a computational plastic-damage method for modeling the...

Scientia Iranica A (2019) 26(4), 2123{2132

Sharif University of TechnologyScientia Iranica

Transactions A: Civil Engineeringhttp://scientiairanica.sharif.edu

Invited Paper

A computational plastic-damage method for modelingthe FRP strengthening of concrete arches

T. Ahmadpoura;b, Y. Navid Tehrania, and A.R. Khoeia;�

a. Center of Excellence in Structures and Earthquake Engineering, Department of Civil Engineering, Sharif University ofTechnology, Tehran, P.O. Box 11155-9313, Iran.

b. Department of Civil Engineering, School of Science and Engineering, Sharif University of Technology, International Campus,Kish Island, P.O. Box 76417-76655, Iran.

Received 1 February 2019; accepted 11 March 2019

KEYWORDSConcrete arches;FRP retro�tting;Reinforced concrete;Plastic-damage model;Cohesive fracturemodel.

Abstract. In this paper, a computational technique is presented based on a concreteplastic-damage model to investigate the e�ect of FRP strengthening of reinforced concretearches. A plastic-damage model was utilized to capture the behavior of concrete. Theinterface between the FRP and concrete was modeled using a cohesive fracture model. Inorder to validate the accuracy of the damage-plastic model, a single element was employedunder monotonic tension, monotonic compression, and cyclic tension loads. An excellentagreement was observed between the prede�ned strain-stress curve and that obtained by thenumerical model. Furthermore, the accuracy of the cohesive fracture model was investigatedby comparing the numerical results with those of experimental data. Finally, in order toverify the accuracy of the proposed computational algorithm, the results were comparedwith the experimental data obtained through two tests conducted on reinforced concretearches strengthened with FRP.© 2019 Sharif University of Technology. All rights reserved.

1. Introduction

FRP strengthening of concrete is one the most ef-fective retro�tting methods. In fact, a remarkabledevelopment has taken place in retro�tting with theintroduction of FRP materials. The unique featuresof FRP include high durability against environmen-tal degradation factors, high tensile strength, simpleimplementation, low weight, and easy transportation.Hence, a great deal of work has been dedicated to inves-tigating the structural retro�t using the FRP materialsin the last two decades. Most of the studies have been

*. Corresponding author. Tel.: +98 (21) 6600 5818;Fax: +98 (21) 6601 4828E-mail address: [email protected] (A.R. Khoei)

doi: 10.24200/sci.2019.21357

focused on the beams, columns, at slabs, and masonrystructures, while few studies have been performed onthe behavior of FRP strengthening of concrete arches.Since the arch members are utilized in many structuressuch as bridges, uid storage tanks, tunnels, anddomes, study of the methods for retro�tting thesestructures has gained interest, recently.

There are several studies performed on the ma-sonry arches retro�tted with FRP materials thatpresent a signi�cant improvement in structural per-formance [1,2]. The e�ect of FRP strengtheningof concrete arch structures was studied by Chen etal. [3]. They experimentally investigated the responseof concrete arch structures retro�tted by wrappingFRP carbon sheets subjected to explosive impulses.Hamed et al. [4] studied the performance of a re�nedconcrete arch retro�tted with externally bonded com-posite materials, and observed that the maximum load

2124 T. Ahmadpour et al./Scientia Iranica, Transactions A: Civil Engineering 26 (2019) 2123{2132

increased by about 40%. Dagher et al. [5] studied thebending behavior of concrete-�lled tubular FRP archesin bridge structures. To improve the strength, sti�ness,and ductility of reinforced concrete arches, Zhang etal. [6] performed a set of experimental tests to studythe behavior of reinforced concrete arches retro�ttedwith FRP materials.

Characteristics of the concrete plastic behaviorcannot generally be described using the classical theoryof plasticity. Many attempts have been made todemonstrate the behavior of concrete with the classicaltheory of plasticity. Feenstra and de Borst [7] proposedtwo yield criteria to describe the concrete behaviorin tension and compression that showed great agree-ment with experimental data in the biaxial monotonicloading condition. �Cervenka and Papanikolaou [8] pre-sented the three-dimensional combined fracture-plasticmodel for concrete, in which the crack band model wasused together with the smeared crack model to capturethe fracture in tension. Moreover, the behavior ofconcrete in compression was captured by the Menetrey-William failure model, which was capable of simulatingcrushing under high con�nement, cracks in concrete,and closure due to crushing in di�erent directions.Recently, a three-invariant cap plasticity model wasdeveloped by Khoei and Azami [9] and DorMohammadiand Khoei [10] to describe the plastic deformationof granular materials involving the isotropic-kinematichardening and associated plasticity ow rule.

Basically, damage happens in the concrete dueto micro-cracks; in fact, micro-cracks occur because ofthermal expansion at the interface between the cementand aggregate. Several studies have been carried outto model the damage in concrete structures. Ba�zantand O�zbolt [11] proposed a nonlocal micro-plane modelfor the fracture, damage, and size e�ect in concretestructures. Voyiadjis and Abu-Lebdeh [12] presented adamage model based on the bounding surface conceptfor concrete behavior. The combined plastic-damagemodel has been used by researchers to capture the sti�-ness degradation of concrete, in which the damage vari-ables are assumed according to the plastic deformationin a constitutive formulation to calibrate parameterswith experimental data. In the plastic-damage model,the irreversible plastic phenomenon can be modeled us-ing the concept of plasticity in the e�ective stress space,while the sti�ness degradation can be captured usingthe continuum damage mechanics. Lubliner et al. [13]and Yazdani and Schreyer [14] presented a combinedplastic-damage mechanics model for plain concrete.Kattan and Voyiadjis [15,16] proposed a coupled theoryof damage mechanics and �nite strain elasto-plasticity.Lee and Fenves [17] described a plastic-damage modelfor concrete based on the concept of fracture-energyand sti�ness degradation under cyclic loading. Fariaet al. [18] presented a strain-based plastic viscous-

damage model for massive concrete structures. Salariet al. [19] proposed a triaxial constitutive model forelastoplastic behavior of geomaterials that capturedtensile damage. Since the behavior of concrete isdi�erent in tension and compression, di�erent damagemodels are required for each type of loading; however,some studies consider only one damage variable fordi�erent loading conditions [20,21]. On the otherhand, it is important to model the concrete damageusing two separate damage variables for tension andcompression [22,23]. The plastic-damage models havebeen applied based on di�erent damage variables fortension and compression for both brittle and ductilematerials [24-27].

Considering the bene�cial characteristics of FRPmaterials, as well as the ease of implementation of thesematerials in architectural elements, an investigationinto the behavior of reinforced concrete arch struc-tures strengthened with FRP materials is worthwhile.To this end, both the experimental and numericalinvestigations are required to obtain the behavior ofFRP strengthening in concrete arch structures. In thisstudy, a computational technique is presented basedon the plastic-damage model to investigate the e�ectof FRP strengthening on concrete arches. A plastic-damage model is utilized to capture the behavior ofconcrete. The interface between the FRP and concreteis modeled using a cohesive fracture model. To validatethe accuracy of the concrete model, a single elementis considered and subjected to monotonic tension,monotonic compression, and cyclic tension loads. Goodagreement is observed between the prede�ned strain-stress curve and the strain-stress curve obtained bythe numerical analysis. Furthermore, the accuracyof the interface model is investigated by comparingthe results with the experimental data. In orderto verify the computational model of the arch, theexperimental data of two tests conducted on concretearches strengthened with FRP are utilized.

2. Plastic-damage model for concrete

In this study, the plastic-damage model originallyproposed by Lubliner et al. [13] and Lee and Fenves [17]and then, employed by Nguyen et al. [21,22] is em-ployed, in which the plastic-damage model is developedon the basis of the thermo-dynamical approach. Thestrain tensor " is decomposed into the elastic part "eand the plastic part "p, in which the relation betweenstress and strain is de�ned as:

� = E : ("� "p) ; (1)

where E is elasticity modulus, � is stress, and " and"p are total strain and plastic strain, respectively. Bymapping the stress onto the e�ective stress space,the plasticity and damage equations can be solved

T. Ahmadpour et al./Scientia Iranica, Transactions A: Civil Engineering 26 (2019) 2123{2132 2125

independently. Applying the scalar damage variableD, the e�ective stress can be expressed as:

�� = (1�D)E0 : ("� "p) ; (2)

where E0 is the undamaged elastic-sti�ness modulus.Considering the non-associated ow rule, the strainrate _"p can be de�ned as:

_"p = _�r�� (��) ; (3)

where _� denotes the plastic consistency parameter,which is a non-negative function, and � is a scalarplastic potential function. Moreover, the damagevariable k is required to represent the damage statesvariable as:

_k = _�H (��; k) : (4)

2.1. The damage modelIn order to represent the tensile and compressivedamages to concrete material, two damage variables arede�ned. These damage variables have values betweenzero and one for covering the range from undamaged tocompletely damaged concrete. In the Barcelona modelintroduced by Lubliner et al. [13], the uniaxial stress isde�ned as a function of the plastic strain, i.e.:

� = f0 [(1 + a) exp (�b"p)� a (exp (�2"p))] ; (5)

where a and b are dimensionless constants and f0 isthe initial yield stress. Consider an exponential formfor the degradation D as:

1�D = exp (�c"p) : (6)

The e�ective stress can be written as:

��=f0

h(1+a) (exp (�b"p))1�cb�a (exp (�b"p))2� cb

i;

(7)

in which the damage variable for the uniaxial loadingis denoted by k, de�ned as:

k =1g

Z "p

0�("p)d"p; (8)

where g is de�ned as:

g =Z 1

0�("p)d"p; (9)

in which the quantity is the dissipated energy densityduring the forming of microcracking [17]. SubstitutingEq. (5) into Eq. (9), the relation between g, a, and bcan be de�ned as:

g =f0

b

�1 +

a2

�: (10)

The uniaxial stress can be de�ned in terms of k bycombining Eqs. (8) and (10) as:

�=f0

a

h(1+a)

p1+a(2+a)k�1+a(2+a)k

i: (11)

Moreover, the e�ective stress can be expressed in termsof damage variable as:

��=f0

a

h(1+a)�p1+a(2+a)k

i1� cb�p1+a(2+a)k

�:

(12)

Hence, D can be de�ned as:

D = 1� h(1 + a)�p1 + a(2 + a)ki cb: (13)

By taking derivative from Eq. (8), the damage evolu-tion equation for the uniaxial state can be written as:

_k =1gf(k) _"p: (14)

To convert damages from a uniaxial damage evolutionto a multi-axial damage evolution, plastic strain rate iscalculated by the following equation:

_"p = �tr (��) _"pmax + �c (1� r (��)) _"pmin; (15)

where � is the Kronecker delta, _"pmin and _"pmax arealgebraically the minimum and maximum eigenvaluesof the plastic strain rate tensor, and r(��) is a weightfactor expressed as:

r (��) =

8>>><>>>:0; if �� = 0�

3Pi=1h��ii

��3Pi=1j��ij�; otherwise

(16)

Substituting Eq. (12) into Eq. (1), the evolution equa-tion can be obtained:

_k = h (��; k) : _"p; (17)

where:

h (��; k)=�r (��) ft(kt)=gt 0 0

0 0 (1�r (��)) fc(kc)=gc

�:(18)

Finally, applying the de�nition of _"p to Eq. (3), H(��; k)can be obtained as:

H = h � r�� (��) : (19)

2.2. The plasticity model and hardeningfunctions

Yield criterion is the most important part of theplasticity model. It is employed to model the behaviorof concrete under the tensile and compressive loadings.Implementation of similar behavior of tension andcompression in concrete leads to an unrealistic plasticdeformation [13]. In this study, the yield criterionoriginally introduced by Lubliner et al. [13] and then,modi�ed by Lee and Fenves [17] is proposed. The yield


function is de�ned in the e�ective stress space usingthe undamaged con�guration parameters as:

F (�) =1

1� �h�I1 +

p3J2 + ��max

i� cc(k); (20)

where I1 is the �rst invariant and J2 is the secondinvariant of the e�ective deviatoric stress tensor. In theabove equation, � and � are dimensionless constants,in which � depends on the ratio of yield strength underthe biaxial and uniaxial compressions, de�ned as [13]:

� =(fb0=fc0)� 12(fb0=fc0)� 1

; (21)

where fb0 is the biaxial and fc0 is the uniaxial compres-sive yield stress. The experimental values of fb0=fc0are within the range of 1.10 and 1.16, which leadsthe value of � to be between 0.08 and 0.12. Theparameter � is a constant value that is de�ned as adimensionless function of the tensile and compressivecohesion parameters ct and cc in the Barcelona modelas:

� =cc(k)ct(k)

(�� 1)� (1 + �): (22)

The biaxial tensile strength depends on the parameters� and �, and is always slightly lower than the uniaxialtensile strength.

The ow rule is de�ned based on the relationbetween the plastic ow direction and the plasticstrain rate. In this study, a non-associative owrule is required to control the dilatancy in modelingthe frictional behavior of material. Hence, a plasticpotential function, which is of the Drucker-Prager yieldcriteria type, is utilized as:

' =p

2J2 + �pI1; (23)

where the parameter �p is chosen such that a propervalue of dilatancy is obtained.

3. Cohesive fracture model for FRP interface

In the cohesive fracture model, it is assumed that thefracture process zone extends along the crack faces,while in the linear elastic fracture model, the fractureoccurs in the crack tip region. The basic assumptionof this model is that while the fracture process zoneoccurs, the material is still capable of transferringstresses. The micro-cracks appear close to the interfaceand the macro-cracks occur by the assemblage of micro-cracks [28]. The simplest constitutive relation describ-ing the fracture process zone is based on the cohesivefracture traction, which is de�ned as a function ofthe separation of two faces along the crack interface.The cohesive constitutive relation includes the tensilestrength of the material ft and the fracture energy Ef .In this model, the e�ective traction and the e�ectivecrack separation are de�ned as:

te =p

(tn)2 + (ts)2; (24)

�e =p

(�n)2 + (�s)2; (25)

where tn and ts are the normal and tangential trac-tions, and �n and �s are the normal and slidingdisplacements of the fracture surface, respectively.The damage initiation occurs when the traction orseparation reaches the critical value, i.e., te � t0 or�e � �0.

The constitutive law can be de�ned between thecohesive traction tj and crack separation �i usingtj = t(�i) or _tj = Tji _�i, where Tji is the constitutivetangent sti�ness tensor of cohesive fracture [29,30]. Inthis study, the delamination model proposed by Turonet al. [31] is utilized based on the continuum damagemodel. The free energy can be de�ned per unit area ofthe crack interface as:'(�; d) = (1� d)'0(�i)� d'0 (�1i h��1i) ;i = 1; 2; (26)

where d is a scalar damage variable and '0 is afunction of the displacement separation, de�ned as'0(�) = 1

2�iT 0ij�j , with T 0 denoting the constitutive

undamaged tangent sti�ness tensor. In Eq. (26), h�iis the MacAuley bracket de�ned as h�i = 1

2 (� + j�j)and �ij is the Kronecker delta. The negative valueof �1 means that the interface is in contact and thedamage cannot occur in the normal direction. Bytaking the derivative from the free energy Eq. (26),the constitutive equation for the crack interface can beobtained as:

ti =@'@�i

= (1� d)T 0ij�j � dT 0

ij�1ih��1i: (27)

3.1. The damage criterion and damageevolution law

The damage criterion can be de�ned as a function ofthe displacement separation as:

�F��e; �d

�= G (�e)�G � �d

� � 0; (28)

where �d is the damage threshold and G is a functionof damage evolution, which is de�ned in the range of[0; 1] as:

G (�e) =�f ��e ��0��e (�f ��0)

: (29)

Depending on the de�nition of damage, the damageevolution can be given by d = 1 � T=T 0. If the linearcohesive constitutive relation is considered, T and T 0

can be de�ned as:

T 0 =t0

�0 ; (30)

T =te

�e =�t0 ��e ��f��e (�f ��0)

: (31)

The damage is initiated when the e�ective separation


�e exceeds the initial damage threshold. Now, it isrequired to de�ne an evolution law for the damagemodel. The evolution law can be de�ned as:

_d = _�@ �F��e; �d

�@�e = _�

@G (�e)@�e ; (32)

where _� is the damage consistency parameter thatshould satisfy the loading-unloading conditions, i.e.:

_� � 0; �F��e; �d

� � 0; _�F��e; �d

�= 0: (33)

In order to derive the constitutive tangent sti�nesstensor, the damage model is implemented througha nonlinear approach. Taking the derivative fromEq. (27) leads to:

_ti =�ijT 0ij

�1� d

�1 + �1j

h��ji�j

��_�j

� �ijT 0ij

�1 + �1j

h��ji�j

��j _d; (34)

and the evolution of the damage variable d can beobtained as:

_d=

8>>>>><>>>>>:_G(�e) =

@G(�e)@�e

_�e =�f�0

�f ��01

(�e)2 ;

for �d < �e < �f

0; for �d>�e or �e>�f

(35)

Finally, the constitutive tangent sti�ness tensor, T tanji ,

in the constitutive law, _tj = T tanji

_�i, can be de�ned as:

T tanji =

8>>><>>>:�ijT 0

ij [1� dHj ]� T 0ijHjHi

�f�0

�f��01

(�e)2 ;for �d < �e < �f

�ijT 0ij [1� dHj ]; for �d > �e or �e > �f

(36)

where Hj = 1 + �1jh��ji=�j .

4. Numerical simulation results

4.1. Validation of the plastic-damage modelfor concrete

In order to verify and validate the performance ofthe proposed plastic-damage model for the concretebehavior, a single element of 10 � 10 cm is modeled,as shown in Figure 1. This single element is modeledunder the monotonic uniaxial compressive and mono-tonic uniaxial tensile loadings as well as the cyclicuniaxial tensile loading. The material parametersfor the numerical modeling of the concrete elementare obtained from the experimental test conductedby Gopalaratnam and Shah [32]. In Figure 2(a)

Figure 1. A concrete element proposed for veri�cation ofthe plastic-damage model of concrete behavior.

and (b), the strain-stress curves are plotted for themonotonic uniaxial compression and uniaxial tensionloadings. Complete agreement can be seen betweenthe predicted results and the experimental stress-straincurves proposed for the compression and tension of theconcrete. Also, the strain-stress curve of the tensilecyclic loading is plotted in Figure 2(c); it shows thatthe damage model can properly describe the behaviorof concrete in tensile cyclic loading. It can be seenin Figure 2(c) that the strain-stress curve obtained bythe numerical analysis is in excellent agreement withthat obtained by the experimental test. This exampleclearly demonstrates that the proposed plastic-damagemodel can e�ciently be used to capture the behaviorof concrete.

4.2. Validation of the cohesive fracture modelfor debonding

In order to verify the cohesive interface model proposedbetween the FRP and concrete, the results of themodel are compared with those of the debonding testreported by Au and B�uy�uk�ozt�urk [33]. The cohesivemodel is employed along the interface between theFRP and concrete through the FE analysis. Thematerial properties of the concrete and FRP as wellas the interface between them are obtained by theexperimental test. In Figure 3, the setup of theexperimental test is presented together with the in-terface fracture characterization of debonding in FRPplated concrete. In Figure 4, a comparison of theforce-displacement curves is presented between theexperimental and numerical results. It clearly showsthat the cohesive interface model can properly capturethe interface behavior between the FRP and concrete.The di�erence between two diagrams in the softeningpart of the force-displacement curve can be attributed


Figure 2. The stress-strain curves of a concrete elementwith the damage-plasticity model: (a) The monotonicuniaxial compression test, (b) the monotonic uniaxialtension test, and (c) the cyclic uniaxial tensile test.

Figure 3. The debonding test: (a) The setup ofexperimental test and (b) the interface fracture of FRPstrip together with the specimen con�guration.

Figure 4. The debonding test; a comparison of theforce-displacement curves between the experimental andnumerical results.

to the lack of uniformity of the adhesive thickness andthe presence of air bubbles.

4.3. Numerical and experimentalinvestigations into concrete arch

In order to illustrate the performance of the proposedcomputational algorithm, the two desired concretearches strengthened with FRP are analyzed numeri-cally and the results are compared with the experi-mental tests; the �rst experiment was conducted byZhang et al. [6] and the second one was conductedat the Strong Floor Laboratory of Sharif University


of Technology [34]. In order to present the accuracyof the proposed computational algorithm, the force-displacement curves obtained by the �nite elementanalysis are compared with those reported throughthe experimental tests. The reinforced concrete archis modeled using the four-node bilinear element andthe rebar is modeled using a two-node beam element.The rebars are connected to the concrete using theembedded technique inside the element.

In the �rst case, the concrete arch strengthenedwith internal FRP, originally conducted by Zhang etal. [6], is modeled using the proposed computationalalgorithm, as shown in Figure 5. In this �gure, theconcrete arch specimen is shown with its geometry,boundary conditions, and the FE mesh. It wasobserved in the experimental investigation that thecracks were �rst initiated in the middle of the spanand then, propagated by increasing the load throughthe shoulders. It was also observed that a �ve-hingearch was formed where the structure became unsta-ble. It is interesting to highlight that the �ve-hingestructure was also detected through the numericalanalysis of the concrete arch. In Figure 6, a com-

Figure 5. The concrete arch strengthened with internalFRP conducted by Zhang et al. [6]: (a) The concrete archspecimen and (b) the geometry, boundary conditions, andthe FE mesh of the concrete arch.

Figure 6. The concrete arch strengthened with internalFRP conducted by Zhang et al. [6]; a comparison of theforce-displacement curves between the experimental andnumerical results.

parison of the force-displacement curves is presentedbetween the experimental and numerical results; itclearly demonstrates that the proposed computationalalgorithm can properly capture the behavior of theconcrete arch. Obviously, a slight di�erence can beseen between the numerical analysis and experimentaldata at the beginning of the loading, which is dueto the local splitting of the sample at the time ofsitting of the sample; it cannot be modeled in thenumerical model. Furthermore, the numerical analysisdemonstrates higher strength than the experiment,which can be due to uncertainties in the propertiesof the materials utilized in the laboratory as well asthe reduced concrete stress in high strains. Accordingto the results, it can be concluded that the numericalanalysis adequately shows good agreement with theexperiments.

In the second case, the concrete arch strengthenedwith the internal and external FRPs experimentallyconducted at the Strong Floor Laboratory of SharifUniversity of Technology [34] is modeled, as shown inFigure 7. The data of one test is employed to verifythe accuracy of the proposed computational model.The concrete arch specimen is 35 cm high with aspan length of 110 cm and a rectangular cross-sectionwith the dimensions of 30 � 10 cm. The internal andexternal parts of the arch are retro�tted by an FRPlayer with the thickness of 0.35 mm. Three longitudinalbars with a diameter of 8 mm and stirrups with adiameter of 6 mm, with the spacing of 100 mm, areused (Figure 7(c)). All rebars have the strength of400 MPa. The compressive strength of the concretevaries between 47 and 54 MPa; a compressive strengthof 48 MPa is considered in the numerical analysis. The


Figure 7. The concrete arch strengthened with internaland external FRPs conducted at Sharif University ofTechnology: (a) The setup of experimental test, (b)problem de�nition, and (c) the geometry, boundaryconditions, and FE mesh of concrete arch.

strain-stress curves of the concrete in compression andtension are de�ned according to the recommendationsof the CEB-FIP 2010. It can be observed that thefailure of the arch occurs in a shear failure modedue to the excessive distance between the stirrups, ascan be seen in Figure 8. The maximum distance ofthe stirrups should be half the e�ective height of thesection. Given the section height of 100 mm, the stirrupspacing should be limited to a maximum of 50 mm;however, the distance of stirrups is selected equal to100 mm in the current experimental test for practicalconcerns. Because the tensile stress occurs along theinterface between the FRP and concrete at the innerface of the arch, debonding happens at this region, as

Figure 8. The concrete arch strengthened with internaland external FRPs conducted at Sharif University ofTechnology: (a) The crack trajectories obtained byexperimental test and (b) the contour of plastic strainobtained by the numerical analysis.

Figure 9. The concrete arch strengthened with internaland external FRPs conducted at Sharif University ofTechnology; a comparison of the force-displacement curvesbetween the experimental and numerical results.

shown in Figure 8. A comparison between Figure 8(a)and (b) illustrates that the proposed computationalalgorithm can be used to accurately capture the cracktrajectories. In Figure 9, the force-de ection curves areplotted for the experiment and numerical model, whichare in good agreement.


5. Conclusion

In the present paper, a computational technique ispresented based on the plastic-damage model to in-vestigate the e�ect of FRP strengthening on concretearches. A plastic-damage model was utilized to capturethe behavior of concrete. The interface betweenthe FRP and concrete was modeled using a cohesivefracture model. In order to validate the accuracy ofthe concrete model, a single element was consideredand exposed to monotonic tension, monotonic com-pression, and cyclic tension loads. Good agreementwas observed between the prede�ned strain-stress curveand the strain-stress curve obtained by the numericalanalysis. It demonstrated that the proposed plastic-damage model could e�ciently be used to capture thebehavior of concrete. Furthermore, the accuracy of thecohesive interface model between the FRP and concretewas investigated by comparing the results with theexperimental data obtained by the debonding test. Itclearly showed that the cohesive interface model couldproperly capture the interface behavior between theFRP and concrete. Finally, in order to illustrate theperformance of the proposed computational algorithm,the two desired concrete arches strengthened withFRP were numerically analyzed and the results werecompared with the experimental tests conducted atthe Strong Floor Laboratory of Sharif University ofTechnology. It was shown that the results of the pro-posed computational model had adequate agreementwith those of experiments.

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Biographies

Tahmaz Ahmadpour received his BSc degree inCivil Engineering from Iran University of Science andTechnology, Tehran, Iran, in 2001 and his MSc degreein Structural Engineering from Sahand University ofTechnology, Tabriz, Iran, in 2004. He is currently aPhD candidate in Civil Engineering at the Interna-tional Campus of Sharif University of Technology. Hismain research interests are computational fracture anddamage mechanics for brittle materials and ExtendedFinite Element Method (X-FEM).

Yousef Navid Tehrani received his BSc degree inCivil Engineering from Iran University of Science andTechnology, Tehran, Iran, in 2014 and his MSc degreein Structural Engineering from Sharif University ofTechnology, Tehran, Iran, in 2017. He is currentlyworking as a Research Assistant with Professor Amir R.Khoei. His main research interests are computationalplasticity, computational fracture and damage mechan-ics, material characterization, and multiscale modeling.

Amir R. Khoei received his PhD in Civil Engineeringfrom the University of Wales Swansea in UK in 1998.He is currently a Professor in the Civil EngineeringDepartment at Sharif University of Technology. Heis a member of the editorial board in the journals ofFinite Elements in Analysis and Design and EuropeanJournal of Computational Mechanics. He has beenselected several times as a Distinguished Professor atSharif University of Technology and was selected as aDistinguished Professor by the Ministry of Science, Re-search and Technology in 2008. He is the silver medalwinner of Khwarizmi International Award organizedby the Iranian Research Organization for Science andTechnology.

a computational plastic-damage method for modeling the...

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