A Coulomb-based model to simulate concrete cracking using cohesive elements
Source abstract
Abstract
This paper presents a constitutive model for cohesive elements to simulate crack formation and propagation in mode I and mixed mode in quasi-brittle materials. The model is based on the plasticity theory and features a Coulomb-based yield function, a non-associated flow rule and an implicit stress integration scheme. It also incorporates concepts of nonlinear fracture mechanics to model the softening behavior of the fracture process. Two softening laws are investigated, a bilinear and an exponential law. The results from concrete crack propagation simulations of several classical experiments are presented. Numerical load–CMOD and load–displacement curves showing softening behavior are in very good agreement when compared with experimental data. In summary, the model is able to provide accurate predictions of the whole fracture process on all cases studied.
Source: openaire · Quality: candidate unverified · Source record ↗
Research context
OpenAlex topics: Numerical methods in engineering · Rock Mechanics and Modeling · Geotechnical Engineering and Underground Structures
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
References (79)
Show source-provided references
1. Asferg JL (2006) Modeling of concrete fracture applying the extended finite element method, Ph.D. thesis, Technical University of Denmark
2. Barenblatt GI (1962) The mathematical theory of equilibrium of cracks in brittle fracture. Adv Appl Mech 7:55–12910.1016/S0065-2156(08)70121-2 ↗
3. Barros JA, Figueiras JA (2001) Model for the analysis of steel fibre reinforced concrete slabs on grade. Comput Struct 79(1):97–106 arXiv:1012.576510.1016/S0045-7949(00)00061-4 ↗
4. Basaran C, Nie S (2007) A thermodynamics based damage mechanics model for particulate composites. Int J Solids Struct 44(3):1099–111410.1016/j.ijsolstr.2006.06.001 ↗
5. Beer G (1985) An isoparametric joint/interface element for finite element analysis. Int J Numer Methods Eng 21(4):585–60010.1002/nme.1620210402 ↗
6. Belytschko T, Gracie R, Venturav G (2009) A review of extended/generalized finite element methods for material modeling. Model Simul Mater Sci Eng 17(4):04300110.1088/0965-0393/17/4/043001 ↗
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. Caggiano A, Etse G, Martinelli E (2012) Zero-thickness interface model formulation for failure behavior of fiber-reinforced cementitious composites. Comput Struct. https://doi.org/10.1016/j.compstruc.2012.01.01310.1016/j.compstruc.2012.01.013 ↗
9. Carol I, Prat P, López C (1997) Normal/shear cracking model: application to discrete crack analysis. J Eng Mech 123:765–77310.1061/(ASCE)0733-9399(1997)123:8(765) ↗
10. Cendón DA, Gálvez JC, Elices M, Planas J (2000) Modelling the fracture of concrete under mixed loading. Int J Fract 103(3):293–31010.1023/A:1007687025575 ↗
11. Červenka J, Červenka V, Laserna S (2018) On crack band model in finite element analysis of concrete fracture in engineering practice. Eng Fract Mech 197:27–4710.1016/j.engfracmech.2018.04.010 ↗
12. Comi C, Perego U (2001) Fracture energy based bi-dissipative damage model for concrete. Int J Solids Struct 38(36):6427–645410.1016/S0020-7683(01)00066-X ↗
13. 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 ↗
14. Cunha VM, Barros JA, Sena-Cruz JM (2011) An integrated approach for modelling the tensile behaviour of steel fibre reinforced self-compacting concrete. Cement Concrete Res 41(1):64–7610.1016/j.cemconres.2010.09.007 ↗
15. Cunha VM, Barros JA, Sena-Cruz JM (2012) A finite element model with discrete embedded elements for fibre reinforced composites. Comput Struct 94–95:22–3310.1016/j.compstruc.2011.12.005 ↗
16. Cusatis G, Cedolin L (2006) Confinement-shear lattice CSL model for fracture propagation in concrete. Comput Methods Appl Mech Eng 195:7154–717110.1016/j.cma.2005.04.019 ↗
17. Dahlblom O, Ottosen NS (1990) Smeared crack analysis using generalized fictitious crack model. J Eng Mech 116:55–7610.1061/(ASCE)0733-9399(1990)116:1(55) ↗
18. de Borst R, Nauta P (1985) Non-orthogonal cracks in a smeared finite element model. Eng Comput 2:35–4610.1108/eb023599 ↗
19. Donadon MV, Iannucci L (2006) An objectivity algorithm for strain softening material models. In: Proceedings of the 9th international LS-DYNA users conference. (1):43–54
20. Du X, Jin L, Guowei M (2013) Numerical modeling tensile failure behaviour of concrete at mesoscale using extended finite element method. Int J Damage Mech 23:872–89810.1177/1056789513516028 ↗
21. Dugdale DS (1960) Yielding of steel sheets containing slits. J Mech Phys Solids 8:100–10410.1016/0022-5096(60)90013-2 ↗
22. Fries T-P, Belytschko T (2006) The intrinsic XFEM: a method for arbitrary discontinuities without additional unknowns. Int J Numer Methods Eng 68:1358–138510.1002/nme.1761 ↗
23. Gaedicke C, Roesler J (2010) Fracture-based method to determine flexural capacity of concrete beams on soil. Road Mater Pavement Des 11(2):361–38510.1080/14680629.2010.9690280 ↗
24. Galvez JC, Cendón D, Planas J, Guinea G, Elices M (1998) Fracture of concrete under mixed loading-experimental results and numerical prediction. Fract Mech Concrete Struct 3:729–738
25. Gálvez JC, Červenka J, Cendón DA, Saouma V (2002) A discrete crack approach to normal/shear cracking of concrete. Cement Concrete Res 32(10):1567–158510.1016/S0008-8846(02)00825-6 ↗
26. García-Álvarez VO, Gettu R, Carol I (2012) Analysis of mixed-mode fracture in concrete using interface elements and a cohesive crack model. Sadhana Acad Proc Eng Sci 37(1):187–205
27. Gerstle WH, Xie M (1992) FEM modeling of fictitious crack propagation in concrete. J Eng Mech 118:416–43410.1061/(ASCE)0733-9399(1992)118:2(416) ↗
28. Ghosh A, Chaudhuri P (2013) Computational modeling of fracture in concrete using a meshfree meso-macro-multiscale method. Comput Mater Sci 69:204–21510.1016/j.commatsci.2012.11.025 ↗
29. Gupta A, Akbar H (1984) Cracking in reinforced concrete analysis. J Struct Eng 110:1735–174610.1061/(ASCE)0733-9445(1984)110:8(1735) ↗
30. Gupta P, Pereira J, Kim D-J, Duarte C, Eason T (2012) Analysis of three-dimensional fracture mechanics problems: a non-intrusive approach using a generalized finite element method. Eng Fract Mech 90:41–6410.1016/j.engfracmech.2012.04.014 ↗
31. Hillerborg A, Modeer M, Peterson P (1976) Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements. Cement Concrete Res 6:773–78210.1016/0008-8846(76)90007-7 ↗
32. 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 ↗
33. Hordijk DA (1992) Tensile and tensile fatigue behaviour of concrete; experiments, modelling and analyses. vol 37, 1st edn. Heron, Netherlands
34. Jiang H, Meng D (2018) 3D numerical modelling of rock fracture with a hybrid finite and cohesive element method. Eng Fract Mech 199(April):280–29310.1016/j.engfracmech.2018.05.037 ↗
35. Jin Z-H, 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 ↗
36. 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 ↗
37. Li J, Kaliakin VN (1993) Numerical simulation of interfaces in geomaterials: development of new zero-thickness interface elements, Master’s thesis, University of Delaware
38. Mahabadi O, Kaifosh P, Marschall P, Vietor T (2014) Three-dimensional fdem numerical simulation of failure processes observed in opalinus clay laboratory samples. J Rock Mech Geotech Eng 6:591–60610.1016/j.jrmge.2014.10.005 ↗
39. Manzoli O, Gamino A, Rodrigues E, Claro G (2012) Modeling of interfaces in two-dimensional problems using solid finite elements with high aspect ratio. Comput Struct 94:70–8210.1016/j.compstruc.2011.12.001 ↗
40. Manzoli OL, Maedo MA, Bitencourt LAG, Rodrigues EA (2016) On the use of finite elements with a high aspect ratio for modeling cracks in quasi-brittle materials. Eng Fract Mech 153:151–17010.1016/j.engfracmech.2015.12.026 ↗
41. Mariani S, Perego U (2003) Extended finite element method for quasi-brittle fracture. Int J Numer Methods Eng 58:103–12610.1002/nme.761 ↗
42. Mazars J (1986) A description of micro- and macroscale damage of concrete structures. Eng Fract Mech 25(5):729–73710.1016/0013-7944(86)90036-6 ↗
43. Mazars J, Pijaudier-Cabot G (1996) From damage to fracture mechanics and conversely: a combined approach. Int J Solids Struct 33(20):3327–334210.1016/0020-7683(96)00015-7 ↗
44. 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 ↗
45. Moës N, Belytschko T (2002) Extended finite element method for cohesive crack growth. Eng Fract Mech 69:813–83310.1016/S0013-7944(01)00128-X ↗
46. 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 53:94–10510.1016/j.ijimpeng.2012.02.003 ↗
47. Ngo D, Scordelis AC (1967) Finite element analysis of reinforced concrete beams. ACI Proc 64:152–163
48. Nguyen GD (2005) A thermodynamic approach to constitutive modelling of concrete using damage mechanics and plasticity theory, Ph.D. thesis, University of Oxford
49. Nguyen VP (2014) An open source program to generate zero-thickness cohesive interface elements. Adv Eng Softw 74:27–3910.1016/j.advengsoft.2014.04.002 ↗
50. Nilson A (1968) Nonlinear analysis of reinforced concrete by the finite element method. ACI J 65:757–766
51. Nooru-Mohamed MB (1992) Mixed-mode fracture of concrete: an experimental approach, Ph.D. thesis, Delft University of Technology
52. Pandolfi A, Ortiz M (2002) An efficient adaptive procedure for three-dimensional fragmentation simulations. Eng Comput 18(2):148–15910.1007/s003660200013 ↗
53. Pandolfi A, Krysl P, Ortiz M (1999) Finite element simulation of ring expansion and fragmentation: the capturing of length and time scales through cohesive models of fracture. Int J Fract 95(1):279–29710.1023/A:1018672922734 ↗
54. Park K, Paulino GH (2013) Cohesive zone models: a critical review of traction-separation relationships across fracture surfaces. Appl Mech Rev 64(6):06080210.1115/1.4023110 ↗
55. Park K, Paulino GH, Roesler JR (2008) Determination of the kink point in the bilinear softening model for concrete. Eng Fract Mech 75(13):3806–381810.1016/j.engfracmech.2008.02.002 ↗
56. 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 ↗
57. 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(1):59–7810.1007/s00366-007-0069-7 ↗
58. Penna SS (2011) Formulacao multipotencial para modelos de degradacao elastica, Ph.D. thesis, Federal University of Minas Gerais, Brazil
59. Pituba JJC, Fernandes GR (2011) Anisotropic damage model for concrete. J Eng Mech 137(9):610–62410.1061/(ASCE)EM.1943-7889.0000260 ↗
60. Plesha ME, Ballarini R, Parulekar A (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) ↗
61. Roesler JR, Paulino G, Park K, Gaedicke C (2007) Concrete fracture prediction using bilinear softening. Cement Concrete Compos 29(4):300–31210.1016/j.cemconcomp.2006.12.002 ↗
62. 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 ↗
63. Sánchez M, Manzoli O, Guimarães L (2014) Modeling 3-D desiccation soil crack networks using a mesh fragmentation technique. Comput Geotech 62:27–3910.1016/j.compgeo.2014.06.009 ↗
64. Sancho JM, Planas J, Gálvez JC, Reyes E, Cendon DA (2006) An embedded cohesive crack model for finite element analysis of mixed mode fracture of concrete. Fatigue Fract Eng Mater Struct 29:1056–106510.1111/j.1460-2695.2006.01076.x ↗
65. Segura J, Carol I (2010) Numerical modelling of pressurized fracture evolution in concrete using zero-thickness interface elements. Eng Fract Mech 77:1386–139910.1016/j.engfracmech.2010.03.014 ↗
66. Shi C, van Dam AG, van Mier JGM, Sluys LJ (2000) Crack interaction in concrete. Mater Build Struct EUROMAT 6:125–131
67. Simone A (2007) Partition of unity-based discontinuous finite elements: GFEM, PUFEM, XFEM. Revue Européenne de Génie Civil 11:1045–106810.1080/17747120.2007.9692976 ↗
68. Song SH, Paulino GH, Buttlar WG (2006) Simulation of crack propagation in asphalt concrete using an intrinsic cohesive zone model. J Eng Mech 132(11):1215–122310.1061/(ASCE)0733-9399(2006)132:11(1215) ↗
69. Tabiei A, Zhang W (2017) Cohesive element approach for dynamic crack propagation: artificial compliance and mesh dependency. Eng Fract Mech 180:23–4210.1016/j.engfracmech.2017.05.009 ↗
70. 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 ↗
71. Winkler B (2011) Traglastuntersuchungen von unbewehrten und bewehrten betonstrukturen auf der grundlage eines objektiven werkstoffgesetzes fur beton, Master’s thesis, University of Innsbruck
72. Winkler B, Hofstetter G, Lehar H (2004) Application of a constitutive model for concrete to the analysis of a precast segmental tunnel lining. Int J Numer Anal Methods Geomech 28:797–81910.1002/nag.362 ↗
73. Wittmann FH, Rokugo K, Bruhwiler E, Mihashi H, Simopnin P (1988) Fracture energy and strain softening of concrete as determined by compact tension specimens. Mater Struct 21:21–3210.1007/BF02472525 ↗
74. Xie D, Waas AM (2006) Discrete cohesive zone model for mixed-mode fracture using finite element analysis. Eng Fract Mech 73(13):1783–179610.1016/j.engfracmech.2006.03.006 ↗
75. Xu XP, Needleman A (1994) Numerical simulations of fast crack growth in brittle solids. J Mech Phys Solids 42(9):1397–143410.1016/0022-5096(94)90003-5 ↗
76. Xu W, Zang M, Sakamoto J (2015) Modeling mixed mode fracture of concrete by using the combined discrete and finite elements method. Int J Comput Methods 13(01):165000710.1142/S0219876216500079 ↗
77. 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 ↗
78. Yang ZJ, Chen JF (2005) Finite element modelling of multiple cohesive discrete crack propagation in reinforced concrete beams. Eng Fract Mech 72:2280–229710.1016/j.engfracmech.2005.02.004 ↗
79. 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 131:669–68610.1016/j.engfracmech.2014.10.017 ↗