ilizarov sa kompozitnim prstenom

11

Advanced textile composite ring for Ilizarov external� xator system

K P Baidya1, S Ramakrishna1, M Rahman1 and A Ritchie2*1Department of Mechanical and Production Engineering, National University of Singapore, Singapore2Department of Mechanical and Production Engineering, Nanyang Technological University, Singapore

Abstract: The use of a radiolucent composite material permits easier and more accurate radiographicevaluation of the bone healing process, and results in a much lighter system. The � nite elementmethod (FEM) is employed to determine the worst possible in-service loading condition and the ringdimensions are modi� ed accordingly. Half-ring prototypes are produced using two types of compositematerials: knitted aramid � bre fabric reinforced epoxy and random short carbon (RSC) � brereinforced epoxy. The in-plane compressive strength and axial stiVness of the complete frame aretested according to ASTM speci� cations. The performance is evaluated, and compared with anexisting system in simulated in-service conditions.

Keywords: Ilizarov external � xator, composite material, in-plane compressive strength, axial stiVness

NOTATION ing or a plaster cast) would prove insuYcient. TheIlizarov system is also used in limb lengthening and inthe correction of congenital and pathological ortho-E Young’s moduluspaedic deformities. Limb correction is a gradual process,F

z,aaxial component of wire tension in wire a

which lengthens and realigns the bone to restore normalI second moment of area of cross-sectionfunction [1–4 ]. The Ilizarov apparatus (Fig. 1) consistst thickness of ring (axial dimension)of a number of standardized interchangeable compo-Ta component of wire tension in wire a innents that can be assembled in various con� gurations,the plane of the ringdepending on the application [4, 5 ]. The bone fragmentsw width of ring (radial dimension)are held in position by tensioned 1.5 or 1.8 mm diameterW weight of patienttrans� xation wires (Kirschner or K-wires). The K-wires

åa, åb

, åcstrains measured from 0–45–90 ß strain are tensioned to 500–1300 N, giving the system its stiV-gauge rosette ness. The wires are typically secured to circular rings,

î Poisson’s ratio which in turn are connected to one another by threadedô shear stress vertical support rods. When necessary, olive or stop

wires are used in conjunction with smooth Kirschnerwires to restrict movement of the bone fragments. A

Subscripts variety of hinges, telescopic rods and specialized compo-nents may also be incorporated into the system. Thecomp compositerings are a vital part of the system, and the diameter ofss stainless steelthe ring, and the distance between the rings, has a majorin� uence on the stiVness of the system. Gasser et al. [6 ]showed a 250 per cent increase in axial compression1 INTRODUCTIONstiVness for a complete frame assembly when the ringradius was decreased from 16 to 6.25 cm. It is thoughtExternal � xators are used in the treatment of fracturesthat some micromotion at the fracture site may be ben-where conservative reduction and treatment (e.g. splint-e� cial to bone healing [7 ], and emphasizes one advan-tage of the Ilizarov system—that the stiVness of theThe MS was received on 1 October 1999 and was accepted after revision

for publication on 20 April 2000. system can be ‘tailored’ to the patient. Most commercial* Corresponding author: Department of Mechanical and Production Ilizarov external � xator components are made fromEngineering, Nanyang Technological University, North Spine (N3),Level 2, 50 Nanyang Avenue, Singapore 639798. stainless steel, titanium, or aluminium, which are radio-

H05399 © IMechE 2001 Proc Instn Mech Engrs Vol 215 Part H

12 K P BAIDYA, S RAMAKRISHNA, M RAHMAN AND A RITCHIE

Fig. 1 Schematic diagram of the Ilizarov system

opaque (Fig. 2). The metal components of the system necessary to use a larger cross-section, due to the reducedmay obscure the fracture site, hindering evaluation of Young’s modulus of the composite material. However,the healing progress. the overall weight of the system will be reduced due to

The principal objective of this work was to design a the lower density of the � bre reinforced composite mate-radiolucent ring using composite materials that would rial. Two composite systems, knitted Kevlar reinforcedreplace the existing metal rings satisfactorily. In order epoxy and random short chopped carbon � breto achieve the required stiVness in the ring, it will be reinforced epoxy are examined in this study. When com-

pared with other conventional textile fabrics, knittedfabrics are easy to produce and of lower cost. Inaddition, knitted fabrics are highly extensible [8 ], whichallows them to be formed into complex shapes. Randomshort carbon � bre also has similar advantages. Two fun-damental interrelated considerations for external � xatorsystems are stability and rigidity [9 ]. These were assessedin mechanical tests, and the radiolucency of the designwas assessed by radiography. This study focused onthe ring components of the external � xator and theirperformance when used in a complete frame.

2 EXPERIMENTAL INVESTIGATION

The design and the � nite element (FE) model were veri-� ed experimentally. It was also necessary to determinethe mechanical properties of the composites, which wereused to produce the ring prototypes. The ring prototypeswere tested to evaluate compressive strength and stiV-ness. Two diVerent reinforcements, knitted Kevlar-29,and random short carbon (T-300, with a � lament lengthof between 6 and 8 mm) (Fig. 3) were used in an epoxymatrix. The matrix used was a mixture of Chemicrete

Fig. 2 Radiograph of stainless steel frame R-50 resin and H-64 hardener.

H05399 © IMechE 2001Proc Instn Mech Engrs Vol 215 Part H

13ADVANCED TEXTILE COMPOSITE RING FOR ILIZAROV EXTERNAL FIXATOR SYSTEMS

combined with the matrix in the mould, whereas 6–8 mmrandom short carbon (RSC) � bre was mixed with thematrix and poured into the mould. Post-curing of theprototype was necessary at a temperature of 80 ß C for8 h.

2.3 Test for radiolucency

One of the principal criteria in selection of the reinforce-ment for the ring material is radiolucency, as radio-graphic examination of fractures is essential to themanagement of patients. Radiographs of the Kevlarreinforced composite and metallic � xator rings weretaken to provide an indication of radiolucency (Fig. 4).The radiograph shows that composite rings are moreradiolucent than the metal rings. The short choppedcarbon � bre ring (not shown, as it was not visible on theX-ray plate) was almost completely radiolucent givingless shadow than the Kevlar ring. Therefore carbon � brewas shown to be the most suitable reinforcement.

2.4 Mechanical tests

Mechanical tests are necessary to validate the suitabilityof the composite system to clinical application. Since therings carry a large compressive load due to the wiretension it was necessary to test the in-plane compressiveFig. 3 Schematic diagrams of the reinforcements used:strength. Axial compressive stiVness was also checked(a) knitted fabric; (b) random short � bresfor comparison with the metal frame.

2.1 Composite material properties 2.4.1 In-plane compressive test

Determination of the mechanical properties of the com- The in-plane compressive strength for the ring is testedposite materials used was important. Flat panel samples according to the ASTM standard [11 ]. This test methodof the composites were fabricated using a hand lay-up is used to measure the compressive strength and stiVnessmould. Spacers of 1 mm thickness with a distance of of circular ring elements of external � xators, when10 mm between two consecutive spacers were � xed on a loaded in the plane of the ring. This test also providespolypropylene (PP) sheet. Epoxy resin was applied to an indication of the ability of the ring to sustain the highthe reinforcement material and placed between the spa- wire tensions, and the consistency of the product but iscers. Another PP sheet was placed on top of the mould not intended to predict the clinical eYcacy or safety ofand excess resin was squeezed out using roller pressure. the tested product. The test set-up is shown in Fig. 5.The composite was cured at room temperature for 24 h. The test machine is an Instron-8516.The panels were post-cured at a temperature of 80 ß Cfor 8 h, and tested according to ASTM standard 2.4.2 Axial compressive strength of the frameF1746-96 [10 ] to verify the elastic properties used in the

Axial compression is the usual loading mechanism forFEM analysis. The stiVness of the composite materialweight-bearing bones and is the most important modewas also highly dependent on � bre volume fraction.of loading for an Ilizarov � xator in clinical use [12 ].Compressive stiVness and � xation stability may beincreased by the use of more wires, using olive wires,2.2 Prototype manufactureand by decreasing the spacing between rings.

The ring prototype was fabricated using a three-piececompression mould and a hand lay-up technique. The Test procedure. The method used for testing of axial

compressive strength was the proposed ISO-1438resin was subjected to a vacuum during the lay-upprocess to remove gas bubbles. The same matrix International Standard [13 ], which is intended to evalu-

ate the stability of various con� gurations of external(Chemicrete R-50 resin and H-64 hardener) was used forboth reinforcements. Knitted Kevlar reinforcement was � xator devices. In this study, four rings of 200 mm



Fig. 4 Comparative radiograph

diameter are used, with two rings on each side of the 2.5.2 In-plane compressive test resultsfracture gap. The complete assembly was tested in axial

The test results are shown in Fig. 7. This test provides acompression with an MTS-858 Mini Bionix Machine.comparison of the two diVerent reinforcement materials.Perspex tubes of 30 mm outer diameter and 4 mm wallThe results show that the random short carbon (RSC)thickness were used as bone analogues. A gap of 20 mm� bre ring is both stiVer and of higher strength in in-planebetween the fragments was maintained to ensure thatcompressive loading. A summary of the results of thethe entire load is transmitted through the � xator. Thein-plane compressive strength test is given in Table 2.wires were tensioned to 1200 N. Axial load was appliedThe knitted Kevlar ring failed in a progressive or ‘duc-quasi-statically for the external � xator ring assemblytile’ manner, while the RSC ring failed in a brittle(Fig. 6). GFRA-120-type strain gauges were placed atmanner. For both the materials fracture was initiateddiVerent locations on the surface of the topmost ring tonear the hole region. On visual examination of the frac-monitor the strain.ture surfaces and crack direction, defects in the com-posite were observed. It may be concluded that thesedefects contributed to the failure.2.5 Results

2.5.1 Material properties 2.5.3 Axial compression test results

For the assembly test only the RSC ring was used, dueExperimental tests were carried out to characterize thecomposite material used in ring prototype fabrication. to its superior performance. The axial compressive stiV-

ness of a frame using RSC rings was then compared withResults from testing of � at composite panel samples todetermine material properties are shown in Table 1. As a frame using steel rings. The ability of the � xator to

resist axial motion, i.e. motion along the central axisexpected, the material properties were highly dependenton the � bre volume fraction. of the bone, was de� ned as its axial stiVness [14 ]. A



3 FINITE ELEMENT MODELLING

3.1 Introduction

Finite element analysis (FEA) was used to determine theworst-case loading situation that can be expected in clini-cal use. The angulation between crossing wires is animportant factor to be considered while studying theIlizarov system, as it is not always possible to insert thewires so that they intersect at the ideal angle of 90 ß . Theload cases were de� ned in terms of the position of thebone and the angle at which the wires crossed. The angleand point of intersection of the wires are dependent onthe local anatomy, as adequate clearance must be givento blood vessels and nerves. The most critical situationoccurs when the wires are crossing at an eccentric pos-ition as it results in increased stress in the rings [16, 17 ].The guidelines given by Chao and Huiskes [18 ] wereimplemented in the stress analysis of the external� xator ring.

It was decided to use the � nite element method (FEM)as this oVers a means of estimating de� ection as well aspredicting the stress states in the rings. Another reasonfor the use of the FEM was that once the geometricmodel has been set up in the system, the application ofloads and analysis is rapid.

Four diVerent loading cases (Fig. 9) were analysed:(a) bone position at the centre of the ring, wires crossingat right-angles (centre–90); (b) bone position at thecentre of the ring, wires crossing at an acute angle(centre–angle); (c) bone position oVset from centre ofring, wires crossing at right-angles (oVset–90) and(d) bone position oVset from centre of ring, wires cross-Fig. 5 Test set-up for in-plane compressive strength testing at an acute angle (oVset–angle). Each load case wasanalysed for three commonly used ring radii (ring radiiload–de� ection curve for the axial compression test ofof 40, 70 and 100 mm).a complete frame structure is shown in Fig. 8.

Principal stresses and strains were calculated from the3.1.1 Design modi� cation of the ringstrain gauge measurements according to the standard

relationships for a two-dimensional state of stress (plane The � xator ring was redesigned on the basis of compara-stress) [15 ]. The strain gauges showed that very high tive material properties. The bending stiVness (EI ) valuesstrains were observed near the holes carrying the vertical for rings made from the two diVerent materials must besupport rods. The von Mises stress was found to be as equivalent [19 ]. As a � rst approximation, the compositehigh as 110 MPa and the strain gauges also recorded materials (knitted Kevlar and random short carbonplastic deformation when the system was unloaded. � bres) are assumed to be isotropic, due to the randomTable 3 shows the axial and comparative stiVness of the nature of the � bre orientation. The design must satisfytwo systems tested. Axial compressive stiVness was cal- the requirements that the stress is well below the yieldculated as the force per unit de� ection, and compared limit and that the deformation is less than 1 per cent ofwith the standard stainless steel frame tested. The com- the nominal diameter. Thusparative stiVness was calculated on the basis of the

EIstainless steel

=EIcompositede� ection in the direction of the bone axis, and was

de� ned as for the cross-section I=tw3/12, wherew=width of the ring

Comparative stiffness=force6ring radius

deflectiont=thickness of the ring

which leads toExperimental results for the axial compressive test werein� uenced by the relaxation and slippage of the wires (tw3)ss

(tw3)comp

=Ess

Ecomp

(1)through the bone model and the clamps on the rings.



(a) (b)

Fig. 6 (a) Schematic diagram showing the set-up for axial testing. (b) Position of strain gauges on top ring

Table 1 Experimentally determined mechanical properties for 3.1.2 Geometryknitted Kevlar and random short carbon composite

A pseudo three-dimensional model was generated usingspecimensPATRAN [20 ], an FE analysis software package

Tensile Tensile Fracture (McNeill-Schwendler Corporation). A total of 2592strength modulus strain

four-noded quadrilateral two-dimensional solid elements(MPa) (GPa) (%)were used to create the model. The software checks the

Knitted Kevlar 114 8.79 3.51 model before analysis to ensure element edge angles andShort-chopped carbon 130 9.32 2.46

element faces are within 45–135ß . Three diVerent modelsof ring inner radii 40, 70 and 100 mm were used for eachload case. The stainless steel ring to be replaced has across-sectional width of 14 mm and a thickness of 4 mm.This analysis was used to give a starting point in the

design of the composite ring. FE analysis was then used 3.1.3 Boundary conditionsto validate the design, using experimentally determinedmechanical properties of the composite materials. The In an Ilizarov external � xator the rings are connected

using vertical supporting rods and other components toFEA showed that the highest stresses occurred in theregion of the holes. A machined (drilled) hole would build a cage-like frame. Typically, three or four crossed

Kirschner wires of 1.5 or 1.8 mm diameter connect theserve to weaken the ring in this area, so the mould wasdesigned to produce a ring with holes, rather than a frame to each bone end. There should be no motion

of the frame in the direction of the bone axis whenpreformed ring into which holes would have to bedrilled. the system is in use. The Z axis is de� ned to be the



Fig. 7 Results of in-plane compressive test

Table 2 Summary of results of in-plane compressive tests Therefore the component of the tensile force in thez direction (parallel to the axis of the bone) is calculated

Knittedaccording to the relationShort-chopped Kevlar

In-plane properties carbon � bre � bre

Fz,a=

Taån

1T

nA3W

2 BCompressive stiVness (N/mm) 96.34 36.477Compressive yield strength (N) 1135 560Maximum compressive strength (N) 1426 560

wheren=the number of wires carrying the total loadT

a=pre-tension in the wire aperpendicular to the plane of the ring (the x–y plane).

W=body weight (N) of the patientIn the model, movement in the z (axial ) direction wasconstrained at the vertical support points. No rotational

In a typical Ilizarov con� guration, the load is trans-constraints were imposed on the movement of themitted from the bone to the frame by four K-wires. Thesupporting sections.wire tensions were incorporated into the model asvectors, with a radial component of 785 N and an axial3.1.4 Loadscomponent of 85.8 N.

Tensions on the wires in the model were in accordance In practice, equal wire tensions are achieved bywith the guidelines for surgeons given by Golyakhovsky tensioning the wires simultaneously using two wireand Frankel [21 ]. The wire tension in the model was tensioners [21 ].120 kg (1177 N). According to the biomechanical calcu-lations of Pauwels [22 ], the compressive force carried by 3.1.5 Material propertiesthe femur is three times the body weight, and in thisstudy a body weight of 70 kg was used. For the purposes The most commonly used materials for Ilizarov external

� xators are stainless steel and aluminium. Standardof the model, it is assumed that the axial displacementsdue to the weight force are equal for all wires, and that values for the mechanical properties of stainless steel

(E=210 GPa, î=0.31) were used [23 ] for the ring mate-the vertical component of the tensile force is pro-portional to the radial pre-tension and the axial tension. rial in the FE model. The material properties used in the



Fig. 8 Comparative axial compressive stiVness

Table 3 Summary of results of axial compressive tests Mises stress (Fig. 12 ) in the 100 mm radius ring wasfound to be 460 MPa while for the 40 mm ring it was

Axialonly 171 MPa. The ring size also has a signi� cant eVectWeight stiVness Comparative

Radiolucency (g) (N/mm) stiVness on overall stiVness of the system, as is clear from Fig. 6.The classical curved beam theory [24 ] and stress con-

Stainless steel No 105 60.92 3674.56centration tables [25 ] were used to verify the results ofShort-chopped

carbon Yes 70 39.91 2545.65 the FE modelling for the 70 mm radius ring with thewires crossing at an angle of 90 ß at the centre. Curvedbeam theory predicts a bending moment of 9.88 N mat the supports, and the stress concentration tables pre-analysis of the composite system were determineddict a nominal stress of 46.7 MPa and a maximum stressexperimentally.of 93.6 MPa. The FE modelling predicts a stress band

3.1.6 Analysis of 88.6–101 MPa at the corresponding position (óõõ , thestress tangential to the hole,=óvm, the von Mises equiv-

The stresses in the system are assessed using the von alent stress at this position as the radial stress at theMises equivalent stress, calculated according to the yield

surface is zero).criterion at the surface (where plane stress conditions

High stresses are to be expected with an eccentricwill exist).

bone position, where the wires crossing at an acuteangle apply uneven forces to the rings. The modelshows expected high levels of stresses in the Ilizarov3.2 Resultsring, and localized yielding may occur at sites of highstress. Larger ring radii result in higher stress con-Both ABAQUS/Post (HKS Inc.) and PATRAN wereditions, which can cause large deformations. From theused for the stress analysis. Figures 10 and 11 show con-results it may be concluded that the worst-case loadtour plots of the stresses in the Ilizarov ring. The resultsoccurs when the bone is at an eccentric position andshow a high stress concentration around the holes adjac-the wires are crossing at an acute angle. This worst-ent to the oVset carrying the wire. Stresses were found

to increase with increasing ring radius. The highest von case load was used in the design calculations. The



Fig. 9 The diVerent load cases analysed: (a) centre, crossing at 90ß ; (b) centre, crossing at an acute angle;(c) oVset, crossing at 90ß ; (d) oVset, crossing at an acute angle

thickness and width of the ring had to be increased to rings of varying diameter, as the value is independent of7 and 22 mm from the original values of 4 and 14 mm the ring diameter.respectively, to suit the design requirement. The strain gauge results were found to agree with

the FE model in the case of the steel ring, as can beseen from Table 4. However, the results for the carbon� bre reinforced epoxy ring were rather too high,re� ecting a higher than expected strain. This may be4 DISCUSSION AND CONCLUSIONSexplained by the use of the material propertiesobtained from the testing of � at specimens, as theThe FE model was employed to determine the worstsame � bre volume fractions were not obtained inpossible loading case, and to redesign the ring to con� rmmanufacture of the ring prototypes. If the propertiesmaterial suitability. The in-plane compressive test pro-for epoxy (E=1.8 GPa and î=0.41) are used to cal-vides the easiest method for comparison of rings madeculate the stress, then ‘lower bound’ von Mises stressesfrom two diVerent materials. The deformation found forof 18.4 MPa at strain gauge 1 and 11.36 at strainthe ring prototype was within the 1 per cent design limitgauge 2 are obtained. The exact value of the stressand the composite material was able to sustain the speci-may be assumed to lie between these two bounds, and� ed load. The improved performance of the shortthe values for the FEM lie closer to the lower bound.random chopped carbon � bre ring may be attributed to

The assembly tests for the � xator show that the ringa higher volume fraction than was achieved in the knittedprototypes produced were marginally less stiV than theKevlar composite, owing to the diYculties encounteredsteel rings. Although the carbon � bre ring is not asin packing the knitted fabric into the mould. The axialstiV as the stainless steel system, it can withstand thestiVness for this system was comparable with the resultloading conditions and the deformation is withinfound by Kummer [9 ]. Comparative stiVness was intro-acceptable limits. The component has a mass of two-duced when two diVerent material systems were com-thirds of its metallic equivalent. The principal advan-pared. Comparative stiVness will allow a better

comparison than compressive stiVness when used for tage of this system lies in its radiolucency.



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(a)

(b)

Fig. 11 Contour plot of von Mises equivalent stresses on FE models of (a) 100 mm radius composite ringand (b) 70 mm radius steel ring

Table 4 Comparison of strain gauge and FEM stress data

Experimental results FEMAxial

Ring type loading Position ó1 (MPa) ó2 (MPa) óvm (MPa) óvm (MPa)

Steel Unloaded 1 19.8 Õ 50.7 63.0 57.1Steel 700 N 1 21.4 Õ 58.8 71.9 73.6Composite 700 N 1 57.8 Õ 48.4 92.1 21.0Composite 700 N 2 14.8 Õ 48.0 56.8 13.6



Fig. 12 Graph showing comparative maximum von Mises stress for ring models studied

Fig. 13 Deformation of rings calculated by FEM for diVerent load cases



Segment Bridge Elements, Annual Book of ASTMACKNOWLEDGEMENTStandards, Vol. 03.01, February 1997 (American Society forTesting and Materials, Philadelphia, Pennsylvania).The authors wish to acknowledge the help provided by

12 Carter, D. R. Biomechanics of bone. In The Biomechanicsthe Clinical Research Centre, National University of Trauma (Eds A. M. Nahum and J. Melvin), 1985, p. 157Hospital, Singapore. (Appleton-Century-Crofts, Norwalk, Connecticut).

13 ISO-1438 Standard Test Method for Determining theStiVness of External Fixator Systems, Draft Standard, 1997(International Standardization Organization).REFERENCES

14 Kummer, F. J. Technical note: evaluation of new Ilizarovrings. Bull. Hosp. Jt Dis. Orthop. Inst., 1990, 50, 88.

1 Ilizarov, G. The Transosseous Osteosynthesis: Theoretical 15 Dally, J. W. and Riley, W. F. Experimental Stress Analysis,and Clinical Aspects of the Regeneration and Growth of 3rd edition, 1991, p. 48 (McGraw-Hill, New York).Tissue, 1992 (Springer-Verlag, Berlin, New York). 16 Podolsoky, A. and Chao, E. Y. S. Biomechanical perform-

2 Frankel, V. H., Gold, S. and Golyakhovsky, V. The Ilizarov ances of Ilizarov external � xators. Trans. Orthop. Res.,technique. Bull. Hosp. Jt Dis. Orthop. Inst., 1988, 48(1), 1990, 15, 416.17–27. 17 Fleming, B., Paley, D., Kristiansen, T. and Pope, M. A

3 Ilizarov, G. The principles of the Ilizarov method. Bull. biomechanical analysis of the Ilizarov external � xator. Clin.Hosp. Jt Dis. Orthop. Inst., 1988, 48 (1), 1–11. Orthop. Related Res., 1989, 241, 95.

4 Green, S. A. Editorial comments. Clin. Orthop. Related 18 Chao, E. S. and Huiskes, R. Guidelines for external � xationRes., 1992, 280, 22–25. frame rigidity and stresses. J. Orthop. Res., 1986, 4, 68–75.

5 Bagnoli, G. The Ilizarov Method, 1990 (B.C. Draker Inc., 19 Rothbart, H. A. Mechanical Design Handbook, 1996Philadelphia, Pennsylvania). (McGraw-Hill, New York).

6 Gasser, B., Boman, B., Wyder, D. and Schneider, E. StiVness 20 Patran User Manual (Macneill-Schwindler Corporation,characterization of the circular Ilizarov device as opposed Los Angeles, California).to conventional external � xators. J. Biomech. Engng, 1990, 21 Golyakhovsky, V. and Frankel, V. H. Operative Manual of112, 15. Ilizarov Techniques, 1993 (Mosby, St Louis, Missouri).

7 Kempson, G. E. and Campbell, D. The comparative stiVness 22 Pauwels, F. Biomechanics of the Locomotor Apparatus,of external � xator frames. Injury, 1981, 12, 297. 1980 (Springer-Verlag, Berlin) (translated from German

8 Powel, P. C. Engineering with Fibre-Polymer Laminates, edition, 1965).1994 (Chapman and Hall, London). 23 Nomine, A. M., Dubois, D., Miannay, D., Balladon, P. and

9 Kummer, F. J. Biomechanics of the Ilizarov external � xator. Hertier, J. Creep and cyclic tension behaviour of a typeClin. Orthop. Related Res., 1992, 280 (7), 11–14. 316L stainless steel at room temperature. In Low-Cycle

10 D3039/D3039M Standard Test Method For Tensile Fatigue and Life Prediction (Eds C. Amzallag, B. N. LeisProperties of Polymer Matrix Composite Materials, Annual and P. Rabbe), 1982 (American Society for Testing andBook of ASTM Standards, Vol. 14.02, October 1995 Materials, Philadelphia, Pennsylvania).(American Society for Testing and Materials, Philadelphia, 24 Ugural, A. C. and Fenster, S. K. Advanced Strength andPennsylvania). Applied Elasticity, 1981 (Edward Arnold, London).

11 ASTM: F1746-96 Standard Test Method for Determining 25 Pilkey, W. D. Formulas for Stress, Strain and StructuralMatrices, 1994 (John Wiley, New York).In-Plane Compressive Properties of Circular Ring or Ring


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