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Frontiers of Structural and Civil Engineering

Front. Struct. Civ. Eng.    2020, Vol. 14 Issue (3) : 586-598     https://doi.org/10.1007/s11709-020-0573-z
REVIEW
Computational modeling of fracture in concrete: A review
Luthfi Muhammad MAULUDIN1,2(), Chahmi OUCIF1
1. Institute of Structural Mechanics, Bauhaus Universität Weimar, Weimar 99423, Germany
2. Teknik Sipil, Politeknik Negeri Bandung, Gegerkalong Hilir Ds.Ciwaruga, Bandung 40012, Indonesia
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Abstract

This paper presents a review of fracture modeling of concrete. The complex material, such as concrete, has been widely used in construction industries and become trending issue in the last decades. Based on comprehensive literature review, there are two main approaches considered to-date of concrete fracture modeling, such as macroscopic and micromechanical models. The purpose of this review is to provide insight comparison from different techniques in modeling of fracture in concrete which are available. In the first section, an overview of fracture modeling in general is highlighted. Two different approaches both of macroscopic and micromechanical models will be reviewed. As heterogeneity of concrete material is major concern in micromechanical-based concrete modeling, one section will discuss this approach. Finally, the summary from all of reviewed techniques will be pointed out before the future perspective is given.

Keywords concrete fracture      macroscopic      micromechanical      heterogeneity     
Corresponding Author(s): Luthfi Muhammad MAULUDIN   
Just Accepted Date: 04 April 2020   Online First Date: 21 May 2020    Issue Date: 13 July 2020
 Cite this article:   
Luthfi Muhammad MAULUDIN,Chahmi OUCIF. Computational modeling of fracture in concrete: A review[J]. Front. Struct. Civ. Eng., 2020, 14(3): 586-598.
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http://journal.hep.com.cn/fsce/EN/10.1007/s11709-020-0573-z
http://journal.hep.com.cn/fsce/EN/Y2020/V14/I3/586
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Fig.1  The schematic model of fixed cracks and rotating cracks [72]. (a) Rotating crack; (b) fixed crack. (Reprinted from International Journal of Solids and Structures, 42(5–6), Rabczuk T, Akkermann J, Eibl J, A numerical model for reinforced concrete structures, 1327–1354, Copyright 2005, with permission from Elsevier.)
Fig.2  Schematic of cohesive models applied in a particle method: Rigid model (bold line) and Non-rigid model (dash line).
Fig.3  The schematic of particle crack model for the crack.
Fig.4  Bond model used in steel reinforcement. (a) Radial cracks are generated around the reinforcement; (b) the interaction between concrete and the rib, and the crushed of concrete caused by pulling out force in the reinforcement [47]. (Reprinted from Engineering Fracture Mechanics, 75(16), Rabczuk T, Zi G, Bordas S, Nguyen-Xuan H, A geometrically non-linear three-dimensional cohesive crack method for reinforced concrete structures, 4740–4758, Copyright 2008, with permission from Elsevier.)
Fig.5  Schematic of Voronoi construction of lattice model with equal randomness, A/s = 0.5. (a) 3×3 2D mesh; (b) 3×3×3 3D mesh [77]. (Reprinted from Engineering Fracture Mechanics, 70(7–8), Lilliu G, van Mier J G M, 3D lattice type fracture model for concrete, 927–941, Copyright 2003, with permission from Elsevier.)
Fig.6  Basic concept of microplane model. (a) Idealization of contact planes; (b) decomposition of strain tensor into microplane. Reproduced from Ref. [107]. (Reprinted from International Journal of Solids and Structures, 38(16), Ožbolt J, Li Y, Kožar I, Microplane model for concrete with relaxed kinematic constraint, 2683–2711, Copyright 2001, with permission from Elsevier.)
Fig.7  The schematic of two-scale methodology for probabilistic-based model of unidirectional fiber-reinforced composite [113]. (Reprinted from Composites Science and Technology, 66(11), Trias D, Costa J, Fiedler B, Hobbiebrunken T, Hurtado J E, A two scale method for matrix cracking probability in fiber-reinforced composites based on a statistical representative volume element, 1766–1777, Copyright 2006, with permission from Elsevier.)
Fig.8  Xray transformation from. (a) Pixel-based image; (b) simple grid mesh; (c) smoothed mesh. Reproduced from Ref [115]. (Reprinted from Engineering Fracture Mechanics, 133, Ren W, Yang Z, Sharma R, Zhang C, Withers P J, Two-dimensional x-ray CT image based meso-scale fracture modelling of concrete, 24–39, Copyright 2015, with permission from Elsevier.)
Fig.9  Generated 2D random circular aggregate particles (black) inside mortar matrix (gray) along with the interfacial layers (white).
Fig.10  Schematic of crack propagation criterion based on heterogeneous fracture strength. (a) Idealization model. (b) Typical used in the model [129]. (Reprinted from Computer Methods in Applied Mechanics and Engineering, 197(45–48), Yang Z, Xu X F, A heterogeneous cohesive model for quasi-brittle materials considering spatially varying random fracture properties, 4027–4039, Copyright 2008, with permission from Elsevier.)
1 Z P Bažant, M R Tabbara, M T Kazemi, G Pijaudier-Cabot. Random particle model for fracture of aggregate or fiber composites. Journal of Engineering Mechanics, 1990, 116(8): 1686–1705
https://doi.org/10.1061/(ASCE)0733-9399(1990)116:8(1686)
2 J E Bolander Jr, S Saito. Fracture analyses using spring networks with random geometry. Engineering Fracture Mechanics, 1998, 61(5–6): 569–591
https://doi.org/10.1016/S0013-7944(98)00069-1
3 A Ragab Mohamed, W Hansen. Micromechanical modeling of crack-aggregate interaction in concrete materials. Cement and Concrete Composites, 1999, 21(5–6): 349–359
https://doi.org/10.1016/S0958-9465(99)00016-5
4 E Schlangen, J van Mier. Micromechanical analysis of fracture of concrete. International Journal of Damage Mechanics, 1992, 1(4): 435–454
https://doi.org/10.1177/105678959200100404
5 J van Mier, A Vervuurt. Numerical analysis of interface fracture in concrete using a lattice-type fracture model. International Journal of Damage Mechanics, 1997, 6(4): 408–432
https://doi.org/10.1177/105678959700600403
6 P Grassl, M Jirásek. Meso-scale approach to modelling the fracture process zone of concrete subjected to uniaxial tension. International Journal of Solids and Structures, 2010, 47(7–8): 957–968
https://doi.org/10.1016/j.ijsolstr.2009.12.010
7 C M López, I Carol, A Aguado. Meso-structural study of concrete fracture using interface elements. I: Numerical model and tensile behavior. Materials and Structures, 2008, 41(3): 583–599
https://doi.org/10.1617/s11527-007-9314-1
8 C M López, I Carol, A Aguado. Meso-structural study of concrete fracture using interface elements. II: Compression, biaxial and brazilian test. Materials and Structures, 2008, 41(3): 601–620
https://doi.org/10.1617/s11527-007-9312-3
9 N A Labanda, S M Giusti, B M Luccioni. Meso-scale fracture simulation using an augmented Lagrangian approach. International Journal of Damage Mechanics, 2016, 27(1): 1056789516671092
10 T Rabczuk, J Eibl. Modelling dynamic failure of concrete with mesh-free methods. International Journal of Impact Engineering, 2006, 32(11): 1878–1897
https://doi.org/10.1016/j.ijimpeng.2005.02.008
11 T Rabczuk, G Zi. Numerical fracture analysis of prestressed concrete beams. International Journal of Concrete Structures and Materials, 2008, 2(2): 153–160
https://doi.org/10.4334/IJCSM.2008.2.2.153
12 T Rabczuk, S P Xiao, M Sauer. Coupling of mesh-free methods with finite elements: basic concepts and test results. International Journal for Numerical Methods in Biomedical Engineering, 2006, 22(10): 1031–1065
13 T Rabczuk, G Zi. A meshfree method based on the local partition of unity for cohesive cracks. Computational Mechanics, 2007, 39(6): 743–760
https://doi.org/10.1007/s00466-006-0067-4
14 T Rabczuk, T Belytschko. A three-dimensional large deformation mesh-free method for arbitrary evolving cracks. Computer Methods in Applied Mechanics and Engineering, 2007, 196(29–30): 2777–2799
https://doi.org/10.1016/j.cma.2006.06.020
15 T Rabczuk, S Bordas, G Zi. A three-dimensional meshfree method for continuous multiple-crack initiation, propagation and junction in statics and dynamics. Computational Mechanics, 2007, 40(3): 473–495
https://doi.org/10.1007/s00466-006-0122-1
16 G Zi, T Rabczuk, W Wall. Extended meshfree methods without branch enrichment for cohesive cracks. Computational Mechanics, 2007, 40(2): 367–382
https://doi.org/10.1007/s00466-006-0115-0
17 T Rabczuk, P. Areias A Meshfree Thin Shell for Arbitrary Evolving Cracks Based on An Extrinsic Basis. Christchurch: University of Canterbury, 2006
18 P Areias, J Reinoso, P Camanho, T Rabczuk. A constitutive-based element-by-element crack propagation algorithm with local mesh refinement. Computational Mechanics, 2015, 56(2): 291–315
https://doi.org/10.1007/s00466-015-1172-z
19 P Areias, M Msekh, T Rabczuk. Damage and fracture algorithm using the screened Poisson equation and local remeshing. Engineering Fracture Mechanics, 2016, 158: 116–143
https://doi.org/10.1016/j.engfracmech.2015.10.042
20 P Areias, J Reinoso, P P Camanho, J César de Sá, T Rabczuk. Effective 2D and 3D crack propagation with local mesh refinement and the screened Poisson equation. Engineering Fracture Mechanics, 2018, 189: 339–360
https://doi.org/10.1016/j.engfracmech.2017.11.017
21 P Areias, T Rabczuk. A novel two-stage discrete crack method based on the screened Poisson equation and local mesh refinement. Computational Mechanics, 2016, 58(6): 1003–1018
https://doi.org/10.1007/s00466-016-1328-5
22 P Areias, T Rabczuk, M Msekh. Phase-field analysis of finite-strain plates and shells including element subdivision. Computer Methods in Applied Mechanics and Engineering, 2016, 312: 322–350
https://doi.org/10.1016/j.cma.2016.01.020
23 M A Msekh, N Cuong, G Zi, P Areias, X Zhuang, T Rabczuk. Fracture properties prediction of clay/epoxy nanocomposites with interphase zones using a phase field model. Engineering Fracture Mechanics, 2018, 188: 287–299
https://doi.org/10.1016/j.engfracmech.2017.08.002
24 P Areias, T Rabczuk, D Dias-da Costa. Element-wise fracture algorithm based on rotation of edges. Engineering Fracture Mechanics, 2013, 110: 113–137
https://doi.org/10.1016/j.engfracmech.2013.06.006
25 P Areias, T Rabczuk, P Camanho. Initially rigid cohesive laws and fracture based on edge rotations. Computational Mechanics, 2013, 52(4): 931–947
https://doi.org/10.1007/s00466-013-0855-6
26 P Areias, T Rabczuk. Finite strain fracture of plates and shells with configurational forces and edge rotations. International Journal for Numerical Methods in Engineering, 2013, 94(12): 1099–1122
https://doi.org/10.1002/nme.4477
27 T Rabczuk, T Belytschko. Application of particle methods to static fracture of reinforced concrete structures. International Journal of Fracture, 2006, 137(1–4): 19–49
https://doi.org/10.1007/s10704-005-3075-z
28 T Rabczuk, G Zi, S Bordas, H Nguyen-Xuan. A simple and robust three-dimensional cracking-particle method without enrichment. Computer Methods in Applied Mechanics and Engineering, 2010, 199(37–40): 2437–2455
https://doi.org/10.1016/j.cma.2010.03.031
29 T Rabczuk, R Gracie, J H Song, T Belytschko. Immersed particle method for fluid-structure interaction. International Journal for Numerical Methods in Engineering, 2010, 81(1): 48–71
30 H Ren, X Zhuang, Y Cai, T Rabczuk. Dual-horizon peridynamics. International Journal for Numerical Methods in Engineering, 2016, 108(12): 1451–1476
https://doi.org/10.1002/nme.5257
31 H Ren, X Zhuang, T Rabczuk. Dual-horizon peridynamics: A stable solution to varying horizons. Computer Methods in Applied Mechanics and Engineering, 2017, 318: 762–782
https://doi.org/10.1016/j.cma.2016.12.031
32 C Anitescu, M N Hossain, T Rabczuk. Recovery-based error estimation and adaptivity using high-order splines over hierarchical t-meshes. Computer Methods in Applied Mechanics and Engineering, 2018, 328: 638–662
https://doi.org/10.1016/j.cma.2017.08.032
33 N Nguyen-Thanh, K Zhou, X Zhuang, P Areias, H Nguyen-Xuan, Y Bazilevs, T Rabczuk. Isogeometric analysis of large-deformation thin shells using RHT-splines for multiple-patch coupling. Computer Methods in Applied Mechanics and Engineering, 2017, 316: 1157–1178
https://doi.org/10.1016/j.cma.2016.12.002
34 B Nguyen, H Tran, C Anitescu, X Zhuang, T Rabczuk. An isogeometric symmetric galerkin boundary element method for two-dimensional crack problems. Computer Methods in Applied Mechanics and Engineering, 2016, 306: 252–275
https://doi.org/10.1016/j.cma.2016.04.002
35 T Q Thai, T Rabczuk, Y Bazilevs, G Meschke. A higher-order stress based gradient-enhanced damage model based on isogeometric analysis. Computer Methods in Applied Mechanics and Engineering, 2016, 304: 584–604
https://doi.org/10.1016/j.cma.2016.02.031
36 N Nguyen-Thanh, N Valizadeh, M Nguyen, H Nguyen-Xuan, X Zhuang, P Areias, G Zi, Y Bazilevs, L De Lorenzis, T Rabczuk. An extended isogeometric thin shell analysis based on Kirchhoff-Love theory. Computer Methods in Applied Mechanics and Engineering, 2015, 284: 265–291
https://doi.org/10.1016/j.cma.2014.08.025
37 S S Ghorashi, N Valizadeh, S Mohammadi, T Rabczuk. T-spline based XIGA for fracture analysis of orthotropic media. Computers & Structures, 2015, 147: 138–146
https://doi.org/10.1016/j.compstruc.2014.09.017
38 M Silani, H Talebi, A M Hamouda, T Rabczuk. Nonlocal damage modelling in clay/epoxy nanocomposites using a multiscale approach. Journal of Computational Science, 2016, 15: 18–23
https://doi.org/10.1016/j.jocs.2015.11.007
39 H Talebi, M Silani, T Rabczuk. Concurrent multiscale modeling of three dimensional crack and dislocation propagation. Advances in Engineering Software, 2015, 80: 82–92
https://doi.org/10.1016/j.advengsoft.2014.09.016
40 H Talebi, M Silani, S P Bordas, P Kerfriden, T Rabczuk. A computational library for multiscale modeling of material failure. Computational Mechanics, 2014, 53(5): 1047–1071
https://doi.org/10.1007/s00466-013-0948-2
41 P R Budarapu, R Gracie, S P Bordas, T Rabczuk. An adaptive multiscale method for quasi-static crack growth. Computational Mechanics, 2014, 53(6): 1129–1148
https://doi.org/10.1007/s00466-013-0952-6
42 P R Budarapu, R Gracie, S W Yang, X Zhuang, T Rabczuk. Efficient coarse graining in multiscale modeling of fracture. Theoretical and Applied Fracture Mechanics, 2014, 69: 126–143
https://doi.org/10.1016/j.tafmec.2013.12.004
43 F Amiri, C Anitescu, M Arroyo, S P A Bordas, T Rabczuk. XLME interpolants, a seamless bridge between XFEM and enriched meshless methods. Computational Mechanics, 2014, 53(1): 45–57
https://doi.org/10.1007/s00466-013-0891-2
44 L Chen, T Rabczuk, S P A Bordas, G Liu, K Zeng, P Kerfriden. Extended finite element method with edge-based strain smoothing (ESM-XFEM) for linear elastic crack growth. Computer Methods in Applied Mechanics and Engineering, 2012, 209–212: 250–265
https://doi.org/10.1016/j.cma.2011.08.013
45 T Rabczuk, S Bordas, G Zi. On three-dimensional modelling of crack growth using partition of unity methods. Computers & Structures, 2010, 88(23–24): 1391–1411
https://doi.org/10.1016/j.compstruc.2008.08.010
46 P Areias, T Rabczuk, P Camanho. Finite strain fracture of 2d problems with injected anisotropic softening elements. Theoretical and Applied Fracture Mechanics, 2014, 72: 50–63
https://doi.org/10.1016/j.tafmec.2014.06.006
47 T Rabczuk, G Zi, S Bordas, H Nguyen-Xuan. A geometrically non-linear three-dimensional cohesive crack method for reinforced concrete structures. Engineering Fracture Mechanics, 2008, 75(16): 4740–4758
https://doi.org/10.1016/j.engfracmech.2008.06.019
48 P M Areias, T Rabczuk. Quasi-static crack propagation in plane and plate structures using set-valued traction-separation laws. International Journal for Numerical Methods in Engineering, 2008, 74(3): 475–505
https://doi.org/10.1002/nme.2182
49 R De Borst. Some recent developments in computational modelling of concrete fracture. International Journal of Fracture, 1997, 86(1–2): 5–36
https://doi.org/10.1023/A:1007360521465
50 A R C Murthy, G Palani, N R Iyer. State-of-the-art review on fracture analysis of concrete structural components. Sadhana, 2009, 34(2): 345–367
https://doi.org/10.1007/s12046-009-0014-0
51 M Wu, B Johannesson, M Geiker. A review: Self-healing in cementitious materials and engineered cementitious composite as a self-healing material. Construction & Building Materials, 2012, 28(1): 571–583
https://doi.org/10.1016/j.conbuildmat.2011.08.086
52 K Van Tittelboom, N De Belie. Self-healing in cementitious materials: A review. Materials (Basel), 2013, 6(6): 2182–2217
https://doi.org/10.3390/ma6062182
53 A Talaiekhozan, A Keyvanfar, A Shafaghat, et al. A review of self-healing concrete research development. Journal of Environmental Treatment Techniques, 2014, 2(1): 1–11
54 Z Lv, D. Chen Overview of recent work on self-healing in cementitious materials. Materiales de Construccion, 2014, 64(316): 034
55 E Ahn, H Kim, S H Sim, S W Shin, M Shin. Principles and applications of ultrasonic-based nondestructive methods for self-healing in cementitious materials. Materials (Basel), 2017, 10(3): 278
https://doi.org/10.3390/ma10030278
56 L Mauludin, C. Oucif Modeling of self-healing concrete: A review. Journal of Applied and Computational Mechanics, 2017, 5: 526–539
https://doi.org/10.22055/jacm.2017.23665.1167.
57 L M Mauludin, C Oucif. The effects of interfacial strength on fractured microcapsule. Frontiers of Structural and Civil Engineering, 2019, 13(2): 353–363
58 L M Mauludin, C Oucif. Interaction between matrix crack and circular capsule under uniaxial tension in encapsulation-based self-healing concrete. Underground Space, 2018, 3(3): 181–189
https://doi.org/10.1016/j.undsp.2018.04.004
59 L M Mauludin, X Zhuang, T Rabczuk. Computational modeling of fracture in encapsulation-based self-healing concrete using cohesive elements. Composite Structures, 2018, 196: 63–75
https://doi.org/10.1016/j.compstruct.2018.04.066
60 C Oucif, L Mauludin. Continuum damage-healing and super healing mechanics in brittle materials: A state-of-the-art review. Applied Sciences (Basel, Switzerland), 2018, 8(12): 2350
https://doi.org/10.3390/app8122350
61 C Oucif, K Ouzaa, L M. Mauludin Cyclic and monotonic behavior of strengthened and unstrengthened square reinforced concrete columns. Journal of Applied and Computational Mechanics, 2019, 5: 517–525
https://doi.org/10.22055/JACM.2017.23514.1159
62 T Rabczuk. Computational methods for fracture in brittle and quasi brittle solids: State-of-the-art review and future perspectives, ISRN. Applied Mathematics, 2013: 332–369
63 J M Djoković, R R Nikolić, J Bujnak. Fundamental problems of modeling the fracture processes in concrete I: Micromechanics and localization of damages. Procedia Engineering, 2013, 65: 186–195
https://doi.org/10.1016/j.proeng.2013.09.029
64 J M Djoković, R R Nikolić, J Bujnak. Fundamental problems of modeling the fracture processes in concrete II: Size effect and selection of the solution approach. Procedia Engineering, 2013, 65: 196–205
https://doi.org/10.1016/j.proeng.2013.09.030
65 L Jendele, J Cervenka, V Saouma, R Pukl. On the choice between discrete or smeared approach in practical structural fe analyses of concrete structures. In: The Fourth International Conference on Analysis of Discontinuous Deformation. Glasgow: University of Glasgow, 2001
66 A Hillerborg, M Modéer, P E Petersson. Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements. Cement and Concrete Research, 1976, 6(6): 773–781
https://doi.org/10.1016/0008-8846(76)90007-7
67 M Jirásek, T Zimmermann. Rotating crack model with transition to scalar damage. Journal of Engineering Mechanics, 1998, 124(3): 277–284
https://doi.org/10.1061/(ASCE)0733-9399(1998)124:3(277)
68 X P Xu, A Needleman. Numerical simulations of dynamic crack growth along an interface. International Journal of Fracture, 1996, 74(4): 289–324
https://doi.org/10.1007/BF00035845
69 E Samaniego Alvarado. Contributions to the Continuum Modelling of Strong Discontinuities in Two-dimensional Solids. Dissertation for the Doctoral Degree. Barcelona: Universitat Politécnica de Catalunya, 2003
70 T Belytschko, Y Y Lu, L Gu. Element-free galerkin methods. International Journal for Numerical Methods in Engineering, 1994, 37(2): 229–256
https://doi.org/10.1002/nme.1620370205
71 G N Wells, L Sluys. A new method for modelling cohesive cracks using finite elements. International Journal for Numerical Methods in Engineering, 2001, 50(12): 2667–2682
https://doi.org/10.1002/nme.143
72 T Rabczuk, J Akkermann, J Eibl. A numerical model for reinforced concrete structures. International Journal of Solids and Structures, 2005, 42(5–6): 1327–1354
https://doi.org/10.1016/j.ijsolstr.2004.07.019
73 T Rabczuk, T Belytschko. Cracking particles: A simplified meshfree method for arbitrary evolving cracks. International Journal for Numerical Methods in Engineering, 2004, 61(13): 2316–2343
https://doi.org/10.1002/nme.1151
74 A Hrennikoff. Solution of problems of elasticity by the framework method. Journal of Applied Mechanics, 1941, 8(4): 169–175
75 E Schlangen, J van Mier. Simple lattice model for numerical simulation of fracture of concrete materials and structures. Materials and Structures, 1992, 25(9): 534–542
https://doi.org/10.1007/BF02472449
76 E Schlangen, E Garboczi. Fracture simulations of concrete using lattice models: Computational aspects. Engineering Fracture Mechanics, 1997, 57(2–3): 319–332
https://doi.org/10.1016/S0013-7944(97)00010-6
77 G Lilliu, J G M van Mier. 3D lattice type fracture model for concrete. Engineering Fracture Mechanics, 2003, 70(7–8): 927–941
https://doi.org/10.1016/S0013-7944(02)00158-3
78 G Cusatis, D Pelessone, A Mencarelli. Lattice discrete particle model (LDPM) for failure behavior of concrete. I: Theory. Cement and Concrete Composites, 2011, 33(9): 881–890
https://doi.org/10.1016/j.cemconcomp.2011.02.011
79 G Cusatis, A Mencarelli, D Pelessone, J Baylot. Lattice discrete particle model (LDPM) for failure behavior of concrete. II: Calibration and validation. Cement and Concrete Composites, 2011, 33(9): 891–905
https://doi.org/10.1016/j.cemconcomp.2011.02.010
80 G Cusatis, Z P Bažant, L Cedolin. Confinement-shear lattice model for concrete damage in tension and compression: I. Theory. Journal of Engineering Mechanics, 2003, 129(12): 1439–1448
https://doi.org/10.1061/(ASCE)0733-9399(2003)129:12(1439)
81 G Cusatis, Z P Bažant, L Cedolin. Confinement-shear lattice model for concrete damage in tension and compression: II. Computation and validation. Journal of Engineering Mechanics, 2003, 129(12): 1449–1458
https://doi.org/10.1061/(ASCE)0733-9399(2003)129:12(1449)
82 G Cusatis, Z P Bažant, L Cedolin. Confinement-shear lattice CSL model for fracture propagation in concrete. Computer Methods in Applied Mechanics and Engineering, 2006, 195(52): 7154–7171
https://doi.org/10.1016/j.cma.2005.04.019
83 D. Pelessone Discrete Particle Method, Technical Report. Engineering and Software System Solutions, Inc., 2005
84 P Menetrey, K Willam. Triaxial failure criterion for concrete and its generalization. Structural Journal, 1995, 92(3): 311–318
85 P Grassl, K Lundgren, K Gylltoft. Concrete in compression: A plasticity theory with a novel hardening law. International Journal of Solids and Structures, 2002, 39(20): 5205–5223
https://doi.org/10.1016/S0020-7683(02)00408-0
86 V K Papanikolaou, A J Kappos. Confinement-sensitive plasticity constitutive model for concrete in triaxial compression. International Journal of Solids and Structures, 2007, 44(21): 7021–7048
https://doi.org/10.1016/j.ijsolstr.2007.03.022
87 J Červenka, V K Papanikolaou. Three dimensional combined fracture-plastic material model for concrete. International Journal of Plasticity, 2008, 24(12): 2192–2220
https://doi.org/10.1016/j.ijplas.2008.01.004
88 P Folino, G Etse. Performance dependent model for normal and high strength concretes. International Journal of Solids and Structures, 2012, 49(5): 701–719
https://doi.org/10.1016/j.ijsolstr.2011.11.020
89 M Ortiz. A constitutive theory for the inelastic behavior of concrete. Mechanics of Materials, 1985, 4(1): 67–93
https://doi.org/10.1016/0167-6636(85)90007-9
90 I Carol, E Rizzi, K Willam. On the formulation of anisotropic elastic degradation. I. Theory based on a pseudo-logarithmic damage tensor rate. International Journal of Solids and Structures, 2001, 38(4): 491–518
https://doi.org/10.1016/S0020-7683(00)00030-5
91 X Tao, D V Phillips. A simplified isotropic damage model for concrete under bi-axial stress states. Cement and Concrete Composites, 2005, 27(6): 716–726
https://doi.org/10.1016/j.cemconcomp.2004.09.017
92 G Z Voyiadjis, P I Kattan. A comparative study of damage variables in continuum damage mechanics. International Journal of Damage Mechanics, 2009, 18(4): 315–340
https://doi.org/10.1177/1056789508097546
93 L Jason, A Huerta, G Pijaudier-Cabot, S Ghavamian. An elastic plastic damage formulation for concrete: Application to elementary tests and comparison with an isotropic damage model. Computer Methods in Applied Mechanics and Engineering, 2006, 195(52): 7077–7092
https://doi.org/10.1016/j.cma.2005.04.017
94 P Grassl, M Jirásek. Damage-plastic model for concrete failure. International Journal of Solids and Structures, 2006, 43(22–23): 7166–7196
https://doi.org/10.1016/j.ijsolstr.2006.06.032
95 G D Nguyen, A M Korsunsky. Development of an approach to constitutive modelling of concrete: Isotropic damage coupled with plasticity. International Journal of Solids and Structures, 2008, 45(20): 5483–5501
https://doi.org/10.1016/j.ijsolstr.2008.05.029
96 G D Nguyen, G T Houlsby. A coupled damage-plasticity model for concrete based on thermodynamic principles: Part I: Model formulation and parameter identification. International Journal for Numerical and Analytical Methods in Geomechanics, 2008, 32(4): 353–389
https://doi.org/10.1002/nag.627
97 G Z Voyiadjis, Z N Taqieddin, P I Kattan. Anisotropic damage-plasticity model for concrete. International Journal of Plasticity, 2008, 24(10): 1946–1965
https://doi.org/10.1016/j.ijplas.2008.04.002
98 P Grassl. On a damage-plasticity approach to model concrete failure. Proceedings of the Institution of Civil Engineers, 2009, 162(em4): 221–231
99 P Sánchez, A Huespe, J Oliver, G Diaz, V Sonzogni. A macroscopic damage-plastic constitutive law for modeling quasi-brittle fracture and ductile behavior of concrete. International Journal for Numerical and Analytical Methods in Geomechanics, 2012, 36(5): 546–573
https://doi.org/10.1002/nag.1013
100 B V Hofstetter G. Review and enhancement of 3D concrete models for large-scale numerical simulations of concrete structures. International Journal for Numerical and Analytical Methods in Geomechanics, 2013, 37(3): 221–246
https://doi.org/10.1002/nag.1096
101 J Oliver, A E Huespe, E Samaniego, E Chaves. Continuum approach to the numerical simulation of material failure in concrete. International Journal for Numerical and Analytical Methods in Geomechanics, 2004, 28(78): 609–632
https://doi.org/10.1002/nag.365
102 J Tailhan, P Rossi, S Dal Pont. Macroscopic probabilistic modeling of concrete cracking: First 3D results. In: The 7th International Conference on Fracture Mechanics of Concrete and Concrete Structures. Seoul: Korea Concrete Institute, 2010, 238–242
103 R K Abu Al-Rub, S M Kim. Computational applications of a coupled plasticity-damage constitutive model for simulating plain concrete fracture. Engineering Fracture Mechanics, 2010, 77(10): 1577–1603
https://doi.org/10.1016/j.engfracmech.2010.04.007
104 Z P Bažant, P G Gambarova. Crack shear in concrete: Crack band microplane model. Journal of Structural Engineering, 1984, 110(9): 2015–2035
https://doi.org/10.1061/(ASCE)0733-9445(1984)110:9(2015)
105 Z P Bažant, Y Xiang, P C Prat. Microplane model for concrete. I: Stress-strain boundaries and finite strain. Journal of Engineering Mechanics, 1996, 122(3): 245–254
https://doi.org/10.1061/(ASCE)0733-9399(1996)122:3(245)
106 Z P Bažant, B H Oh. Microplane Model for Fracture Analysis of Concrete Structures, Technical Report. Northwestern University, Technological Institute, 1983
107 J Ožbolt, Y Li, I Kožar. Microplane model for concrete with relaxed kinematic constraint. International Journal of Solids and Structures, 2001, 38(16): 2683–2711
https://doi.org/10.1016/S0020-7683(00)00177-3
108 Z Yang, X Su, J F Chen, G Liu. Monte Carlo simulation of complex cohesive fracture in random heterogeneous quasi-brittle materials. International Journal of Solids and Structures, 2009, 46(17): 3222–3234
https://doi.org/10.1016/j.ijsolstr.2009.04.013
109 X Su, Z Yang, G Liu. Monte Carlo simulation of complex cohesive fracture in random heterogeneous quasi-brittle materials: A 3D study. International Journal of Solids and Structures, 2010, 47(17): 2336–2345
https://doi.org/10.1016/j.ijsolstr.2010.04.031
110 J Teng, W Zhu, C Tang. Mesomechanical model for concrete. Part II: Applications. Magazine of Concrete Research, 2004, 56(6): 331–345
https://doi.org/10.1680/macr.2004.56.6.331
111 H Zhu, S Zhou, Z Yan, W Ju, Q Chen. A 3D analytical model for the probabilistic characteristics of self-healing model for concrete using spherical microcapsule. Computers and Concrete, 2015, 15(1): 37–54
https://doi.org/10.12989/cac.2015.15.1.037
112 A Caballero, C L’opez, I Carol. 3D meso-structural analysis of concrete specimens under uniaxial tension. Computer Methods in Applied Mechanics and Engineering, 2006, 195(52): 7182–7195
https://doi.org/10.1016/j.cma.2005.05.052
113 D Trias, J Costa, B Fiedler, T Hobbiebrunken, J E Hurtado. A two scale method for matrix cracking probability in fibre-reinforced composites based on a statistical representative volume element. Composites Science and Technology, 2006, 66(11–12): 1766–1777
https://doi.org/10.1016/j.compscitech.2005.10.030
114 A Al-Ostaz, A Diwakar, K I Alzebdeh. Statistical model for characterizing random microstructure of inclusion-matrix composites. Journal of Materials Science, 2007, 42(16): 7016–7030
https://doi.org/10.1007/s10853-006-1117-1
115 W Ren, Z Yang, R Sharma, C Zhang, P J Withers. Two-dimensional X-ray CT image based meso-scale fracture modelling of concrete. Engineering Fracture Mechanics, 2015, 133: 24–39
https://doi.org/10.1016/j.engfracmech.2014.10.016
116 Y Huang, Z Yang, W Ren, G Liu, C Zhang. 3D meso-scale fracture modelling and validation of concrete based on in-situ X-ray Computed Tomography images using damage plasticity model. International Journal of Solids and Structures, 2015, 67–68: 340–352
https://doi.org/10.1016/j.ijsolstr.2015.05.002
117 X Du, L Jin, G Ma. Numerical modeling tensile failure behavior of concrete at mesoscale using extended finite element method. International Journal of Damage Mechanics, 2014, 23(7): 872–898
https://doi.org/10.1177/1056789513516028
118 S V Zemskov, H M Jonkers, F J Vermolen. A mathematical model for bacterial self-healing of cracks in concrete. Journal of Intelligent Material Systems and Structures, 2014, 25(1): 4–12
https://doi.org/10.1177/1045389X12437887
119 X Zhou, H Hao. Mesoscale modelling of concrete tensile failure mechanism at high strain rates. Computers & Structures, 2008, 86(21–22): 2013–2026
https://doi.org/10.1016/j.compstruc.2008.04.013
120 X Wang, Z Yang, J Yates, A Jivkov, C Zhang. Monte Carlo simulations of mesoscale fracture modelling of concrete with random aggregates and pores. Construction & Building Materials, 2015, 75: 35–45
https://doi.org/10.1016/j.conbuildmat.2014.09.069
121 X Wang, Z Yang, A P Jivkov. Monte Carlo simulations of mesoscale fracture of concrete with random aggregates and pores: A size effect study. Construction & Building Materials, 2015, 80: 262–272
https://doi.org/10.1016/j.conbuildmat.2015.02.002
122 X Wang, M Zhang, A P Jivkov. Computational technology for analysis of 3D meso-structure effects on damage and failure of concrete. International Journal of Solids and Structures, 2016, 80: 310–333
https://doi.org/10.1016/j.ijsolstr.2015.11.018
123 X Wang, A P Jivkov. Combined numerical-statistical analyses of damage and failure of 2D and 3D mesoscale heterogeneous concrete. Mathematical Problems in Engineering, 2015, 2015: 1–12
https://doi.org/10.1155/2015/702563
124 P S Koutsourelakis, G Deodatis. Simulation of multidimensional binary random fields with application to modeling of two-phase random media. Journal of Engineering Mechanics, 2006, 132(6): 619–631
https://doi.org/10.1061/(ASCE)0733-9399(2006)132:6(619)
125 X F Xu, L Graham-Brady. A stochastic computational method for evaluation of global and local behavior of random elastic media. Computer Methods in Applied Mechanics and Engineering, 2005, 194(42–44): 4362–4385
https://doi.org/10.1016/j.cma.2004.12.001
126 L Graham-Brady, X F Xu. Stochastic morphological modeling of random multiphase materials. Journal of Applied Mechanics, 2008, 75(6): 061001
https://doi.org/10.1115/1.2957598
127 T. Most Stochastic crack growth simulation in reinforced concrete structures by means of coupled finite element and meshless methods. Dissertation for the Doctoral Degree. Weimar: Bauhaus-Universität Weimar, 2005
128 M Bruggi, S Casciati, L Faravelli. Cohesive crack propagation in a random elastic medium. Probabilistic Engineering Mechanics, 2008, 23(1): 23–35
https://doi.org/10.1016/j.probengmech.2007.10.001
129 Z Yang, X F Xu. A heterogeneous cohesive model for quasi-brittle materials considering spatially varying random fracture properties. Computer Methods in Applied Mechanics and Engineering, 2008, 197(45–48): 4027–4039
https://doi.org/10.1016/j.cma.2008.03.027
130 P Grassl, D Grégoire, L Rojas Solano, G Pijaudier-Cabot. Meso-scale modelling of the size effect on the fracture process zone of concrete. International Journal of Solids and Structures, 2012, 49(13): 1818–1827
https://doi.org/10.1016/j.ijsolstr.2012.03.023
131 K M Hamdia, M Silani, X Zhuang, P He, T Rabczuk. Stochastic analysis of the fracture toughness of polymeric nanoparticle composites using polynomial chaos expansions. International Journal of Fracture, 2017, 206(2): 215–227
https://doi.org/10.1007/s10704-017-0210-6
132 K M Hamdia, X Zhuang, P He, T Rabczuk. Fracture toughness of polymeric particle nanocomposites: Evaluation of models performance using Bayesian method. Composites Science and Technology, 2016, 126: 122–129
https://doi.org/10.1016/j.compscitech.2016.02.012
133 K M Hamdia, T Lahmer, T Nguyen-Thoi, T Rabczuk. Predicting the fracture toughness of PNCS: A stochastic approach based on ann and anfis. Computational Materials Science, 2015, 102: 304–313
https://doi.org/10.1016/j.commatsci.2015.02.045
134 N Vu-Bac, T Lahmer, X Zhuang, T Nguyen-Thoi, T Rabczuk. A software framework for probabilistic sensitivity analysis for computationally expensive models. Advances in Engineering Software, 2016, 100: 19–31
https://doi.org/10.1016/j.advengsoft.2016.06.005
135 K M Hamdia, M A Msekh, M Silani, N Vu-Bac, X Zhuang, T Nguyen-Thoi, T Rabczuk. Uncertainty quantification of the fracture properties of polymeric nanocomposites based on phase field modeling. Composite Structures, 2015, 133: 1177–1190
https://doi.org/10.1016/j.compstruct.2015.08.051
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