal framework, occlusal material, bone and gingiva, respectively.

650 O. Kayabas�ı et al. / Advances in Engineering Software 37 (2006) 649–658

side of the bone (cancellous bone) is modeled with linearisotropic material model of E = 2.13 and m = 0.3.

2.2.2. Loading conditions

Static and dynamic analyses of the implant should beconducted to ensure about the safety of the design. In theliterature, implant are often worked according to theresults of static analysis. Static finite element (FE) analysesare mostly conducted under masticatory forces. However,dynamic effects may add up to about 10–20% or more load-ing to implant which must be taken into account not tocause fracture or fatigue failure of the implant. To investi-gate how static and dynamic analysis results differ fromeach other, implant is analyzed under static masticatoryand dynamic load.

The preload condition was achieved by the use of con-tact analysis in the finite element models. For this purpose,target and contact surfaces between the individual parts ofthe model were defined by not merging the nodes betweenthe components. Contact elements were determinedbetween implant threads and bone, the mating surfaces ofthe implant and abutment, and at a distance of 0.005 mmbetween the contacting surfaces. Contact analysis assured

the union and the transfer of the loads and deformationbetween the different components, featuring a coefficientof friction of 0.3 [20]. Manufacturers’ recommended tor-ques for implant insertion, abutment connecting are listedin Table 2. The preload was developed within the screwby placing thermal load on the mating surfaces of implantcomplex.

Loading of the implants, in 3-D, with forces of 17.1 N,114.6 N, and 23.4 N in a lingual, an axial, and a mesio-distal direction, respectively (Fig. 3), simulated averagemasticatory force in a natural, oblique direction. Thesecomponents represented masticatory force of 118.2 N inthe angle of approximately 75� to the occlusal plane. This3-D loading acted on the lingual inclination of buccal cuspof the crown. The force magnitudes, as well as the actingpoint, were chosen based on the work of Mericske-Stern.The FEM model was fixed at the bottom surface of man-dibula as shown in Fig. 3.

Implant-supported prosthesis has unsuccessful resultsunder dynamic loading conditions although same prosthe-sis has safety results under static loading conditions bymeans of fatigue resistance so for dynamic analysis, time-dependent masticatory load (Fdynamic) is applied. Timehistory of the dynamic load components for 5 s is demon-strated in Fig. 4. These estimations were based on theassumption that an individual has three episodes of chew-ing per day, each 15 min in duration at a chewing rate of

Fig. 2. Finite element models of implant (a), abutment (b), metal framework (c) and occlusal material (d).

Table 1Mechanical properties of materials used in the study

Material Young’smodulus(GPa)

Poissonratio (m)

Yield strength(MPa)

Ti–6Al–4V 110 0.32 800Cobalt–chromium alloy 220 0.30 720Feldsphatic porcelain 61.2 0.19 500Bone 14.7 0.30 130Gingiva 0.0196 0.30 –Cement 14 0.35 29

Table 2Manufacturer’s recommended torque values

Type of torque Place of application Amount oftorque (N mm)

Insertion torque Bone–implant interface 3500Tightening torque Abutment–implant interface 3500

O. Kayabas�ı et al. / Advances in Engineering Software 37 (2006) 649–658 651

60 cycles per minute (1 Hz). This is equivalent to 2700chewing cycles per day or roughly 106 cycles per year[21,22].

The tooth was assumed to be initially at a uniform tem-perature of 36 �C, simulated the draught of a hot (60 �C)and a cold (15 �C) liquid. A transient finite element thermalanalysis was carried out using program to establish thenodal point temperatures at each time step. It was assumedthat these temperatures were kept constant for a period of1 s, which means that hot and cold liquids were held for 1 sin the mouth [23–26].

Finite element analyses of the implants are carried outusing ANSYS on a P4 2.0 GHz Intel processor PC.

2.3. Fatigue analysis

A good dental implant design should satisfy maximumor an infinite fatigue life. This can only be ensured by phys-ical testing or a fatigue analysis. In this study, fatigue life ofthe dental implant upon finite element stress analysis is pre-dicted using the computer code of ANSYS/Workbench(ANSYS, 2003). Fatigue calculations of the implant areconducted for Ti–6Al–4V alloy material. In fatigue calcula-tions, fatigue material model shown in Fig. 5 are used.Fig. 5 known as S–N curves shows fatigue properties ofTi–6Al–4V alloy in terms alternating stress versus numberof cycles. Fatigue life of prosthesis is calculated based onGoodman, Soderberg, Gerber and mean-stress fatigue the-ories which are illustrated in Table 3.

Fig. 3. Applied loads and boundary conditions of FEM model.

0

20

40

60

80

100

120

140

0 1 2 3 4 5 6Time (s)

Forc

e (N

)

mesio-distal direction lingual direction axial direction

Fig. 4. Dynamic loading in 5 min.

0

100

200

300

400

500

600

700

800

900

1000

1.E+00 1.E+02 1.E+04 1.E+06 1.E+08 1.E+10Number of Cycles

Alte

rnat

ing

Stre

ss (

MPa

)

Ti-6Al-4VCobalt-chromium alloy

Fig. 5. Fatigue curves (S–N curve) for Ti–6Al–4V and cobalt–chromiumalloy materials.

Table 3Fatigue theories and formulas used in fatigue life predictions

Fatigue theories Fatigue formulas

Goodman ra

Se

� �þ rm

Su

� �¼ 1

N

Soderberg ra

Se

� �þ rm

Sy

� �¼ 1

N

Gerber Nra

Se

� �þ Nrm

Su

� �2¼ 1


In Table 3, N indicates safety factor for fatigue life inloading cycle, Se for endurance limit and Su for ultimatetensile strength of the material. Mean stress rm and alter-nating stress ra are defined respectively as

rm ¼rmax þ rminð Þ

2ð1Þ

ra ¼rmax � rminð Þ

2ð2Þ

Von Misses stresses obtained from finite element analy-ses are utilized in fatigue life calculations. All fatigue anal-yses are performed according to infinite life criteria (i.e.N = 109 cycles).

3. Results

Maximum Von Mises stresses that occurred at theimplant, abutment, metal framework, occlusal surfacematerial and bone for all loading conditions forces are pre-sented in Table 4.

3.1. Implant

Fig. 6 represent the stress distribution in the implant fix-ture in static and dynamic loading. Maximum stresses were

located at the first thread of the implant for both loadingconditions. Maximum Von Mises stresses for the implant instatic and dynamic loading were 118.317 and 177.476 MPa,respectively. For the static and dynamic loading, the maxi-mum stress values within the implant body were 25.6% and38.41% of the yield strength, respectively. Maximum stressvalues at the implant body of two loading conditions werelower than the yield strength (yield point for CP titanium,462 MPa).

3.2. Abutment

The maximum stress values under two different loadingconditions were concentrated at the connection betweenthe shank and first thread of the abutment as it is shownin Fig. 7. The highest Von Mises stress value was foundfor the abutment in dynamic loading. However, the loweststress value was calculated for the abutment in static load-ing. For the static loading, the maximum stress valuewithin the abutment was 28.99% of the yield stress. Maxi-mum stresses within abutment of dynamic loading reached43.7% of the yield stress. For all two loading conditions,maximum Von Mises stress values in the abutment didnot reach the yield strength.

3.3. Metal framework

Fig. 8 represent the stress distribution in the metalframework in static and dynamic loading. Maximum stres-ses were located at the occlusal surface of the metal frame-work. Maximum Von Mises stresses for the metalframework in static and dynamic loading were 110.919and 173.613 MPa, respectively. For the static and dynamicloading, the maximum stress values within the metal frame-work were 15% and 24% of the yield stress, respectively.Maximum stress values at the metal framework of two

Table 4Maximum Von Mises stresses after static and dynamic loads (MPa)

Equivalent (Von Mises) stress

Static loading(MPa)

Dynamic loading(MPa)

Implant 118.317 177.476Abutment 113.955 182.328Metal framework 110.919 173.613Occlusal surface material 32.641 48.691Bone 17.831 28.530

Fig. 6. Stress distribution in the implant fixture in static and dynamic loading.


loading conditions were lower than the yield stress (yieldpoint for Co–Cr alloy, 720 MPa).

3.4. Occlusal surface material

The maximum stress values, after two different loadingconditions were concentrated at the occlusal surface asshown in Fig. 9. The highest Von Mises stress value wasfound for dynamic loading. However, the lowest stressvalue was calculated for the occlusal surface material in

static loading. Maximum Von Mises stresses for the occlu-sal surface material in static and dynamic loading were32.641 and 48.691 MPa, respectively. For the static load-ing, the maximum stress value within the occlusal surfacematerial was 46% of the yield stress (yield point for felds-phatic porcelain, 69 MPa). Maximum stresses within occlu-sal surface material of dynamic loading reached 85% of theyield stress. For all two loading conditions, maximum VonMises stress values in the occlusal surface material did notreach the yield strength.

Fig. 7. Stress distribution in the abutment in static and dynamic loading.

Fig. 8. Stress distribution in the metal framework in static and dynamic loading.

Fig. 9. Stress distribution in the occlusal surface material in static and dynamic loading.


3.5. Cortical and spongy bone

Maximum stresses were located within the cortical bonesurrounding the implant and within the neck of implant.There was no stress within the spongy bone. MaximumVon Mises stress values within the cortical bone surround-ing the implant neck were 17.831 MPa for static loadingand 28.530 MPa for dynamic loading. For the static load-ing, the maximum stress value within the cortical bonewas 25% of the yield stress (yield point for cortical bone,69 MPa). Maximum stresses within cortical bone ofdynamic loading reached 41% of the yield stress. For alltwo loading conditions, maximum Von Mises stress valuesin the cortical bone did not reach the yield strength.

Prior to the fatigue analysis Von Mises stresses obtaineddue to the applied loads were compared with the previousworks to validate the model and to ensure the model safetyagainst static failure. In Fig. 10 safety factor for implantwhen applied preload. These values are under the yieldstrength value of the material. All the analysis were per-formed according to infinite life criteria (1e9 cycles). It isimportant that these maximum equivalent stress valuesshould be lower than the endurance limit of the material.The endurance limits of Ti–6Al–4V and cobalt–chromiumalloy are 138 MPa and 156 MPa respectively. Finite ele-ment analyses conducted in this study showed that implantgeometry type is safe against fatigue load with Ti–6Al–4Vmaterial. This results are shown in Fig. 11.

The axial load in the screw was determined versus axialdisplacement of the screw head measured contact area. Theresult are expressed in Fig. 12. Clinically, axial preload isapplied by torque. Within the elastic domain, higher torquevalues shows nearly linear relationships between the axialdisplacement and clamping.

4. Discussion

The finite element method is one of the most frequentlyused methods in stress analysis in both industry and science[27]. It is used for analyzing hip joints, knee prostheses,and dental implants [28,14,29]. The results of the FEA

Fig. 10. Stress distribution in the cortical and spongy bone in static and dynamic loading.

Fig. 11. Safety factor for Ti–6Al–4V and cobalt–chromium.

Fig. 12. The relationship between preload and axial deformation.


computation depend on many individual factors, includingmaterial properties, boundary conditions, interface defini-tion, and also on the overall approach to the model [27].It is apparent that the presented model was only anapproximation of the clinical situation. The applicationof a 3-D model simulation with the nonsymmetric loadingby the masticatory force on a dental implant resulted in amore satisfactory modeling of ‘‘clinical reality’’ than thatachieved with two-dimensional models used in otherstudies [30,31].

The basic purpose of the bioengineering in dentistrywhich analyzed biomechanical principles in in vitro studieswas to extrapolate the findings relevant to the risk factorsinstead of experiencing them empirically in clinical applica-tions. However, the stress levels that actually cause biolog-ical response, such as resorption and remodeling of thebone, are not comprehensively known. Therefore, the dataof stress provided from finite element analysis require sub-stantiation by clinical research [32,33].

Modeling the exact geometry of the implant complex,including the thread helix of the screw and the screw bore,was essential for finite element analysis [34]. Modeling ofthe thread allowed simulation of the tightening of the abut-ment screw into the screw bore of the implant and insertingthe implant into the osteotomy site in the finite elementanalysis during torque applications.

Several assumptions were made in the development ofthe model in the present study. The structures in the modelwere all assumed to be homogeneous and isotropic and topossess linear elasticity. The properties of the materialsmodeled in this study, particularly the living tissues, forinstance, it is well documented that the cortical bone ofthe mandible is transversely isotropic and inhomogeneous[35]. Cement thickness layer was also ignored [36,37]. Allinterfaces between the materials were assumed to bebonded or osseointegrated [38–40]. Implant–bone interface(100%) was established, which does not necessarily simu-late clinical situations [38]. These are inherent limitationsof this study.

In this study, Von Mises stress values occurred less thanthe other numeric works that not to apply tighten torque toimplant–bone interface and implant–abutment interface[32,39]. For this reason, finite element model is modelednearly clinical application and applied tighten torque toimplant–bone interface and implant–abutment interface isconsidered.

When applying FEA to dental implants, it is importantto consider not only axial loads and horizontal forces(moment-causing loads) but also a combined load (obliqueocclusal force) because the latter represents more realisticocclusal directions and, for a given force, will result inlocalized stress in cortical bone [41]. So in this study,118.2 N force was applied to 75� angular to occlusal planethat simulate chew force to oblique direction.

Crestal bone loss and early implant failure after loadingresults most often from excess stress at the implant–boneinterface [42]. This phenomenon is explained by the evalu-

ation of FE analysis of stress contours in the bone. Themechanical distribution of stress occurs primarily wherebone is in contact with the implant [1]. The smaller the areaof bone contacting the implant body, the greater the overallstress, when all factors are equal [14]. Cortical bone, havinga higher modulus of elasticity than trabecular bone, isstronger and more resistant to deformation [43]. For thisreason, cortical bone will bear more load than trabecularbone in clinical situations [35,44]. Static and dynamic anal-yses of the implant should be conducted to ensure aboutthe safety of the design. In the literature, implant is oftendesigned according to the results of static analysis. Staticfinite element (FE) analyses are mostly conducted underloading. However, dynamic effects may add up to about10–20% or more loading to the implant which must betaken into account not to cause fracture or fatigue failureof the prosthesis. To investigate how static and dynamicanalysis results differ from each other, implant is analyzedunder static load and dynamic chewing load. The otherwork that supported this work is Zhang and Chen’s work.Zhang and Chen compared dynamic with static loading inthree-dimensional FEA models with a range of differentelastic moduli for the implant. Their results showed that,compared with the static load models, the dynamic loadmodel resulted in higher maximum stress at the bone–implant interface as well as a greater effect on stress levelswhen elastic modulus was varied [45].

A finite element study demonstrated that maximumstresses concentrated at the connection between the headand first thread of the prosthetic connection screws in thecomplete arch screw-retained implant-supported fixed par-tial denture. This study also showed that the maximumstress value was concentrated at the unthreaded shank ofboth abutment and prosthetic screws. Functional stressbetween 200 and 700 psi is reported to maintain existingalveolar bone height [46,47].

It has been reported that stress outside this range ishighly likely to cause degeneration of bone tissue. In addi-tion, bone atrophy occurs if the stresses are too low. Main-tenance of bone levels can be achieved by proper implantand prosthesis design. This aspect can be better understoodby the use of computer aided analyses and studies [46].

5. Conclusion

One of the most important factor in the implant designinvestigate static, dynamic and fatigue behaviors of dentalimplant. In this study, static, dynamic and fatigue behav-iors of dental implant are investigated that different condi-tions than the other works. For the loading conditionstested, the maximum stress values did not reach the yieldstrength of abutment and prosthetic screws of theimplant/abutment joint systems evaluated. It is seem thatthe implant is durable all condition static and dynamicloading at the end of work.

Implant can be designed and studied in computer envi-ronment before it is implemented on the patient. This will


save time for the design and prevent any permanent dam-age caused by miss-implementation of implant.

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11.2Anexo(2)

JUNE 2001 THE JOURNAL OF PROSTHETIC DENTISTRY 585

In the past 2 decades, finite element analysis (FEA)has become an increasingly useful tool for the predic-tion of the effects of stress on the implant and itssurrounding bone. Vertical and transverse loads frommastication induce axial forces and bending momentsand result in stress gradients in the implant as well asin the bone. A key factor for the success or failure of adental implant is the manner in which stresses aretransferred to the surrounding bone. Load transferfrom implants to surrounding bone depends on thetype of loading, the bone–implant interface, the lengthand diameter of the implants, the shape and character-istics of the implant surface, the prosthesis type, andthe quantity and quality of the surrounding bone. FEAallows researchers to predict stress distribution in thecontact area of the implants with cortical bone andaround the apex of the implants in trabecular bone.

Although the precise mechanisms are not fullyunderstood, it is clear that there is an adaptive remod-elling response of the surrounding bone to this stress.Implant features causing excessive high or low stressesmay contribute to pathologic bone resorption or boneatrophy. This article reviews the current status of theapplication of FEA in implant dentistry. Assumptionsmade in the use of FEA in implant dentistry aredescribed, and findings from FEA studies are discussedin relation to the bone–implant interface, theimplant–prosthesis connection, and multiple-implantprostheses.

ASSUMPTIONS IN THE USE OF FEA INTHE IMPLANT-BONEBIOMECHANICAL SYSTEM

For problems involving complicated geometries, itis very difficult to achieve an analytical solution.Therefore, the use of numerical methods such as FEAis required. FEA is a technique for obtaining a solutionto a complex mechanical problem by dividing theproblem domain into a collection of much smaller andsimpler domains (elements) in which the field variablescan be interpolated with the use of shape functions. Anoverall approximated solution to the original problemis determined based on variational principles. In otherwords, FEA is a method whereby, instead of seeking asolution function for the entire domain, one formu-lates the solution functions for each finite element andcombines them properly to obtain the solution to thewhole body. Because the components in a dentalimplant-bone system are extremely complex geometri-cally, FEA has been viewed as the most suitable toolfor analyzing them. A mesh is needed in FEA to dividethe whole domain into elements. The process of creat-ing the mesh, elements, their respective nodes, anddefining boundary conditions is referred to as “dis-cretization” of the problem domain.

FEA was initially developed in the early 1960s tosolve structural problems in the aerospace industry buthas since been extended to solve problems in heattransfer, fluid flow, mass transport, and electromagnet-ics. In 1976, Weinstein et al1 were the first to use FEAin implant dentistry; subsequently, FEA was appliedrapidly in that field. Atmaram and Mohamed2-4 ana-lyzed the stress distribution in a single-tooth implantto understand the effect of elastic parameters andgeometry of the implant, implant length variation, andpseudo-periodontal ligament incorporation. Borchersand Reichart5 performed a 3-dimensional FEA of animplant at different stages of bone interface develop-ment. Cook et al6 applied FEA to porous rooted

Application of finite element analysis in implant dentistry: A review of the literature

Jian-Ping Geng, BDS, MSD,a Keson B. C. Tan, BDS (Hons), MSD,b and Gui-Rong Liu, PhDc

Faculty of Dentistry and Faculty of Engineering, National University of Singapore, Singapore

Finite element analysis (FEA) has been used extensively to predict the biomechanical performanceof various dental implant designs as well as the effect of clinical factors on implant success. Byunderstanding the basic theory, method, application, and limitations of FEA in implant dentistry,the clinician will be better equipped to interpret results of FEA studies and extrapolate theseresults to clinical situations. This article reviews the current status of FEA applications in implantdentistry and discusses findings from FEA studies in relation to the bone–implant interface, theimplant–prosthesis connection, and multiple-implant prostheses. (J Prosthet Dent 2001;85:585-98.)

aResearch Scholar, Department of Restorative Dentistry, Faculty ofDentistry.

bAssociate Professor, Department of Restorative Dentistry, Facultyof Dentistry.

cAssociate Professor, Centre for Advanced Computations inEngineering Science, Faculty of Engineering.

THE JOURNAL OF PROSTHETIC DENTISTRY GENG, TAN, AND LIU

586 VOLUME 85 NUMBER 6

dental implants. Meroueh et al7 performed an FEA foran osseointegrated cylindrical implant. Williams et al8carried out an FEA on cantilevered prostheses on den-tal implants, and Akpinar et al9 used FEA to simulatethe combination of a natural tooth and implant.

The principal difficulty in simulating the mechanicalbehavior of dental implants is the modelling of humanbone tissue and its response to applied mechanicalforce. Certain assumptions need to be made to makethe modelling and solving process possible. The com-plexity of the mechanical characterization of bone andits interaction with implant systems has forced authorsto make major simplifications. Some assumptionsinfluence the accuracy of the FEA results significantly.These include: (1) detailed geometry of the bone andimplant to be modelled,10 (2) material properties,10

(3) boundary conditions,10 and (4) the interfacebetween bone and implant.11

Geometry

The first step in FEA modelling is to represent thegeometry of interest in the computer. In some 2-dimensional FEA studies, the bone was modelled asa simplified rectangular configuration with theimplant.11-13 Some 3-dimensional FEA models treatedthe mandible as an arch with rectangular section.14,15

Recently, with the development of digital imagingtechniques, more efficient methods are available forthe development of anatomically accurate models.These include the application of specialized softwarefor the direct transformation of 2- or 3-dimensionalinformation in image data from computed tomogra-phy (CT) or magnetic resonance imaging (MRI) intoFEA meshes. The automated inclusion of some mate-rial properties from measured bone density values isalso possible.16,17 This allows more precise modellingof the geometry of the bone–implant system. In theforeseeable future, the creation of FEA models forindividual patients, based on advanced digital tech-niques, will become possible and perhaps evencommonplace.

Material properties

Material properties greatly influence the stress andstrain distribution in a structure. These properties canbe modelled in FEA as isotropic, transversely isotro-pic, orthotropic, and anisotropic. In an isotropicmaterial, the properties are the same in all directions;therefore, only 2 independent material constants exist.An anisotropic material has different properties whenmeasured in different directions. There are manymaterial constants depending on the degree ofanisotropy (transversely isotropic, orthotropic).

In most reported studies, the assumption is madethat the materials are homogeneous and linear andthat they have elastic material behavior characterized

by 2 material constants of Young’s modulus andPoisson’s ratio. Early FEA studies ignored the trabec-ular bone network simply because the capability todetermine the trabecular pattern was not available.Therefore, it was assumed that trabecular bone has asolid pattern inside the inner cortical bone shell. Bothbone types were modelled simplistically as linear,homogeneous, and isotropic materials. A range of dif-ferent material parameters have been recommendedfor use in previous FEA studies (Table I).5,18-33

Several authors34-37 have pointed out that corticalbone is neither homogeneous nor isotropic (Table II).This nonhomogenous, anisotropic, composite struc-ture of bone possesses different values for ultimatestrain and modulus of elasticity when bone is tested incompression compared with in tension. Test condi-tions also affect the material properties measured.Rieger et al12 reported that a range of stresses (1.4 to5.0 MPa) appears to be needed for healthy mainte-nance of bone. Stresses outside this range have beenreported to cause bone resorption.

Boundary conditions

Most FEA studies modelling the mandible set theboundary conditions as fixed. Recently, Zhou et al38

developed a more realistic 3-dimensional mandibularFEA model from transversely scanned CT image data.The functions of the mastication muscles and the liga-menteous and functional movement of thetemporomandibular joints (TMJ) were simulated bymeans of cable elements and compressive gap ele-ments, respectively. The authors concluded that cableand gap elements can be used to set boundary condi-tions in their mandibular FEA model, improving themodel mimicry and accuracy. Expanding the domainof the model can reduce the effect of inaccurate mod-elling of the boundary conditions. This, however, is atthe expense of computing and modelling time. Teixeraet al39 concluded that in a 3-dimensional mandibularmodel, modelling the mandible at distances greaterthat 4.2 mm mesially or distally from the implant didnot result in any significant further yield in FEA accu-racy. The use of infinite elements can be a good way tomodel boundary conditions.

Bone–implant interface

Most FEA models assume a state of optimalosseointegration, meaning that cortical and trabecularbone are assumed to be perfectly bonded to theimplant. This does not occur so exactly in clinical situ-ations. Therefore, the imperfect contact and its effecton load transfer from implant to supporting bone needto be modelled more carefully. Current FEA programsprovide several types of contact algorithms for simula-tion of contacts. It is therefore now technically feasibleto conduct such a simulation. The friction between

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JUNE 2001 587

contact surfaces can also be modelled with contactalgorithms. The friction coefficients, however, have tobe determined through experimentation.

Bone is a porous material with complex micro-structure. The higher load-bearing capacity of densecortical bone compared with the more porous trabecu-lar bone is generally recognized. On implant insertion,cortical and/or trabecular bone, starting at theperiosteal and endosteal surfaces, gradually form a par-tial-to-complete encasement of the implant. However,the degree of encasement is dependent on the stressesgenerated and the location of the implant in the jaw.37

The anterior mandible is associated with 100% corticalosseointegration; this percentage decreases toward theposterior mandible. The least cortical osseointegration(<25%) is seen in the posterior maxilla. The degree ofosseointegration appears to be dependant on bonequality and stresses developed during healing and func-tion. To study the influence of osseointegration ingreater detail at the bone trabeculae contact to implantlevel, Sato et al40 set up 4 types of stepwise assignmentalgorithms of elastic modulus according to the bonevolume in the cubic cell (Fig. 1). They showed thattheir 300 µm element size was valid for modelling thebone–implant interface.

Summary

In summary, stress distribution depends on assump-tions made in modelling geometry, material properties,boundary conditions, and the bone–implant interface.To obtain more accurate stress predictions, advanceddigital imaging techniques can be applied to model thebone geometry more realistically; the anisotropic andnonhomogenous nature of the material must be con-sidered; and boundary conditions must be carefullytreated with the use of computational modelling tech-niques. In addition, modelling of the bone–implantinterface should incorporate the actual osseointegrationcontact area in cortical bone as well as the detailed tra-becular bone contact pattern through the use ofcontact algorithms in FEA.

Table I. Material parameters used in finite element analysis studies of dental implants

Material Elastic modulus (Pa) Poisson’s ratio Author

Enamel 4.14 × 104 0.3 Davy et al18

4.689 × 104 0.30 Wright and Yettram19

8.25 × 104 0.33 Farah et al20

8.4 × 104 0.33 Farah et al21

Dentin 1.86 × 104 0.31 Reinhardt et al22

1.8 × 104 0.31 MacGregor et al23

Parodontal membrance 171 0.45 Atmaram and Mohammed24

69.8 0.45 Reinhardt et al22

6.9 0.45 Farah et al21

Cortical bone 2727 0.30 Rice et al25

1.0 × 104 0.30 Farah et al21

1.34 × 104 0.30 Cook et al26

1.5 × 104 0.30 Cowin27

Trabecular bone 150 0.30 Cowin27

250 0.30 MacGregor et al23

790 0.30 Knoell28

1.37 × 103 0.31 Borchers and Reichart5

Mucosa 10 0.40 Maeda and Wood29

Pure titanium 117 × 103 0.30 Sakaguichi and Borgersen30

Ti-6Al-4V 110 × 103 0.33 Colling31

Type 3 gold alloy 100 × 103 0.30 Sakaguichi and Borgersen30

80 × 103 0.33 Lewinstein et al32

Ag-Pd alloy 95 × 103 0.33 Craig33

Co-Cr alloy 218 × 103 0.33 Craig33

Porcelain 68.9 × 103 0.28 Lewinstein et al32

Resin 2.7 × 103 0.35 Craig33

Resin composite 7 × 103 0.2 Craig33

Table II. Anistropic properties of cortical bone

Cortical shell

Elastic (MPa) Diaphyseal Metaphyseal

Longitudinal 17,500 9,650Transverse 11,500 5,470



THE BONE–IMPLANT INTERFACE

Analyzing force transfer at the bone–implant inter-face is an essential step in the overall analysis ofloading, which determines the success or failure of animplant. It has long been recognized that bothimplant and bone should be stressed within a certainrange for physiologic homeostasis. Overload can causebone resorption or fatigue failure of the implant,whereas underloading of the bone may lead to disuseatrophy and subsequent bone loss.41,42 With the use ofload cells in rabbit calvaria, Hassler et al43 showed thatthe target compressive stress level for maximum bonegrowth occurs at 1.8 MPa, levelling off to a controllevel at 2.8 MPa. Skalak44 stated that close appositionof bone to the titanium implant surface means thatunder loading, the interface moves as a unit withoutany relative motion; this is essential for the transmis-sion of stress from the implant to the bone at all partsof the interface.

In centric loading, several FEA studies45-47 ofosseointegrated implants demonstrate that when max-imum stress concentration is located in cortical bone,it is in the contact area with the implant, and when themaximum stress concentration is in trabecular bone, itoccurs around the apex of the implant. In corticalbone, stress dissipation is restricted to the immediatearea surrounding the implant; in trabecular bone, afairly broader distant stress distribution occurs.

Stress transmission and biomechanicalimplant design problems

FEA can simulate the interaction phenomenabetween implants and the surrounding tissues.Analysis of the functional adaptation process is facili-tated by the ability to investigate the various loading,implant, and surrounding tissue variables. Load trans-fer at the bone–implant interface depends on the:

(1) type of loading; (2) material properties of theimplant and prosthesis; (3) implant geometry, lengthand diameter as well as shape; (4) implant surfacestructure; (5) nature of the bone–implant interface;and (6) quality and quantity of the surrounding bone.Most efforts have been directed at optimizing implantgeometry to maintain the beneficial stress level in avariety of loading scenarios.

Loading

When applying FEA to dental implants, it is impor-tant to consider not only axial loads and horizontalforces (moment-causing loads) but also a combinedload (oblique occlusal force) because the latter repre-sents more realistic occlusal directions and, for a givenforce, will cause the highest localized stress in corticalbone.48 Barbier et al49 investigated the influence ofaxial and nonaxial occlusal loads on the bone remodel-ling phenomena around IMZ implants in a dogmandible simulated with FEA. A strong correlationbetween the calculated stress distributions in the sur-rounding bone tissue and the remodelling phenomenain the comparative animal model was observed. Theauthors concluded that the highest bone remodellingevents coincide with the regions of highest equivalentstress and that the major remodelling differencesbetween axial and nonaxial loading are determinedlargely by the horizontal stress component of theengendered stresses. The importance of avoiding orminimizing horizontal loads thus was emphasized.

Zhang and Chen50 compared dynamic with staticloading in 3-dimensional FEA models with a range ofdifferent elastic moduli for the implant. Their resultsshowed that, compared with the static load models,the dynamic load model resulted in higher maximumstress at the bone–implant interface as well as a greatereffect on stress levels when elastic modulus was varied.

In summary, both static and dynamic loading ofimplants have been modelled with FEA. In static loadstudies, it is necessary to include oblique occlusalforces to achieve more realistic modelling. Most stud-ies conclude that excessive horizontal force should beavoided. The effects of dynamic loading require fur-ther investigation.

Prosthesis and implant material properties

High-rigidity prostheses are recommended becausethe use of low elastic moduli alloys for the superstruc-ture predicts larger stresses at the bone–implantinterface on the loading side than the use of a rigidalloy for a superstructure with the same geometry.51

Stegariou et al52 used 3-dimensional FEA to assessstress distribution in bone, implant, and abutmentwhen a gold alloy, porcelain, or resin (acrylic or com-posite) was used for a 3-unit prosthesis. In almost allsituations, stress in the bone–implant interface with

Fig. 1. Four types of stepwise assignment algorithms of elas-tic modulus according to bone volume in cubic cell. E = elastic modulus (GPa). (Reproduced with permissionfrom J Oral Rehabil 1999;26:641.)


JUNE 2001 589

the resin prostheses was similar to or higher than thatin the models with the other 2 prosthetic materials.However, in his classical mechanical analysis, Skalak44

stated that the presence of a resilient element in animplant prosthesis superstructure would reduce thehigh load rates that occur when occluding unexpect-edly on a hard object. For this reason, he suggestedthe use of acrylic resin teeth. Nevertheless, severalother studies53,54 could not demonstrate any signifi-cant differences in the force absorption quotient ofgold, porcelain, or resin prostheses.

The elasticity moduli of different implant materialsalso influences the implant–bone interface. Implantmaterials with too low moduli are to be avoided;Malaith et al55 suggested that implant materials have amodulus of elasticity of at least 110,000 N/mm2.Rieger et al56 indicated that serrated geometry led tohigh-stress concentrations at the tips of the bonyingrowth and near the neck of the implant. Low mod-uli of elasticity emphasized these concentrations. Thenontapered, screw-type geometry showed high-stressconcentrations at the base of the implant when highmoduli were modelled and at the neck of the implantwhen low moduli were modelled. The authors con-cluded that a tapered endosseous implant with a highelastic modulus would be most suitable for dentalimplantology. However, the design must not causehigh-stress concentrations, which commonly lead tobone resorption, at the implant neck. Stoiber57 report-ed that in the construction of an appropriate screwimplant, special attention must be paid to the rigidityof the implant rather than to thread design.

In summary, although the effect of prosthesis mate-rial properties is still being debated, it is wellestablished that implant material properties greatlyaffect the location of stress concentrations at theimplant–bone interface.

Implant geometry: length, diameter, andshape

Large implant diameters provide for more favorablestress distributions.55,58 FEA has been used to showthat stresses in cortical bone decrease in inverse pro-portion to an increase in implant diameter with bothvertical and lateral loads.58 However, Holmgren et al48

showed that using the widest diameter implant is notnecessarily the best choice when considering stress dis-tribution to surrounding bone; within certainmorphologic limits, an optimum dental implant sizeexists for decreasing the stress magnitudes at thebone–implant interface.

In general, the use of short implants has not beenrecommended because it is believed that occlusalforces must be dissipated over a large implant area forthe bone to be preserved. Lum59 has shown thatocclusal forces are distributed primarily to the crestal

bone rather than evenly throughout the entire surfacearea of the implant interface. Because masticatoryforces are light and fleeting, these forces are normallywell-tolerated by the bone. It is the bruxing forces thatmust be adequately attenuated, and this may beachieved by increasing the diameter and number ofimplants. A recent clinical study concluded that shortimplants are possible when the peri-implant tissues arein good condition.60

In summary, the optimum length and diameternecessary for long-term success depends on the bonesupport condition. If the bone is in normal condi-tion, length and diameter appear not to be significantfactors for implant success. However, if the bonecondition is poor, large diameter implants are advisedand short implants should be avoided.

With regard to implant shape, theoretical analysisimplies that clinically, whenever possible, an optimumand not necessarily larger dental implant shape shouldbe used based on the specific morphologic limitationsof the mandible.

Holmgren et al48 reported that a stepped cylindri-cal design for press-fit situations is most desirablefrom the standpoint of stress distribution to sur-rounding bone. With the use of FEA to analyze aparasaggital model digitized from a CT-generatedpatient data set, these authors simulated various sin-gle-tooth, 2-dimensional osseointegrated dentalimplant models. The results suggested that stress ismore evenly dissipated throughout the stepped cylin-drical implant than the straight implant type. Afteranalyzing stress concentration patterns using FEA,Rieger et al56 concluded that a tapered endosseousimplant with a high elastic modulus would be mostsuitable. Also using FEA, Mailath et al55 comparedcylindrical and conical implant shapes exposed tophysiologic stresses and examined the occurrence ofstress concentrations at the site of implant entry intobone. They reported that cylindrical implants werepreferable to conical implant shapes.

Siegele and Soltesz61 compared cylindrical, conical,stepped, screw, and hollow cylindrical implant shapesby means of FEA. Both a fixed bond (simulating com-plete load transfer with bioactive materials) and a purecontact (only compression transfer with bioinertmaterials) without friction between implant and bonewere considered interface conditions. The resultsdemonstrated that different implant shapes lead tosignificant variations in stress distributions in bone.The authors stated that implant surfaces with verysmall radii of curvature (conical) or geometric discon-tinuities (stepped) induce distinctly higher stressesthan smoother shapes (cylindrical, screw-shaped).Moreover, a fixed bond between implant and bone inthe medullary region (as may be obtained with abioactive coating) is advantageous for the stress deliv-



ered to bone because it produces a more uniformstress distribution than does a pure contact.

Patra et al37 reported that the tapered thread designof the Branemark implant exhibited higher stress levelsin bone than the parallel profile thread of the BUDimplant (BUD Medical Devices, Inc), which seemed todistribute stresses more evenly. Clift et al62 reportedthat the modification of the standard implant design toinclude a flexible central post resulted in a decrease inthe maximum von Mises stresses and equivalent strainsin cancellous bone. It was postulated that this wouldreduce the likelihood of bone fatigue failure and sub-sequent bone resorption.

Optimum implant shape is related to the bone con-dition and implant material properties. Implantdesigns have adopted various shapes; FEA seems toindicate that for commercially pure titanium (cpTi)implants, smoother profiles engender lower stress con-centrations. The optimal thread design to achieve thebest load transfer characteristics is the subject of cur-rent investigations.

Implant surface structure

Bioactive materials are used as coating on titani-um implants because they have the potential toencourage bone growth up to the surface of theimplant.63 It is claimed that these coatings can pro-duce a fully integrated interface with direct bondingbetween bone and the implant material, leading to amore even transfer of load to the bone along theimplant and thus a reduction in stress concentra-tions.61

Meijer et al64 investigated the influence of a 3-layerflexible coating of Polyactive on bone stress distributionwith the use of a 3-dimensional FEA in a mandibularmodel. Polyactive is a system of poly (ethylene oxide)poly (butylene terephthalate) segmented copolymerswith bone-bonding capacity. In the case of sagittal andtransversal loading, the use of a Polyactive coatingreduced both the minimum principal stress in the boneand the compressive radial stress at the bone–implantinterface. However, it raised the maximum principaland tensile radial stresses. In the case of vertical load-ing, the application of a flexible coating reduced thecompressive radial stress at the bone–implant inter-face around the neck of the implant by a factor of 6.6and the tensile radial stress by a factor of 3.6.Variations in composition and thickness of the coatingdid not affect the results significantly.

Nature of the bone–implant interface

There are 2 types of contact at the bone–implant inter-face: bone–implant contact and fibrous tissue–implantcontact. The clinical concept of fibrous encapsulation ofan implant is considered to be a failure; this condition isno longer modelled in FEA studies.

Surrounding bone quality and quantity

The long-term clinical performance of a dentalimplant is dependent on the preservation of goodquality bone surrounding the implant and a soundinterface between the bone and biomaterial. Goodquality bone is itself dependent on the appropriatelevel of bone remodelling necessary to maintain thebone density and the avoidance of bone microfractureand failure. Both processes are governed by the stressand strain distribution in the bone.

Crestal bone: The crestal bone region is of particularinterest because of the observations of progressivebone resorption (saucerization). Crestal bone loss isobserved around various designs of dental implants. Apossible cause of this bone loss is related to the lowstresses acting on peri-implant bone. On the basis ofboth histologic examination and FEA results,65,66 anequivalent stress of 1.6 MPa has been deemed suffi-cient to avoid crestal bone loss from disuse atrophy inthe canine mandibular premolar region.

Wiskott and Belser67 studied the relationshipbetween the stresses applied and bone homeostasis ofdifferent implant neck designs. It has been observedthat the polished neck of dental implants does notosseointegrate as do textured surfaces. Lack ofosseointegration was postulated to be due to increasedpressure on the osseous bed during implant place-ment, establishment of a physiologic “biologic width,”stress shielding, and lack of adequate biomechanicalcoupling between the load-bearing implant surfaceand the surrounding bone. Any viable osseous struc-ture (including the tissue that surrounds the polishedimplant neck) is subjected to periodic phases of resorp-tion and formation. Hansson68 compared implantswith smooth necks to implants with retention ele-ments all the way up to the crest. His FEA study foundthat retention elements at the implant neck resulted ina major decrease in peak interfacial shear stresses. Hesuggests that these retention elements at the implantneck will counteract marginal bone resorption inaccordance with Wolff’s law.

For the Screw-Vent implant, Clelland et al69

showed that under axial loading, mesial and distalstresses were much lower than those buccal and lingualto the implant. Maximum stress in the bone was lin-gual to the superior portion of the collar. Previouslongitudinal radiographic studies of a similar implantrevealed bone loss mesial and distal to the implant.The authors emphasized that the clinical significanceof the stress transfer to the bone buccal and lingual tothe implant had yet to be determined.

Minimum required load for avoidance of crestalbone loss appears to have been defined,37,65,66 but theupper limit of the physiologic stress range has not yetbeen investigated.


JUNE 2001 591

Cortical bone: The quality and quantity of the sur-rounding bone influences the load transfer fromimplant to bone.46,70 In almost all FEA studies of tita-nium implants, stress concentrations occur around theimplant neck. Under oblique loads with high occlusalstress magnitudes, the elastic limit of bone surround-ing implants may be surpassed and lead tomicrofractures in the cortical bone. Clift et al46

emphasized the importance of having good qualitydense bone around the implant neck that can with-stand stresses in the range of 9 to 18 MPa beforeloading. Failure to achieve this after implantation andsubsequent healing may result in local fatigue failureand resorption at the neck on resumption of physio-logic loading.71 Holmes and Loftus72 used FEA toexamine the influence of bone quality on the transmis-sion of occlusal forces for endosseous dental implants.Placement of implants in bone with greater thicknessof the cortical shell and greater density of the coreresulted in less micromovement and reduced stressconcentration, thereby increasing the likelihood of fix-ture stabilization and tissue integration.

With a 3-dimensional FEA model, Papavasiliou et al73

showed that the absence of cortical bone increased inter-facial stresses at the locations studied. Clift et al71

reported that a reduction, by a factor of 16, in the elas-tic modulus of the bone around the neck of the implantproduced only a 2-fold reduction in the peak stress.

Trabecular (cancellous) bone: Using the degree of direct bone–implant interface as an indicator ofendosseous implant success appears to be misleading, as100% bone apposition is almost never obtained at thesurface of the endosseous dental implant. Investigatingthe 3-dimensional bone interface to hydroxyapatite-coated titanium alloy implants, Wadamoto et al74

generated computer graphics by the integration of datafor serial ground surfaces obtained at 75 µm intervalsof the tissue block involved with the implant. Theauthors found that the bone contact ratio of the wholesurface of each of 3 implants was 80.8%, 68.1%, and68.8%, and the bone contact ratio for each directionand portion varied with the conditions of implantplacement. The bone volume ratios around the implantat the 0 to 300 µm zone were also calculated, and totalratios ranged from 58% to 81%. These results may pro-vide useful quantitative information about the bonestructure around implants and contribute to the devel-opment of more realistic FEA models based on thebiologic bone structure around implants.

Patra et al37 modelled progressive bone lossand partial osseointegration by both 2- and 3-dimensional FEA. When 25%, 75%, and 100%osseointegration was modelled, cortical bone wasshown to carry most of the load, with resulting over-load leading to crestal bone loss. Stress plots showedthat with increasing crestal bone loss, the majority of

the load was transferred directly to the weaker tra-becular bone tissue.

Clelland et al75 investigated a Steri-Oss implant invarious bone models with different cancellous and cor-tical bone conditions using 2-dimensional FEA. Forthe all-cancellous bone model, low stresses and highstrains surrounded the implant apex. For the modelswith a layer of cortical bone added, higher crestalstresses and lower apical strains were observed. Thethicker layer of isotropic cortical bone producedstresses at least 50% less than the thinner layer. Theassumption of transverse isotropy (orthotropy) for thecortical bone layer increased stresses and strains byapproximately 25% compared with isotropic bone. Theauthors concluded that crestal cortical layer thicknessand bone isotropy have a substantial impact on resul-tant stresses and strains.

Summary

Load transmission and resultant stress distribu-tion are significant in determining the success orfailure of an implant. Factors that influence the loadtransfer at the bone–implant interface include thetype of loading, implant and prosthesis materialproperties, implant length and diameter, implantshape, structure of the implant surface, nature of thebone–implant interface, and quality and quantity ofthe surrounding bone. Of these biomechanical fac-tors, implant length, diameter, and shape can bechanged easily. Cortical and cancellous bone qualityand quantity need to be assessed clinically andshould influence implant selection.

IMPLANT–PROSTHESIS CONNECTION

Clinical studies have reported a significant inci-dence of component failure. These include gold screwand abutment screw failures as well as gold cylinder,framework, and implant fractures. The cause of thesefailures is complex and involves cyclic fatigue, oral flu-ids, and varied chewing patterns and loads.

Biomechanically, the following component inter-faces can be found in the Branemark implant: (1)fixture–abutment interface, (2) abutment screw–abutment interface, (3) gold cylinder–abutment inter-face, (4) gold retaining screw–gold cylinder interface,and (5) gold retaining screw–abutment screw inter-face. Long-term screw joint integrity at theimplant–abutment screw joint and abutment–goldcylinder screw joint is essential for prosthetic success.An increasing number of FEA studies focus on biome-chanical problems involving the screw joint and onscrew loosening phenomena.76-79

Screw loosening

The screw loosening problem frequently affectsdental implants and implant-supported prostheses.



When a screw is fastened to fix the prosthesis, a tensileforce (preload) is built up in the shank of the screw.This preload acts on the screw shank from the head ofthe screw to the threads. The preload should be ashigh as possible because it creates a clamping forcebetween the abutment and implant. The screw elon-gates when subjected to tensile forces duringtightening. The more elongation there is, the betterthe stability of the screw in place. Thus, screw designis of significance and should allow maximum torque tobe introduced into the shank of the screw.77

Several authors76,77 have drawn attention to the factthat repeated loading and unloading cycles result inalternating contact and separation of components.Clinical findings of screw loosening and failure proba-bly result from these separation events and fromelevated strains in the screw. The other mechanism ofscrew loosening is related to the fact that no surface iscompletely smooth. Because of the microroughness ofcomponents, when the screw interface is subjected toexternal loads, micromovements occur between thesurfaces. Wear of the contact areas may result fromthese motions, thereby bringing the 2 surfaces closerto each other and causing a decrease in preload in theset of screws.

With prosthesis superstructure distortion, an exter-nal preload can be superimposed on the screw joints ofthe implant prosthesis. This distortion (or lack of pas-sive fit) can impart additional axial forces and bendingmoments on the screw joints and increase the likeli-hood of prosthetic component failure.80

Application of preload: The load-transfer mechanismbetween prosthetic components arises from torqueapplication to the abutment screw and gold screw.Sakaguchi et al76 developed a 2-dimensional FEAmodel for nonlinear contact analysis of Branemarkimplant prosthetic components. They found that whenthe gold retaining screw was fastened into the abut-ment screw, clamping force on the implant wasincreased at the expense of a decrease in the clampingforce at the abutment screw–abutment interface by50%. Maximum tensile stresses in the screw after pre-load were less than 55% of the yield stress.

Cheong et al81 used FEA to predict that, at a pre-load tension of 230 N in the gold retaining screwshank, the clamping force at the abutment–abutmentscrew interface would first be reduced to zero. Withfurther tightening of the gold retaining screw, the rateof increase of stresses in the gold retaining screw wasfaster than that of the abutment screw; thus, it waspredicted that the gold retaining screw would fail first.Failure of the gold retaining screw by yielding wasexpected for a tensile load of approximately 400 Napplied to the gold cylinder. At this 400 N tensile load,the clamping force at the implant–abutment interfacewas reduced to zero. This affects the overall stability of

the implant–prosthesis connection and eventually leadsto component failure.

Because preload application to the gold retainingscrew reduces the clamping force at the abutment–implant interface, it is recommended that a balancepreload be found between the gold retaining screw andabutment screw to make the whole implant–prosthesisconnection more stable.81 The current manufacturerrecommendation for the Branemark system is to usetightening torques of 20 Ncm for titanium abutmentscrews and 10 Ncm for gold retaining screws.

Washer: The addition of a customized washer todental implant screw joint systems may offer a verysimple and inexpensive solution for the persistentproblem of screw loosening. With the use of FEA,Versluis et al79 studied the effect of a washer in aBranemark-type implant on the loosening conditionsof the retaining screw. Their simulation indicated thata washer may significantly increase the axial toleranceof a screw against loosening up to 15 times more thana conventional system without a washer. The authorsindicated that this is accomplished by increasing thetolerance of the implant against deformation.

Screw fracture

Factors that contribute to screw failure include themagnitude and direction of loading, the elastic modu-lus of the prosthesis, and the rigidity of the abutment.

By studying the IMZ implant system with FEA,Holmes et al82 found that with increases in either loadmagnitude or load angle, stress concentrations in com-ponents of the implant system were generallyincreased. In another study, Holmes et al83 alsoshowed that in the IMZ implant, stress concentrationsin bone and in components were much greater undera 30-degree load than under an equal vertical load.Greater deflection and stress concentrations within thecoronal retaining screw were predicted with the use ofthe resin polyoxymethylene (POM) intramobile ele-ment (IME) than with the titanium element in theIMZ implant system. The authors’ FEA model alsofound that stress transmission to bone was not reducedwhen the IME was modelled in POM rather than tita-nium. Maximum stress concentrations occurred in thefastening screw.

Several authors82,84 recommend high elastic modu-lus prostheses to avoid deflection of the prostheticsuperstructure and stress concentrations in the retain-ing screw. Rigid abutment design is also needed todecrease the peak stresses in the screw and the deflec-tion of the superstructure. Two related studies85,86

described an FEA model of 3 different IMZ abutmentdesigns: original threaded intramobile element (IME),abutment complete (ABC), and intramobile connector(IMC). Progressive tightening of the retaining screw(preload) was simulated, and the degree of screw


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tightening necessary to prevent opening of thecrown–abutment interface in extreme loading (500 Nocclusal load at 45 degrees) was determined individu-ally for each system. A correlation was observedbetween the peak stresses in the screw and the deflec-tion of the superstructure. Deflections and stressconcentrations with the IMC were predicted to be inthe same range as with the IME, but much greaterthan with the ABC.

Summary

The screw loosening problem is of concern, especial-ly when considering single-tooth implant prostheses.The application of optimal preload has been the mainmeans of preventing loosening. However, a recent FEAstudy advocates the addition of a washer as a simple andeffective solution for the persistent problem of screwloosening. Stress concentrations in the fastening screwsare influenced by load magnitude and direction. High-rigidity prostheses and rigid abutments have been foundto give more favorable stress distributions in the screws.

MULTIPLE-IMPLANT PROSTHESES

From a biomechanical viewpoint, there are 3 mainclasses of multiple-implant prostheses: (1) implant-supported fixed prostheses (including cantilevereddesigns), (2) implant-supported overdentures, and (3)combined natural tooth and implant-supported pros-theses. FEA studies for these prosthetic situations areusually more complex than for the solitary implant. Inmost studies, 3-dimensional FEA is considered neces-sary and 2-dimensional FEA inadequate.

Because multiple implants are splinted by the pros-thesis framework, stress distribution is more complexthan with the single-tooth implant situation. Loadingat one point of the prosthesis causes stress concentra-tions in all supporting implants to varying degrees.The prosthesis can be loaded not by a single load butby multiple loads and in varying directions. In addi-tion, the flexure of the jaw bones, particularly themandible, under functional loading conditions cancause stress in the bone around the implants and maylead to bone resorption. Stress around the implant canbe caused not only by local deformation of the bonebecause of movement of the implant and interface rel-ative to the surrounding bone, but also by the complexdeformation patterns of the mandible.

Implant-supported fixed prostheses

For implant-supported fixed prostheses, the fac-tors that affect bone-implant stress distribution andultimately the success of the prosthesis includeimplant inclination, implant number and position,the prosthesis splinting scheme, the occlusal sur-face, framework material properties, and differentframework cross-sectional beam shapes.

Canay et al87 compared vertically orientatedimplants with angled implants and found that the incli-nation of implants greatly influences stressconcentrations around the implant-supported fixedprosthesis. The authors found no measurable differ-ences in stress values and contours when a horizontalload was applied to the vertical and angled implants.However, with vertical loading, compressive stress val-ues were 5 times higher around the cervical region ofthe angled implant than around the same area in thevertical implant.

Many clinicians are of the opinion that the selectionof implant positions and the scheme of prosthesissplinting are critical for the longevity and stability of animplant prosthesis. Kregzde88 reported that inducedstresses in bone are sensitive to the scheme of prosthe-sis splinting and implant positions. He used3-dimensional FEA modelling of jaw bones, teeth, andvarious implant numbers, positions, and prosthesisdesigns to attempt optimization of stress distributionto the implants. Induced stresses on implants for dif-ferent schemes of prosthesis splinting and differentimplant positions were found to vary as much as1000%.

The effect of different cross-sectional beam config-urations for implant frameworks also has beeninvestigated with FEA. Korioth and Johann89 com-pared superstructures with different cross-sectionalshapes and material properties during a simulated,complex biting task that modelled the deformationpatterns of the mandible during function. When theysubmitted their model to loads mimicking simultane-ous bending and torsion of the mandibular corpusduring bilateral posterior occlusion, they found thatpredicted implant stresses varied significantly betweenimplant sites for different superstructure shapes.Contrary to expectations, the ideal “I-beam” super-structure cross-section did not yield the lowestprincipal stresses; these were obtained with a verticallyorientated, rectangular-shaped beam superstructure.The authors concluded that implant abutment stresseswere significantly affected by the cross-sectional shapeof the prosthetic superstructure and by diversemandibular loading conditions.

Implant-supported fixed prostheses with cantileversadd additional factors that can influence stress distrib-ution. These factors include cantilever length,cross-sectional beam shapes, and recently, a system foradditional support of the distal extension of the can-tilever. Young et al90 investigated a number of differentcross-sectional beam shapes for cantilever fixed pros-theses for initiation of permanent deformation on endloading. Straight and curved cantilever beams 26 mmlong were modelled in FEA. They found that the “L-shaped” design was more rigid than other designs for agiven mass and that an open “I-section” framework



offered good possibilities, particularly when used ascurved shapes. “L-shaped” cobalt-chromium or stain-less steel frameworks of 26 mm cantilever spanunderwent permanent deformation at end loadingsbetween 130 and 140 N, depending on section curva-ture. The authors caution that good framework designis critical to avoid failures, because it is known thatoccluding loads can exceed these values.

Different material properties affect stress distribu-tion in different ways. Korioth and Johhann89 showedthat an increase in elastic modulus of prosthetic mate-rials does not necessarily lead to a decrease in stresseson all existing implant abutments. Less rigid super-structures seem to not only increase implant abutmentstresses overall but also decrease tensile stresses on themost anterior implant abutments for the modelledcomplex occluding task.

With the use of a 3-dimensional FEA model and a6-implant-supported mandibular complete arch fixedprosthesis, Sertgöz15 investigated the effect of differ-ent occlusal surface materials (resin, resin composite,and porcelain) and different framework materials(gold, silver-palladium, cobalt-chromium, and titani-um alloys) on stress distribution in the fixed prosthesisand surrounding bone. He demonstrated that the useof a prosthesis superstructure material with lower elas-tic modulus did not lead to substantial differences instress patterns or levels in the cortical and cancellousbone surrounding the implants. For the single loadingcondition investigated, the optimal combination ofmaterials was found to be cobalt-chromium for theframework and porcelain for the occlusal surface.

With a 3-dimensional FEA model of a bilateral dis-tal cantilever fixed prosthesis supported by 6 implantsin the mandible, Sertgöz and Guvener91 predicted thatmaximum stresses would occur at the most distalbone–implant interface on the loaded side and thatthese stresses would significantly increase with anincrease in cantilever length. Instead, they found nosignificant change in stress levels associated withimplant length variation. In a 15-year longitudinalclinical follow-up study, however, Lindquist et al92

reported that bone at the distal implants of can-tilevered mandibular implant-supported prosthesesremained very stable and, conversely, more bone losswas observed around the anterior implants. This resultmay have been caused by a multitude of other clinicalfactors. The authors concluded that occlusal loadingfactors such as maximal occlusal force, tooth clench-ing, and cantilever length were of minor importance tobone loss in their study population. This suggests thatextrapolation of FEA studies to clinical situationsshould be approached with caution.

New systems for additional support of the distalextensions of cantilevered prostheses have been sug-gested. The IL system uses a short implant and a

special ball-type attachment to support the distalextension of cantilevered prostheses. With the use of2-dimensional FEA, Lewinstein et al32 compared theIL support system with a conventional cantilever pros-thesis. They concluded that the former dramaticallylowered the stresses in the bone, cantilever, andimplants and thereby potentially reduced failures with-in the implants, prosthesis, and surrounding bone.The system also makes possible the employment of arelatively long-span prosthetic extension in the poste-rior region of the jaw.

In summary, stress distribution in implant-supportedfixed prostheses has been shown by FEA to be influ-enced in various ways by implant inclination, implantnumber and position, the prosthetic splinting scheme,superstructure material properties, and beam design.

Implant-supported overdentures

The use of implant-supported overdentures isviewed as a cost-effective treatment modality. Someclinicians believe that the designed stress-breaking fea-tures of overdenture attachments confer morefavorable biomechanical characteristics compared withimplant-supported fixed prostheses. Implant-support-ed overdenture attachment systems include bar-clips,balls, O-rings, and magnets. The biomechanical factorsrelated to bar-clip attachment systems include thenumber of implants, bar length, stiffener height, andmaterial properties.

Meijer et al93 set up a 3-dimensional model of ahuman mandible with 2 endosseous implants in theinterforaminal region and compared stress distributionwhen the 2 implants were connected by a bar orremained solitary. The most extreme principal stresswas found with oblique occlusal loads, whereas verti-cal occlusal loads resulted in the lowest stress. Themost extreme principal stresses in bone were alwayslocated around the necks of the implants. No signifi-cant differences in stress distribution were predictedwith the highest maximum and lowest minimum prin-cipal stresses being 7.4 and –16.2 MPa in the modelwithout the bar and 6.5 and –16.5 MPa in the modelwith the bar. The same authors also found that a barplaced anterior to the interconnecting line betweenthe 2 implants caused extremely large compressive andtensile stress concentrations in the bone around theimplants. Therefore, in such situations, they advise notconnecting the implants or, if a bar-clip attachment ispreferred, placing additional implants in the frontalregion.94

In a later article, Meijer et al95 used the same modelto study a 4-implant system with the implants eitherconnected by a bar or remaining solitary. The resultsshowed that with uniform loading, there were more orless equal extreme principal stresses around the centraland lateral implants; with nonuniform loading of the


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superstructure, the implant nearest the load showedthe highest stress concentration. With connectedimplants, there was a reduction in the magnitude ofthe extreme principal stresses compared with solitaryimplants.

In the range of alloy stiffness tested, FEA modellingof a 2-implant round bar96 and Hader bar system97 aswell as a 4-implant Hader bar system98 found spanlength and stiffener height to be more significant fac-tors in the adequacy of the overall design thanchanging material properties.

Overdentures supported by a 2-implant ball systemhave been shown to result in better stress distributionin bone than a 2-implant bar system. Menicucci et al99

used 3-dimensional FEA to evaluate transmission ofmasticatory load in mandibular implant-retained over-dentures. Overdentures retained either by 2 ballattachments or by 2 clips on a bar connecting 2implants were compared. For the ball attachment sys-tem, a 35 N load on the first mandibular molar of theoverdenture induced a greater reaction force on thedistal edentulous ridge mucosa of the nonworking sidethan the bar-clip attachment. However, when peri-implant bone stress was considered, such stress wasgreater with the bar-clip attachment than with the ballattachment.

In summary, FEA has been used to investigate thestress distribution obtained when implants are left soli-tary, used with ball attachments, or connected by barsfor clip retention in various configurations anddesigns. Not all studies modelled the overdenture overthe implants and bar superstructure. Bar design factorslike stiffener height and span length were found to sig-nificantly affect stress distribution, whereas theinfluence of various material moduli was comparative-ly less significant.

Combined natural tooth and implant-supported prostheses

Combining natural teeth and implants to supportfixed prostheses has been advocated by certain investi-gators of implant dentistry. Controversy exists as to theadvisability of this design philosophy from a biome-chanical as well as a clinical perspective. A significantclinical consideration in the restoration of partial eden-tulism with implant- and tooth-supported prosthesesis whether implants and natural teeth abutmentsshould be splinted, and if so, in what manner. There isa differential deflection between the viscoelastic intru-sion of a natural tooth in its periodontal ligament andthe almost negligible elastic deformation of anosseointegrated implant. This difference may induce afulcrum-like effect and possibly overstress the implantor surrounding bone. Some factors that biomechani-cally influence the stress distribution include abutmentdesign, implant material properties, the effect of

resilient elements, connector design (precision orsemiprecision attachments), and the degree of splint-ing implants to natural tooth abutments.

For the implant connected with a natural tooth, van Rossen et al100 concluded that a more uniformstress was obtained around implants with stress-absorbing elements of low elastic modulus. They alsoconcluded that the bone surrounding the naturaltooth showed a decrease in peak stresses in such a sit-uation.

el Charkawi et al101 studied the use of a resilientlayer material under the superstructure of the implantin a connected tooth- and implant-supported prosthe-sis model. Their FEA proposed that this newmodification could mimic the structural natural toothunit by allowing movement of the superstructure with-out movement of the implant when the model wasloaded.

Misch and Ismail102 conducted a 3-dimensionalFEA comparing models representing a natural toothand an integrated implant connected by rigid and non-rigid connectors. On the basis of the similarities instress contour patterns and the stress values generatedin both models, the authors concluded that it may beerroneous to advocate a nonrigid connection becauseof a biomechanical advantage. Melo et al103 also inves-tigated tooth- and implant-supported prostheses infree-end partially edentulous situations. Their 2-dimensional FEA predicted that lowest levels of stressin bone occurred when the prosthesis was not con-nected to a natural abutment tooth but instead wassupported by 2 freestanding implant abutments.Nonrigid attachments, when incorporated into a pros-thesis, did not significantly reduce the level of stress inbone. A recent comprehensive review of both clinicaland laboratory studies concluded that the issue of con-necting natural teeth to implants with rigid ornonrigid connectors remains unresolved.104

CONCLUSIONS

FEA has been used extensively in the prediction ofbiomechanical performance of dental implant systems.This article reviewed the use of FEA in relation to thebone–implant interface, the implant–prosthesis con-nection, and multiple-implant prostheses. Assumptionsmade in the use of FEA in implant dentistry have to betaken into account when interpreting the results.

In modelling, some assumptions greatly affect thepredictive accuracy of the FEA model. These includeassumptions involving model geometry, material prop-erties, applied boundary conditions, and thebone–implant interface. To achieve more realistic mod-els, advanced digital imaging techniques can be used tomodel bone geometry in greater detail; the anisotropicand nonhomogenous nature of the material needs to beconsidered; and boundary conditions must be refined.



In addition, modelling of the bone–implant interfaceshould incorporate the actual osseointegration contactarea in cortical bone as well as the detailed 3-dimensional trabecular bone contact pattern.

Load transmission and resultant stress distributionat the bone–implant interface have been the subject ofFEA studies. Factors that influence load transfer at thebone–implant interface include the type of loading,implant and prosthesis material properties, implantlength and diameter, implant shape, structure of theimplant surface, nature of the bone–implant interface,and the quality and quantity of the surrounding bone.Of these biomechanical factors, implant length, diam-eter, and shape can be modified easily in the implantdesign. Cortical and cancellous bone quality and quan-tity need to be assessed clinically and should influenceimplant selection.

Stress distribution in the implant–prosthesis con-nection has been examined by FEA studies because ofthe incidence of clinical problems such as gold andabutment screw failures and implant fracture. Designchanges to avoid or reduce these prosthetic failures byimproving the stress distribution of implant compo-nents have been suggested.

When applied to multiple-implant prosthesisdesign, FEA has suggested improved biomechanicalsituations when factors such as implant inclination,implant position, prosthetic material properties, super-structure beam design, cantilever length, bar system,bar span length and stiffener height, and overdentureattachment type are optimized. For combined naturaltooth and implant-supported prostheses, FEA studieshave not determined conclusively whether rigid orresilient implant systems should be used.

FEA is an effective computational tool that has beenadapted from the engineering arena to dental implantbiomechanics. With FEA, many design feature opti-mizations have been predicted and will be applied topotential new implant systems in the future.

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77. Jorneus L, Jemt T, Carlsson L. Loads and designs of screw joints for sin-gle crowns supported by osseointegrated implants. Int J Oral MaxillofacImplants 1992;7:353-9.

78. Haack JE, Sakaguich RL, Sun T, Coffey JP. Elongation and preload stressin dental implant abutment screws. Int J Oral Maxillofac Implants1995;10:529-36.

79. Versluis A, Korioth TW, Cardoso AC. Numerical analysis of a dentalimplant system preloaded with a washer. Int J Oral Maxillofac Implants1999;14:337-41.

80. Tan KBC. The clinical significance of distortion in implant prosthodon-tics: is there such a thing as passive fit? Ann Acad Med Singapore1995;24:138-57.

81. Cheong WM. FEA of the Nobel Biocare standard abutment during pre-load and applied axial loads. [BEng Thesis.] Singapore: NationalUniversity of Singapore; 2000.

82. Holmes DC, Haganman CR, Aquilino SA. Deflection of superstructureand stress concentrations in the IMZ implant system. Int J Prosthodont1994;7:239-46.

83. Holmes DC, Grigsby WR, Goel VK, Keller JC. Comparison of stress trans-mission in the IMZ implant system with polyoxymethylene or titaniumintramobile element: a finite element stress analysis. Int J Oral MaxillofacImplants 1992;7:450-8.

84. Papavasiliou G, Tripodakis AP, Kamposiora P, Strub JR, Bayne SC. Finiteelement analysis of ceramic abutment-restoration combinations forosseointegrated implants. Int J Prosthodont 1996;9:254-60.

85. Holmes DC, Haganman CR, Aquilino SA, Diaz-Arnold AM, StanfordCM. Finite element stress analysis of IMZ abutment designs: develop-ment of a model. J Prosthodont 1997;6:31-6.

86. Haganman CR, Holmes DC, Aquilino SA, Diaz-Arnold AM, StanfordCM. Deflection and stress distribution in three different IMZ abutmentdesigns. J Prosthodont 1997;6:110-21.

87. Canay S, Hersek N, Akpinar I, Asik Z. Comparison of stress distributionaround vertical and angled implants with finite-element analysis.Quintessence Int 1996;27:591-8.



88. Kregzde M. A method of selecting the best implant prosthesis designoption using three-dimensional finite element analysis. Int J OralMaxillofac Implants 1993;8:662-73.

89. Korioth TW, Johann AR. Influence of mandibular superstructure shapeon implant stresses during simulated posterior biting. J Prosthet Dent1999;82:67-72.

90. Young FA, Williams KR, Draughn R, Strohaver R. Design of prostheticcantilever bridgework supported by osseointegrated implants using thefinite element method. Dent Mater 1998;14:37-43.

91. Sertgöz A, Güvener S. Finite element analysis of the effect of cantileverand implant length on stress distribution in an implant-supported fixedprosthesis. J Prosthet Dent 1996;76:165-9.

92. Lindquist LW, Carlsson GE, Jemt T. A prospective 15-year follow-upstudy of mandibular fixed prostheses supported by ossointegratedimplants. Clinical results and marginal bone loss. Clin Oral Implants Res1996;7:329-36.

93. Meijer HJ, Starmans FJ, Steen WH, Bosman F. A three-dimensional,finite-element analysis of bone around dental implants in an edentuloushuman mandible. Arch Oral Biol 1993;38:491-6.

94. Meijer HJ, Starmans FJ, Steen WH, Bosman F. Location of implants in theinterforaminal region of the mandible and the consequences for thedesign of the superstructure. J Oral Rehabil 1994;21:47-56.

95. Meijer HJ, Starmans FJ, Steen WH, Bosman F. Loading conditions ofendosseous implants in an edentulous human mandible: a three-dimen-sional, finite-element study. J Oral Rehabil 1996;23:757-63.

96. Bidez MW, Chen Y, McLoughlin SW, English CE. Finite element analysis(FEA) studies in 2.5-mm round bar design: the effects of bar length andmaterial composition on bar failure. J Oral Implantol 1992;18:122-8.

97. Bidez MW, McLoughlin SW, Chen Y, English CE. Finite element analysisof two-abutment Hader bar designs. Implant Dent 1993;2:107-14.

98. Bidez MW, Chen Y, McLoughlin SW, English CE. Finite element analysisof four-abutment Hader bar designs. Implant Dent 1993;2:171-6.

99. Menicucci G, Lorenzetti M, Pera P, Preti G. Mandibular implant-retained

overdenture: finite element analysis of two anchorage systems. Int J OralMaxillofac Implants 1998;13:369-76.

100. van Rossen IP, Braak LH, de Putter C, de Groot K. Stress-absorbing ele-ments in dental implants. J Prosthet Dent 1990;64:198-205.

101. el Charkawi HG, el Wakad MT, Naser ME. Modification of osseointe-grated implants for distal-extension prostheses. J Prosthet Dent1990;64:469-72.

102. Misch CM, Ismail YH. Finite element stress analysis of tooth-to-implantfixed partial denture designs. J Prosthodont 1993;2:83-92.

103. Melo C, Matsushita Y, Koyano K, Hirowatari H, Suetsugu T.Comparative stress analyses of fixed free-end osseointegrated prosthesesusing the finite element method. J Oral Implantol 1995;21:290-4.

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Reprint requests to:DR KESON B. C. TAN

DEPARTMENT OF RESTORATIVE DENTISTRY

FACULTY OF DENTISTRY

NATIONAL UNIVERSITY OF SINGAPORE

119074 SINGAPOREFAX: (65) 773-2603E-MAIL: [email protected]

Copyright © 2001 by The Editorial Council of The Journal of ProstheticDentistry.

0022-3913/2001/$35.00 + 0. 10/1/115251

doi:10.1067/mpr.2001.115251

New product news

The January and July issues of the Journal carry information regarding new products of inter-est to prosthodontists. Product information should be sent 1 month prior to ad closing date to:Dr. Glen P. McGivney, Editor, UNC School of Dentistry, 414C Brauer Hall, CB #7450, ChapelHill, NC 27599-7450. Product information may be accepted in whole or in part at the discretionof the Editor and is subject to editing. A black-and-white glossy photo may be submitted toaccompany product information.

Information and products reported are based on information provided by the manufacturer.No endorsement is intended or implied by the Editorial Council of The Journal of ProstheticDentistry, the editor, or the publisher.


11.3Anexo(3)

Element Reference

Contains proprietary and confidential information of ANSYS, Inc.

and its subsidiaries and affiliates

Page: 1

SOLID187

3-D 10-Node Tetrahedral Structural SolidMP ME ST PR PRN DS DSS <> <> <> <> PP VT EME MFS

Product Restrictions

SOLID187 Element Description

SOLID187 element is a higher order 3-D, 10-node element. SOLID187 has a quadratic displacement behavior and is well suited to modeling irregular meshes

(such as those produced from various CAD/CAM systems).

The element is defined by 10 nodes having three degrees of freedom at each node: translations in the nodal x, y, and z directions. The element has plasticity,

hyperelasticity, creep, stress stiffening, large deflection, and large strain

capabilities. It also has mixed formulation capability for simulating deformations of nearly incompressible elastoplastic materials, and fully incompressible

hyperelastic materials. See SOLID187 in the Theory Reference for the Mechanical APDL and Mechanical Applications for more details about this element.

Figure 187.1 SOLID187 Geometry

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SOLID187 Input Data

The geometry, node locations, and the coordinate system for this element are

shown in Figure 187.1.

In addition to the nodes, the element input data includes the orthotropic or

anisotropic material properties. Orthotropic and anisotropic material directions

correspond to the element coordinate directions. The element coordinate system orientation is as described in Linear Material Properties.

Element loads are described in Node and Element Loads. Pressures may be

input as surface loads on the element faces as shown by the circled numbers on Figure 187.1. Positive pressures act into the element. Temperatures may be

input as element body loads at the nodes. The node I temperature T(I) defaults

to TUNIF. If all other temperatures are unspecified, they default to T(I). If all corner node temperatures are specified, each midside node temperature

defaults to the average temperature of its adjacent corner nodes. For any other

input temperature pattern, unspecified temperatures default to TUNIF.

As described in Coordinate Systems, you can use ESYS to orient the material

properties and strain/stress output. Use RSYS to choose output that follows

the material coordinate system or the global coordinate system. For the case of hyperelastic materials, the output of stress and strain is always with respect to

the global Cartesian coordinate system rather than following the

material/element coordinate system.

KEYOPT(6) = 1 or 2 sets the element for using mixed formulation. For details

on the use of mixed formulation, see Applications of Mixed u-P Formulations in

the Element Reference.

You can apply an initial stress state to this element via the INISTATE

command. For more information, see the INISTATE command, and also

Initial Stress Loading in the Basic Analysis Guide.

The effects of pressure load stiffness are automatically included for this element.

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If an unsymmetric matrix is needed for pressure load stiffness effects, use

NROPT,UNSYM.

The next table summarizes the element input. Element Input gives a general

description of element input.

SOLID187 Input Summary

Nodes

I, J, K, L, M, N, O, P, Q, RDegrees of Freedom

UX, UY, UZ

Real ConstantsNone

Material Properties

EX, EY, EZ, ALPX, ALPY, ALPZ (or CTEX, CTEY, CTEZ or THSX, THSY, THSZ),

PRXY, PRYZ, PRXZ (or NUXY, NUYZ, NUXZ),

DENS, GXY, GYZ, GXZ, DAMP

Surface Loads

Pressures --

face 1 (J-I-K), face 2 (I-J-L), face 3 (J-K-L), face 4 (K-I-L)

Body Loads

Temperatures --

T(I), T(J), T(K), T(L), T(M), T(N), T(O), T(P), T(Q), T(R)Body force densities --

The element values in the global X, Y, and Z directions.

Special Features

Plasticity (PLASTIC, BISO, MISO, NLISO, BKIN, MKIN, KINH, CHABOCHE, HILL)

Hyperelasticity (AHYPER, HYPER, BB, CDM)

Viscoelasticity (PRONY, SHIFT)

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Viscoplasticity/Creep (CREEP, RATE)

Elasticity (ELASTIC, ANEL)

Other material (USER, SDAMP, SMA, CAST, EDP, GURSON)

Stress stiffening

Large deflection

Large strain

Initial state

Nonlinear stabilization

Automatic selection of element technology

Birth and death

Linear perturbation

Note: Items in parentheses refer to data tables associated

with the TB command. See "Structures with Material Nonlinearities" in the Theory Reference for the Mechanical APDL and Mechanical Applications for details of the material models.

Note: See Automatic Selection of Element Technologies

and ETCONTROL for more information on selection of element technologies.

KEYOPT(6)

Element formulation:

0 -- Use pure displacement formulation (default)

1 --

Use mixed formulation, hydrostatic pressure is constant in an element (recommended for hyperelastic materials)

2 --

Use mixed formulation, hydrostatic pressure is interpolated linearly in an element (recommended for nearly incompressible

elastoplastic materials)

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SOLID187 Output Data

The solution output associated with the element is in two forms:

Nodal displacements included in the overall nodal solutionAdditional element output as shown in Table 187.1: SOLID187

Element Output Definitions

Several items are illustrated in Figure 187.2. The element stress directions are

parallel to the element coordinate system. The surface stress outputs are in the surface coordinate system and are available for any face (KEYOPT(6)). The

coordinate system for face JIK is shown in Figure 187.2. The other surface

coordinate systems follow similar orientations as indicated by the pressure face node description. Surface stress printout is valid only if the conditions described

in Element Solution are met. A general description of solution output is given in

The Item and Sequence Number Table. See the Basic Analysis Guide for ways to view results.

Figure 187.2 SOLID187 Stress Output

The Element Output Definitions table uses the following notation:

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A colon (:) in the Name column indicates that the item can be accessed by the

Component Name method (ETABLE, ESOL). The O column indicates the

availability of the items in the file Jobname.OUT. The R column indicates the

availability of the items in the results file.

In either the O or R columns, “Y” indicates that the item is always available, a number refers to a table footnote that describes when the item is conditionally available, and “-” indicates that the item is not available.

Table 187.1 SOLID187 Element Output Definitions

Name Definition O R

EL Element Number - Y

NODES Nodes - I, J, K, L - Y

MAT Material number - Y

VOLU: Volume - Y

XC, YC, ZC Location where results are reported Y 3

PRES Pressures P1 at nodes J, I, K; P2 at I, J, L; P3 at J, K, L; P4 at K, I, L

- Y

TEMP Temperatures T(I), T(J), T(K), T(L) - Y

S:X, Y, Z, XY, YZ, XZ Stresses Y Y

S:1, 2, 3 Principal stresses - Y

S:INT Stress intensity - Y

S:EQV Equivalent stress - Y

EPEL:X, Y, Z, XY, YZ,

XZ

Elastic strains Y Y

EPEL:EQV Equivalent elastic strains [6] - Y

EPTH:X, Y, Z, XY, YZ, Thermal strains 1 1

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XZ

EPTH: EQV Equivalent thermal strains [6] 1 1

EPPL:X, Y, Z, XY, YZ,

XZ

Plastic strains [7] 1 1

EPPL:EQV Equivalent plastic strains [6] 1 1

EPCR:X, Y, Z, XY, YZ, XZ

Creep strains 1 1

EPCR:EQV Equivalent creep strains [6] 1 1

EPTO:X, Y, Z, XY, YZ,

XZ

Total mechanical strains (EPEL + EPPL +

EPCR)

Y -

EPTO:EQV Total equivalent mechanical strains (EPEL

+ EPPL + EPCR)

Y -

NL:EPEQ Accumulated equivalent plastic strain 1 1

NL:CREQ Accumulated equivalent creep strain 1 1

NL:SRAT Plastic yielding (1 = actively yielding, 0 = not yielding)

1 1

NL:HPRES Hydrostatic pressure 1 1

SEND: ELASTIC,

PLASTIC, CREEP

Strain energy density - 1

LOCI:X, Y, Z Integration point locations - 4

SVAR:1, 2, ... , N State variables - 5

1. Nonlinear solution, output only if the element has a nonlinear material2. Output only if element has a thermal load

3. Available only at centroid as a *GET item.

4. Available only if OUTRES,LOCI is used.5. Available only if the USERMAT subroutine and TB,STATE are used.

6. The equivalent strains use an effective Poisson's ratio: for elastic and

thermal this value is set by the user (MP,PRXY); for plastic and creep this value is set at 0.5.

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this value is set at 0.5.

7. For the shape memory alloy material model, transformation strains are reported as plasticity strain EPPL.

Table 187.2: SOLID187 Item and Sequence Numbers lists output available

through ETABLE using the Sequence Number method. See The General

Postprocessor (POST1) in the Basic Analysis Guide and The Item and Sequence Number Table in this manual for more information. The following

notation is used in Table 187.2: SOLID187 Item and Sequence Numbers:

Name

output quantity as defined in Table 187.1: SOLID187 Element Output Definitions

Item

predetermined Item label for ETABLE commandI,J,...,R

sequence number for data at nodes I, J, ..., R

Table 187.2 SOLID187 Item and Sequence Numbers

Output Quantity NameETABLE and ESOL Command Input

Item I J K L M,...,R

P1 SMISC 2 1 3 - -

P2 SMISC 4 5 - 6 -

P3 SMISC - 7 8 9 -

P4 SMISC 11 - 10 12 -

See Surface Solution in this manual for the item and sequence numbers for

surface output for ETABLE.

SOLID187 Assumptions and Restrictions

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Page: 9

The element must not have a zero volume.Elements may be numbered either as shown in Figure 187.1 or may

have node L below the I, J, K plane.

An edge with a removed midside node implies that the displacement varies linearly, rather than parabolically, along that edge. See

Quadratic Elements (Midside Nodes) in the Modeling and Meshing Guide for information about using midside nodes.When mixed formulation is used (KEYOPT(6) = 1 or 2), no midside

nodes can be missed.

If you use the mixed formulation (KEYOPT(6) = 1 or 2), the damped eigensolver is not supported. You must use the sparse solver (default).

Stress stiffening is always included in geometrically nonlinear analyses

(NLGEOM,ON). Prestress effects can be activated by the PSTRES command.

SOLID187 Product Restrictions

When used in the product(s) listed below, the stated product-specific

restrictions apply to this element in addition to the general assumptions and

restrictions given in the previous section.

ANSYS Professional.

The only special feature allowed is stress stiffening.

Release 13.0 - © 2010 SAS IP, Inc. All rights reserved.

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