Three-dimensional modeling of fracture in quasi-brittle materials using plasticity and cohesive finite elements
Source abstract
Abstract
This paper presents a three-dimensional discrete approach based on the use of interface cohesive elements with zero thickness to model the crack formation and propagation in quasi-brittle materials. The interface constitutive model incorporates concepts of nonlinear fracture mechanics and plasticity. A Coulomb-based surface is used as yield function, and an exponential traction–separation curve as softening law. The model features a non-associated flow rule with an implicit integration scheme and is able to simulate the propagation of single and multiple cracks in mode I and mixed-mode. The proposed model was tested through extension and shear paths and applied in the simulation of experimental tests in concrete specimens available in the literature. Also, a study on the effect of the use of different bulk elements was performed. Numerical results, including peak loads and load-CMOD curves showing softening behavior, are in good agreement with the experimental data.
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OpenAlex topics: Numerical methods in engineering · Rock Mechanics and Modeling · High-Velocity Impact and Material Behavior
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References (89)
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1. Abbo AJ, Sloan SW (1996) An automatic load stepping algorithm with error control. Int J Numer Methods Eng 39:1737–1759. https://doi.org/10.1002/(SICI)1097-0207(19960530)39:101737:AID-NME9273.0.CO;2-510.1002/(SICI)1097-0207(19960530)39:101737:AID-NME9273.0.CO;2-5 ↗
2. Alfano G, Crisfield MA (2001) Finite element interface models for the delamination analysis of laminated composites: mechanical and computational issues. Int J Numer Methods Eng 50:1701–1736. https://doi.org/10.1002/nme.9310.1002/nme.93 ↗
3. Barenblatt GI (1962) The mathematical theory of equilibrium of cracks in brittle fracture. Adv Appl Mech 7(1):55–12910.1016/S0065-2156(08)70121-2 ↗
4. Beer G (1985) An isoparametric joint/interface element for finite element analysis. Int J Numer Methods Eng 21:585–600. https://doi.org/10.1002/nme.162021040210.1002/nme.1620210402 ↗
5. Belytschko T, Krongauz Y, Organ D, adn Fleming M, Krysl P (1996) Meshless methods: an overview and recent developments. Comput Methods Appl Mech Eng 139:3–4710.1016/S0045-7825(96)01078-X ↗
6. Benedetto MF, Caggiano A, Etse G (2018) Virtual elements and zero thickness interface-based approach for fracture analysis of heterogeneous materials. Comput Methods Appl Mech Eng 338:41–67. https://doi.org/10.1016/j.cma.2018.04.00110.1016/j.cma.2018.04.001 ↗
7. Bocca P, Carpinteri A, Valente S (1990) Size effects in the mixed mode crack propagation: Softening and snap-back analysis. Eng Fract Mech 35(1):159–17010.1016/0013-7944(90)90193-K ↗
8. Brokenshire DR (1995) A study of torsion fracture tests. Ph.D. thesis, Cardiff University
9. Caballero A, Willam KJ, Carol I (2008) Consistent tangent formulation for 3d interface modeling of cracking/fracture in quasi-brittle materials. Comput Methods Appl Mech Eng 197:2804–2822. https://doi.org/10.1016/j.cma.2008.01.01110.1016/j.cma.2008.01.011 ↗
10. Caggiano A, Etse G, Martinelli E (2012) Zero-thickness interface model formulation for failure behavior of fiber-reinforced cementitious composites. Comput Struct 98–99:23–32. https://doi.org/10.1016/j.compstruc.2012.01.01310.1016/j.compstruc.2012.01.013 ↗
11. Carey GF, Ma M (1999) Joint elements, stress post-processing and superconvergent extraction with application to mohr-coulomb failure. Commun Numer Methods Eng 15:335–347. https://doi.org/10.1002/(SICI)1099-0887(199905)15:5335:AID-CNM2483.0.CO;2-I10.1002/(SICI)1099-0887(199905)15:5335:AID-CNM2483.0.CO;2-I ↗
12. Carol I, Prat PC, López CM (1997) Normal/shear cracking model: application to discrete crack analysis. J Eng Mech 123(8):765–773. https://doi.org/10.1061/(ASCE)0733-9399(1997)123:8(765)10.1061/(ASCE)0733-9399(1997)123:8(765) ↗
13. Carrier B, Granet S (2012) Numerical modeling of hydraulic fracture problem in permeable medium using cohesive zone model. Eng Fract Mech 79:312–328. https://doi.org/10.1016/j.engfracmech.2011.11.01210.1016/j.engfracmech.2011.11.012 ↗
14. Cendón DA, Gálvez JC, Elices M, Planas J (2000) Modelling the fracture of concrete under mixed loading. Int J Fract 103:293–310. https://doi.org/10.1023/A:100768702557510.1023/A:1007687025575 ↗
15. Cerfontaine B, Dieudonné AC, Radu JP, Collin F, Charlier R (2015) 3d zero-thickness coupled interface finite element: formulation and application. Comput Geotech 69:124–140. https://doi.org/10.1016/j.compgeo.2015.04.01610.1016/j.compgeo.2015.04.016 ↗
16. Chen X, Bu J, Xu L (2016) Effect of strain rate on post-peak cyclic behavior of concrete in direct tension. Constr Build Mater 124:746–754. https://doi.org/10.1016/j.conbuildmat.2016.08.01210.1016/j.conbuildmat.2016.08.012 ↗
17. Corona E, Reedy ED (2011) Calculations of buckle-driven delamination using cohesive elements. Int J Fract 170(2):191–19810.1007/s10704-011-9609-7 ↗
18. Coutinho ALGA, Martins MAD, Sydenstricker RM, Alves JLD, Landau L (2003) Simple zero thickness kinematically consistent interface elements. Comput Geotech 30:347–374. https://doi.org/10.1016/S0266-352X(03)00013-210.1016/S0266-352X(03)00013-2 ↗
19. Cui W, Potts DM, Zdravković L, Gawecka KA, Tsiampousi A (2019) Formulation and application of 3d thm-coupled zero-thickness interface elements. Comput Geotech 116:103204. https://doi.org/10.1016/j.compgeo.2019.10320410.1016/j.compgeo.2019.103204 ↗
20. Cusatis G, Bazant ZP, Cedolin L (2006) Confinement-shear lattice CSL model for fracture propagation in concrete. Comput Methods Appl Mech Eng 195:7154–7171. https://doi.org/10.1016/j.cma.2005.04.01910.1016/j.cma.2005.04.019 ↗
21. Davila C, Camanho P, de Moura M (2001) Mixed-mode decohesion elements for analyses of progressive delamination. In: Proceedings of the 42nd AIAA/ASME/ASCE/AHS/ASC structures. Structural dynamics and materials conference . https://doi.org/10.2514/6.2001-148610.2514/6.2001-1486 ↗
22. Day RA, Potts DM (1994) Zero thickness interface elements-numerical stability and application. Int J Numer Anal Methods Geomech 18:689–708. https://doi.org/10.1002/nag.161018100310.1002/nag.1610181003 ↗
23. Dugdale DS (1960) Yielding of steel sheets containing slits. J Mech Phys Solids 8:100–10410.1016/0022-5096(60)90013-2 ↗
24. Durand R, Silva FHBT (2019) A coulomb-based model to simulate concrete cracking using cohesive elements. Int J Fract 220:17–43. https://doi.org/10.1007/s10704-019-00395-510.1007/s10704-019-00395-5 ↗
25. Etse G, Caggiano A, Vrech S (2012) Multiscale failure analysis of fiber reinforced concrete based on a discrete crack model. Int J Fract 178:131–146. https://doi.org/10.1007/s10704-012-9733-z10.1007/s10704-012-9733-z ↗
26. Evangelista F, Roesler JR, Proença SP (2013) Three-dimensional cohesive zone model for fracture of cementitious materials based on the thermodynamics of irreversible processes. Eng Fract Mech 97:261–280. https://doi.org/10.1016/j.engfracmech.2012.10.02310.1016/j.engfracmech.2012.10.023 ↗
27. Falk ML, Needleman A, Rice JR (2001) A critical evaluation of cohesive zone models of dynamic fracture. J Phys Arch 11:543–550. https://doi.org/10.1051/jp4:200150610.1051/jp4:2001506 ↗
28. Feist C, Hofstetter G (2007) Validation of 3d crack propagation in plain concrete part I: experimental investigation—the pct3d test. Comput Concr 4:49–66. https://doi.org/10.12989/cac.2007.4.1.04910.12989/cac.2007.4.1.049 ↗
29. Ferté G, Massin P, Moes N (2016) 3d crack propagation with cohesive elements in the extended finite element method. Comput Methods Appl Mech Eng 300:347–374. https://doi.org/10.1016/j.cma.2015.11.01810.1016/j.cma.2015.11.018 ↗
30. Fujita Y, Ishimaru R, Hanai S, Suenaga Y (1997) Study of internal friction angle and tensile strength of plain concrete. J Struct Constr Eng 494:7–14. https://doi.org/10.3130/aijs.62.7_210.3130/aijs.62.7_2 ↗
31. García-Álvarez VO, Gettu R, Carol I (2012) Analysis of mixed-mode fracture in concrete using interface elements and a cohesive crack model. Sadhana 37:187–205. https://doi.org/10.1007/s12046-012-0076-210.1007/s12046-012-0076-2 ↗
32. Garolera D, Carol I, Papanastasiou P (2020) Application of zero-thickness interface elements to sanding prediction analysis. J Petrol Sci Eng 190:107052. https://doi.org/10.1016/j.petrol.2020.10705210.1016/j.petrol.2020.107052 ↗
33. Gasser TC (2007) Validation of 3d crack propagation in plain concrete part II: computational modeling and predictions of the pct3d test. Comput Concr 4:67–82. https://doi.org/10.12989/cac.2007.4.1.06710.12989/cac.2007.4.1.067 ↗
34. Gasser TC, Holzapfel GA (2006) 3d crack propagation in unreinforced concrete. a two-step algorithm for tracking 3d crack paths. Comput Methods Appl Mech Eng 195:5198–5219. https://doi.org/10.1016/j.cma.2005.10.02310.1016/j.cma.2005.10.023 ↗
35. Gerstle WH, Xie M (1992) Fem modeling of fictitious crack propagation in concrete. J Eng Mech 118:416–434. https://doi.org/10.1061/(ASCE)0733-9399(1992)118:2(416)10.1061/(ASCE)0733-9399(1992)118:2(416) ↗
36. Geubelle PH, Baylor JS (1998) Impact-induced delamination of composites: a 2D simulation. Composites B 29(5):589–602. https://doi.org/10.1016/S1359-8368(98)00013-410.1016/S1359-8368(98)00013-4 ↗
37. Geuzaine C, Remacle JF (2009) Gmsh: a 3-d finite element mesh generator with built-in pre- and post-processing facilities. Int J Numer Methods Eng 79:1309–1331. https://doi.org/10.1002/nme.257910.1002/nme.2579 ↗
38. Harper PW, Hallett SR (2008) Cohesive zone length in numerical simulations of composite delamination. Eng Fract Mech 75:4774–4792. https://doi.org/10.1016/j.engfracmech.2008.06.00410.1016/j.engfracmech.2008.06.004 ↗
39. Hillerborg A, Modeer M, Peterson P (1976) Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements. Cem Concr Res 6:773–78210.1016/0008-8846(76)90007-7 ↗
40. Hird CC, Kwok CM (1989) Finite element studies of interface behaviour in reinforced embankments of soft ground. Comput Geotech 8(2):111–13110.1016/0266-352X(89)90060-8 ↗
41. Ho S, Fu W, Wong H (1997) Application of automatic choice of step size for time stepping finite element method to induction motors. IEEE Trans Magn. https://doi.org/10.1109/20.58251110.1109/20.582511 ↗
42. Hordijk DA Tensile and tensile fatigue behaviour of concrete; experimentd, modelling and analyses, vol 37, 1 edn. Heron, Netherlands (1992)
43. Jebli M, Jamin F, Malachanne E, Garcia-Diaz E, El Youssoufi MS (2018) Experimental characterization of mechanical properties of the cement-aggregate interface in concrete. Constr Build Mater 161:16–25. https://doi.org/10.1016/j.conbuildmat.2017.11.10010.1016/j.conbuildmat.2017.11.100 ↗
44. Jefferson AD, Barr BIG, Bennett T, Hee SC (2004) Three dimensional finite element simulations of fracture tests using the Craft concrete model. Comput Concr 1(3):261–284. https://doi.org/10.12989/cac.2004.1.3.26110.12989/cac.2004.1.3.261 ↗
45. Jiang H, Meng D (2018) 3d numerical modelling of rock fracture with a hybrid finite and cohesive element method. Eng Fract Mech 199:280–293. https://doi.org/10.1016/j.engfracmech.2018.05.03710.1016/j.engfracmech.2018.05.037 ↗
46. Jin ZH, Paulino GH, Dodds RH (2003) Cohesive fracture modeling of elastic-plastic crack growth in functionally graded materials. Eng Fract Mech 70(14):1885–191210.1016/S0013-7944(03)00130-9 ↗
47. Khoei AR, Moslemi H, Sharifi M (2012) Three-dimensional cohesive fracture modeling of non-planar crack growth using adaptive FE technique. Int J Solids Struct 49(17):2334–2348. https://doi.org/10.1016/j.ijsolstr.2012.04.03610.1016/j.ijsolstr.2012.04.036 ↗
48. Lens LN, Bittencourt E, D’Avila VMR (2007) Cohesive laws to model concrete rupture—a methodology that takes mesh effects into consideration. Mecánica Comput 13:1440–1452
49. Lens LN, Bittencourt E, D’Avila VM (2009) Constitutive models for cohesive zones in mixed-mode fracture of plain concrete. Eng Fract Mech 76(14):2281–229710.1016/j.engfracmech.2009.07.020 ↗
50. Liu X, Duddu R, Waisman H (2012) Discrete damage zone model for fracture initiation and propagation. Eng Fract Mech 92:1–18. https://doi.org/10.1016/j.engfracmech.2012.04.01910.1016/j.engfracmech.2012.04.019 ↗
51. López CM, Carol I, Aguado A (2008a) Meso-structural study of concrete fracture using interface elements. I: numerical model and tensile behavior. Mater Struct 41:583–599. https://doi.org/10.1617/s11527-007-9314-110.1617/s11527-007-9314-1 ↗
52. López CM, Carol I, Aguado A (2008b) Meso-structural study of concrete fracture using interface elements. II: compression, biaxial and Brazilian test. Mater Struct 41:601–620. https://doi.org/10.1617/s11527-007-9312-310.1617/s11527-007-9312-3 ↗
53. Melenk JM, Babuska L (1996) The partition of unity finite element method: basis theory and applications. Comput Methods Appl Mech Eng 139:289–31410.1016/S0045-7825(96)01087-0 ↗
54. Molinari JF, Gazonas GA, Raghupathy R, Rusinek A, Zhou F (2007) The cohesive element approach to dynamic fragmentation: the question of energy convergence. Int J Numer Methods Eng 69:484–503. https://doi.org/10.1002/nme.177710.1002/nme.1777 ↗
55. Morin D, Bourel B, Bennani B, Lauro F, Lesueur D (2013) A new cohesive element for structural bonding modelling under dynamic loading. Int J Impact Eng 53:94–105. https://doi.org/10.1016/j.ijimpeng.2012.02.00310.1016/j.ijimpeng.2012.02.003 ↗
56. Ng K, Small JC (1997) Behavior of joints and interfaces subjected to water pressure. Comput Geotech 20:71–93. https://doi.org/10.1016/S0266-352X(96)00015-810.1016/S0266-352X(96)00015-8 ↗
57. Ngo D, Scordelis AC (1967) Finite element analysis of reinforced concrete beams. ACI J Proc 152–163
58. Nguyen GD (2005) A thermodynamic approach to constitutive modelling of concrete using damage mechanics and plasticity theory. doctoral thesis, University of Oxford
59. Nguyen VP (2014) An open source program to generate zero-thickness cohesive interface elements. Adv Eng Softw 74:27–39. https://doi.org/10.1016/j.advengsoft.2014.04.00210.1016/j.advengsoft.2014.04.002 ↗
60. Nguyen VP, Lian H, Rabczuk T, Bordas S (2017) Modelling hydraulic fractures in porous media using flow cohesive interface elements. Eng Geol 225:68–81. https://doi.org/10.1016/j.enggeo.2017.04.01010.1016/j.enggeo.2017.04.010 ↗
61. Nilson A.H (1968) Nonlinear analysis of reinforced concrete by the finite element method. ACI J Proc 757–766
62. Nooru-Mohamed MB (1992) Mixed-mode fracture of concrete: an experimental approach. doctoral thesis, Delft University of Technology
63. Ortiz M, Pandolfi A (1999) Finite-deformation irreversible cohesive elements for three-dimensional crack-propagation analysis. Int J Numer Methods Eng 44:1267–1282. https://doi.org/10.1002/(SICI)1097-0207(19990330)44:91267:AID-NME4863.0.CO;2-710.1002/(SICI)1097-0207(19990330)44:91267:AID-NME4863.0.CO;2-7 ↗
64. Pandolfi A, Ortiz M (2002) An efficient adaptive procedure for three-dimensional fragmentation simulations. Eng Comput 18:148–159. https://doi.org/10.1007/s00366020001310.1007/s003660200013 ↗
65. Park K, Paulino GH (2011) Cohesive zone models: a critical review of traction-separation relationships across fracture surfaces. Appl Mech Rev 64(6):060802. https://doi.org/10.1115/1.402311010.1115/1.4023110 ↗
66. Park K, Paulino GH, Roesler JR (2008) Determination of the kink point in the bilinear softening model for concrete. Eng Fract Mech 75:3806–3818. https://doi.org/10.1016/j.engfracmech.2008.02.00210.1016/j.engfracmech.2008.02.002 ↗
67. Park K, Paulino GH, Roesler JR (2009) A unified potential-based cohesive model of mixed-mode fracture. J Mech Phys Solids 57(6):891–90810.1016/j.jmps.2008.10.003 ↗
68. Paulino GH, Celes W, Espinha R, Zhang ZJ (2008) A general topology-based framework for adaptive insertion of cohesive elements in finite element meshes. Eng Comput 24:59–78. https://doi.org/10.1007/s00366-007-0069-710.1007/s00366-007-0069-7 ↗
69. Plesha ME, R., B., A., P (1989) Constitutive model and finite element procedure for dilatant contact problems. J Eng Mech 115(12:2649–266810.1061/(ASCE)0733-9399(1989)115:12(2649) ↗
70. Ralston A (1962) Runge-kutta methods with minimum error bounds. Math Comput 16:431–437. https://doi.org/10.2307/200313310.2307/2003133 ↗
71. Reinhardt HW, Cornelissen HAW (1984) Post-peak cyclic behaviour of concrete in uniaxial tensile and alternating tensile and compressive loading. Cem Concr Res 14:263–270. https://doi.org/10.1016/0008-8846(84)90113-310.1016/0008-8846(84)90113-3 ↗
72. Roesler J, Paulino GH, Park K, Gaedicke C (2007) Concrete fracture prediction using bilinear softening. Cem Concr Compos 29:300–312. https://doi.org/10.1016/j.cemconcomp.2006.12.00210.1016/j.cemconcomp.2006.12.002 ↗
73. Roy YA, Dodds RH (2001) Simulation of ductile crack growth in thin aluminum panels using 3-D surface cohesive elements. Int J Fract 110(1):21–4510.1023/A:1010816201891 ↗
74. Roychowdhury S, Roy YDA, Dodds RH Jr (2002) Ductile tearing in thin aluminum panels: experiments and analyses using large-displacement, 3-d surface cohesive elements. Eng Fract Mech 69:983–1002. https://doi.org/10.1016/S0013-7944(01)00113-810.1016/S0013-7944(01)00113-8 ↗
75. Segura JM, Carol I (2004) On zero-thickness interface elements for diffusion problems. Int J Numer Anal Methods Geomech 28:947–962. https://doi.org/10.1002/nag.35810.1002/nag.358 ↗
76. Segura JM, Carol I (2010) Numerical modelling of pressurized fracture evolution in concrete using zero-thickness interface elements. Eng Fract Mech 77:1386–1399. https://doi.org/10.1016/j.engfracmech.2010.03.01410.1016/j.engfracmech.2010.03.014 ↗
77. Segurado J, LLorca J (2004) A new three-dimensional interface finite element to simulate fracture in composites. Int J Solids Struct 41:2977–2993. https://doi.org/10.1016/j.ijsolstr.2004.01.00710.1016/j.ijsolstr.2004.01.007 ↗
78. Sheng D, Sloan SW, Abbo AJ (2002) An automatic newton-raphson scheme. Int J Geomech. https://doi.org/10.1061/(asce)1532-3641(2002)2:4(471)10.1061/(asce)1532-3641(2002)2:4(471) ↗
79. Stone and Webster Engineering Corporation (1992) Uplift pressures, shear strengths and tensile strengths for stability analysis of concrete gravity dams: Final report. Tech. rep
80. Tabiei A, Zhang W (2017) Cohesive element approach for dynamic crack propagation: artificial compliance and mesh dependency. Eng Fract Mech 180:23–42. https://doi.org/10.1016/j.engfracmech.2017.05.00910.1016/j.engfracmech.2017.05.009 ↗
81. Tejchman J, Bobński J (2013) Continuous and discontinuous modelling of fracture in plain concrete under monotonic loading. In: Continuous and discontinuous modelling of fracture in concrete using FEM. Springer . https://doi.org/10.1007/978-3-642-28463-2_510.1007/978-3-642-28463-2_5 ↗
82. Turon A, Dávila CG, Camanho PP, Costa J (2007) An engineering solution for mesh size effects in the simulation of delamination using cohesive zone models. Eng Fract Mech 74(10):1665–1682. https://doi.org/10.1016/j.engfracmech.2006.08.02510.1016/j.engfracmech.2006.08.025 ↗
83. van den Bosch MJ, Schreurs PJG, Geers MGD (2008) On the development of a 3d cohesive zone element in the presence of large deformations. Comput Mech 42:171–180. https://doi.org/10.1007/s00466-007-0184-810.1007/s00466-007-0184-8 ↗
84. Wells GN, Sluys LJ (2001) A new method for modelling cohesive cracks using finite elements. Int J Numer Methods Eng 50(12):2667–268210.1002/nme.143 ↗
85. Wittmann FH, Rokugo K,E,B, Mihashi H, Simopnin P (1988) Fracture energy and strain softening of concrete as determined by compact tension specimens. Mater Struct 21:21–32. https://doi.org/10.1007/BF0247252510.1007/BF02472525 ↗
86. Xu XP, Needleman A (1994) Numerical simulations of fast crack growth in brittle solids. J Mech Phys Solids 42:1397–1434. https://doi.org/10.1016/0022-5096(94)90003-510.1016/0022-5096(94)90003-5 ↗
87. Xu W, Zang M, Sakamoto J (2016) Modeling mixed mode fracture of concrete by using the combined discrete and finite elements method. Int J Comput Methods 13(01):165000710.1142/S0219876216500079 ↗
88. Yang ZJ, Chen JF (2005) Finite element modelling of multiple cohesive discrete crack propagation in reinforced concrete beams. Eng Fract Mech 72:2280–2297. https://doi.org/10.1016/j.engfracmech.2005.02.00410.1016/j.engfracmech.2005.02.004 ↗
89. Zivaljic N, Nikolic Z, Smoljanovic H (2014) Computational aspects of the combined finite-discrete element method in modelling of plane reinforced concrete structures. Eng Fract Mech 131:669–686. https://doi.org/10.1016/j.engfracmech.2014.10.01710.1016/j.engfracmech.2014.10.017 ↗