Computational modeling of fracture in concrete: A review
Luthfi Muhammad MAULUDIN, Chahmi OUCIF
Computational modeling of fracture in concrete: A review
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.
concrete fracture / macroscopic / micromechanical / heterogeneity
[1] |
Bažant Z P, Tabbara M R, Kazemi M T, Pijaudier-Cabot G. Random particle model for fracture of aggregate or fiber composites. Journal of Engineering Mechanics, 1990, 116(8): 1686–1705
CrossRef
Google scholar
|
[2] |
Bolander J E Jr, Saito S. Fracture analyses using spring networks with random geometry. Engineering Fracture Mechanics, 1998, 61(5–6): 569–591
CrossRef
Google scholar
|
[3] |
Ragab Mohamed A, Hansen W. Micromechanical modeling of crack-aggregate interaction in concrete materials. Cement and Concrete Composites, 1999, 21(5–6): 349–359
CrossRef
Google scholar
|
[4] |
Schlangen E, van Mier J. Micromechanical analysis of fracture of concrete. International Journal of Damage Mechanics, 1992, 1(4): 435–454
CrossRef
Google scholar
|
[5] |
van Mier J, Vervuurt A. Numerical analysis of interface fracture in concrete using a lattice-type fracture model. International Journal of Damage Mechanics, 1997, 6(4): 408–432
CrossRef
Google scholar
|
[6] |
Grassl P, Jirásek M. 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
CrossRef
Google scholar
|
[7] |
López C M, Carol I, Aguado A. Meso-structural study of concrete fracture using interface elements. I: Numerical model and tensile behavior. Materials and Structures, 2008, 41(3): 583–599
CrossRef
Google scholar
|
[8] |
López C M, Carol I, Aguado A. Meso-structural study of concrete fracture using interface elements. II: Compression, biaxial and brazilian test. Materials and Structures, 2008, 41(3): 601–620
CrossRef
Google scholar
|
[9] |
Labanda N A, Giusti S M, Luccioni B M. Meso-scale fracture simulation using an augmented Lagrangian approach. International Journal of Damage Mechanics, 2016, 27(1): 1056789516671092
|
[10] |
Rabczuk T, Eibl J. Modelling dynamic failure of concrete with mesh-free methods. International Journal of Impact Engineering, 2006, 32(11): 1878–1897
CrossRef
Google scholar
|
[11] |
Rabczuk T, Zi G. Numerical fracture analysis of prestressed concrete beams. International Journal of Concrete Structures and Materials, 2008, 2(2): 153–160
CrossRef
Google scholar
|
[12] |
Rabczuk T, Xiao S P, Sauer M. 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] |
Rabczuk T, Zi G. A meshfree method based on the local partition of unity for cohesive cracks. Computational Mechanics, 2007, 39(6): 743–760
CrossRef
Google scholar
|
[14] |
Rabczuk T, Belytschko T. 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
CrossRef
Google scholar
|
[15] |
Rabczuk T, Bordas S, Zi G. A three-dimensional meshfree method for continuous multiple-crack initiation, propagation and junction in statics and dynamics. Computational Mechanics, 2007, 40(3): 473–495
CrossRef
Google scholar
|
[16] |
Zi G, Rabczuk T, Wall W. Extended meshfree methods without branch enrichment for cohesive cracks. Computational Mechanics, 2007, 40(2): 367–382
CrossRef
Google scholar
|
[17] |
Rabczuk T, Areias P. A Meshfree Thin Shell for Arbitrary Evolving Cracks Based on An Extrinsic Basis. Christchurch: University of Canterbury, 2006
|
[18] |
Areias P, Reinoso J, Camanho P, Rabczuk T. A constitutive-based element-by-element crack propagation algorithm with local mesh refinement. Computational Mechanics, 2015, 56(2): 291–315
CrossRef
Google scholar
|
[19] |
Areias P, Msekh M, Rabczuk T. Damage and fracture algorithm using the screened Poisson equation and local remeshing. Engineering Fracture Mechanics, 2016, 158: 116–143
CrossRef
Google scholar
|
[20] |
Areias P, Reinoso J, Camanho P P, César de Sá J, Rabczuk T. Effective 2D and 3D crack propagation with local mesh refinement and the screened Poisson equation. Engineering Fracture Mechanics, 2018, 189: 339–360
CrossRef
Google scholar
|
[21] |
Areias P, Rabczuk T. A novel two-stage discrete crack method based on the screened Poisson equation and local mesh refinement. Computational Mechanics, 2016, 58(6): 1003–1018
CrossRef
Google scholar
|
[22] |
Areias P, Rabczuk T, Msekh M. Phase-field analysis of finite-strain plates and shells including element subdivision. Computer Methods in Applied Mechanics and Engineering, 2016, 312: 322–350
CrossRef
Google scholar
|
[23] |
Msekh M A, Cuong N, Zi G, Areias P, Zhuang X, Rabczuk T. Fracture properties prediction of clay/epoxy nanocomposites with interphase zones using a phase field model. Engineering Fracture Mechanics, 2018, 188: 287–299
CrossRef
Google scholar
|
[24] |
Areias P, Rabczuk T, Dias-da Costa D. Element-wise fracture algorithm based on rotation of edges. Engineering Fracture Mechanics, 2013, 110: 113–137
CrossRef
Google scholar
|
[25] |
Areias P, Rabczuk T, Camanho P. Initially rigid cohesive laws and fracture based on edge rotations. Computational Mechanics, 2013, 52(4): 931–947
CrossRef
Google scholar
|
[26] |
Areias P, Rabczuk T. 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
CrossRef
Google scholar
|
[27] |
Rabczuk T, Belytschko T. Application of particle methods to static fracture of reinforced concrete structures. International Journal of Fracture, 2006, 137(1–4): 19–49
CrossRef
Google scholar
|
[28] |
Rabczuk T, Zi G, Bordas S, Nguyen-Xuan H. A simple and robust three-dimensional cracking-particle method without enrichment. Computer Methods in Applied Mechanics and Engineering, 2010, 199(37–40): 2437–2455
CrossRef
Google scholar
|
[29] |
Rabczuk T, Gracie R, Song J H, Belytschko T. Immersed particle method for fluid-structure interaction. International Journal for Numerical Methods in Engineering, 2010, 81(1): 48–71
|
[30] |
Ren H, Zhuang X, Cai Y, Rabczuk T. Dual-horizon peridynamics. International Journal for Numerical Methods in Engineering, 2016, 108(12): 1451–1476
CrossRef
Google scholar
|
[31] |
Ren H, Zhuang X, Rabczuk T. Dual-horizon peridynamics: A stable solution to varying horizons. Computer Methods in Applied Mechanics and Engineering, 2017, 318: 762–782
CrossRef
Google scholar
|
[32] |
Anitescu C, Hossain M N, Rabczuk T. 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
CrossRef
Google scholar
|
[33] |
Nguyen-Thanh N, Zhou K, Zhuang X, Areias P, Nguyen-Xuan H, Bazilevs Y, Rabczuk T. 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
CrossRef
Google scholar
|
[34] |
Nguyen B, Tran H, Anitescu C, Zhuang X, Rabczuk T. An isogeometric symmetric galerkin boundary element method for two-dimensional crack problems. Computer Methods in Applied Mechanics and Engineering, 2016, 306: 252–275
CrossRef
Google scholar
|
[35] |
Thai T Q, Rabczuk T, Bazilevs Y, Meschke G. A higher-order stress based gradient-enhanced damage model based on isogeometric analysis. Computer Methods in Applied Mechanics and Engineering, 2016, 304: 584–604
CrossRef
Google scholar
|
[36] |
Nguyen-Thanh N, Valizadeh N, Nguyen M, Nguyen-Xuan H, Zhuang X, Areias P, Zi G, Bazilevs Y, De Lorenzis L, Rabczuk T. An extended isogeometric thin shell analysis based on Kirchhoff-Love theory. Computer Methods in Applied Mechanics and Engineering, 2015, 284: 265–291
CrossRef
Google scholar
|
[37] |
Ghorashi S S, Valizadeh N, Mohammadi S, Rabczuk T. T-spline based XIGA for fracture analysis of orthotropic media. Computers & Structures, 2015, 147: 138–146
CrossRef
Google scholar
|
[38] |
Silani M, Talebi H, Hamouda A M, Rabczuk T. Nonlocal damage modelling in clay/epoxy nanocomposites using a multiscale approach. Journal of Computational Science, 2016, 15: 18–23
CrossRef
Google scholar
|
[39] |
Talebi H, Silani M, Rabczuk T. Concurrent multiscale modeling of three dimensional crack and dislocation propagation. Advances in Engineering Software, 2015, 80: 82–92
CrossRef
Google scholar
|
[40] |
Talebi H, Silani M, Bordas S P, Kerfriden P, Rabczuk T. A computational library for multiscale modeling of material failure. Computational Mechanics, 2014, 53(5): 1047–1071
CrossRef
Google scholar
|
[41] |
Budarapu P R, Gracie R, Bordas S P, Rabczuk T. An adaptive multiscale method for quasi-static crack growth. Computational Mechanics, 2014, 53(6): 1129–1148
CrossRef
Google scholar
|
[42] |
Budarapu P R, Gracie R, Yang S W, Zhuang X, Rabczuk T. Efficient coarse graining in multiscale modeling of fracture. Theoretical and Applied Fracture Mechanics, 2014, 69: 126–143
CrossRef
Google scholar
|
[43] |
Amiri F, Anitescu C, Arroyo M, Bordas S P A, Rabczuk T. XLME interpolants, a seamless bridge between XFEM and enriched meshless methods. Computational Mechanics, 2014, 53(1): 45–57
CrossRef
Google scholar
|
[44] |
Chen L, Rabczuk T, Bordas S P A, Liu G, Zeng K, Kerfriden P. 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
CrossRef
Google scholar
|
[45] |
Rabczuk T, Bordas S, Zi G. On three-dimensional modelling of crack growth using partition of unity methods. Computers & Structures, 2010, 88(23–24): 1391–1411
CrossRef
Google scholar
|
[46] |
Areias P, Rabczuk T, Camanho P. Finite strain fracture of 2d problems with injected anisotropic softening elements. Theoretical and Applied Fracture Mechanics, 2014, 72: 50–63
CrossRef
Google scholar
|
[47] |
Rabczuk T, Zi G, Bordas S, Nguyen-Xuan H. A geometrically non-linear three-dimensional cohesive crack method for reinforced concrete structures. Engineering Fracture Mechanics, 2008, 75(16): 4740–4758
CrossRef
Google scholar
|
[48] |
Areias P M, Rabczuk T. 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
CrossRef
Google scholar
|
[49] |
De Borst R. Some recent developments in computational modelling of concrete fracture. International Journal of Fracture, 1997, 86(1–2): 5–36
CrossRef
Google scholar
|
[50] |
Murthy A R C, Palani G, Iyer N R. State-of-the-art review on fracture analysis of concrete structural components. Sadhana, 2009, 34(2): 345–367
CrossRef
Google scholar
|
[51] |
Wu M, Johannesson B, Geiker M. A review: Self-healing in cementitious materials and engineered cementitious composite as a self-healing material. Construction & Building Materials, 2012, 28(1): 571–583
CrossRef
Google scholar
|
[52] |
Van Tittelboom K, De Belie N. Self-healing in cementitious materials: A review. Materials (Basel), 2013, 6(6): 2182–2217
CrossRef
Google scholar
|
[53] |
Talaiekhozan A, Keyvanfar A, Shafaghat A,
|
[54] |
Lv Z, Chen D. Overview of recent work on self-healing in cementitious materials. Materiales de Construccion, 2014, 64(316): 034
|
[55] |
Ahn E, Kim H, Sim S H, Shin S W, Shin M. Principles and applications of ultrasonic-based nondestructive methods for self-healing in cementitious materials. Materials (Basel), 2017, 10(3): 278
CrossRef
Google scholar
|
[56] |
Mauludin L, Oucif C. Modeling of self-healing concrete: A review. Journal of Applied and Computational Mechanics, 2017, 5: 526–539
CrossRef
Google scholar
|
[57] |
Mauludin L M, Oucif C. The effects of interfacial strength on fractured microcapsule. Frontiers of Structural and Civil Engineering, 2019, 13(2): 353–363
|
[58] |
Mauludin L M, Oucif C. Interaction between matrix crack and circular capsule under uniaxial tension in encapsulation-based self-healing concrete. Underground Space, 2018, 3(3): 181–189
CrossRef
Google scholar
|
[59] |
Mauludin L M, Zhuang X, Rabczuk T. Computational modeling of fracture in encapsulation-based self-healing concrete using cohesive elements. Composite Structures, 2018, 196: 63–75
CrossRef
Google scholar
|
[60] |
Oucif C, Mauludin L. Continuum damage-healing and super healing mechanics in brittle materials: A state-of-the-art review. Applied Sciences (Basel, Switzerland), 2018, 8(12): 2350
CrossRef
Google scholar
|
[61] |
Oucif C, Ouzaa K, Mauludin L M. Cyclic and monotonic behavior of strengthened and unstrengthened square reinforced concrete columns. Journal of Applied and Computational Mechanics, 2019, 5: 517–525
CrossRef
Google scholar
|
[62] |
Rabczuk T. 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] |
Djoković J M, Nikolić R R, Bujnak J. Fundamental problems of modeling the fracture processes in concrete I: Micromechanics and localization of damages. Procedia Engineering, 2013, 65: 186–195
CrossRef
Google scholar
|
[64] |
Djoković J M, Nikolić R R, Bujnak J. Fundamental problems of modeling the fracture processes in concrete II: Size effect and selection of the solution approach. Procedia Engineering, 2013, 65: 196–205
CrossRef
Google scholar
|
[65] |
Jendele L, Cervenka J, Saouma V, Pukl R. 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] |
Hillerborg A, Modéer M, Petersson P E. 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
CrossRef
Google scholar
|
[67] |
Jirásek M, Zimmermann T. Rotating crack model with transition to scalar damage. Journal of Engineering Mechanics, 1998, 124(3): 277–284
CrossRef
Google scholar
|
[68] |
Xu X P, Needleman A. Numerical simulations of dynamic crack growth along an interface. International Journal of Fracture, 1996, 74(4): 289–324
CrossRef
Google scholar
|
[69] |
Samaniego Alvarado E. Contributions to the Continuum Modelling of Strong Discontinuities in Two-dimensional Solids. Dissertation for the Doctoral Degree. Barcelona: Universitat Politécnica de Catalunya, 2003
|
[70] |
Belytschko T, Lu Y Y, Gu L. Element-free galerkin methods. International Journal for Numerical Methods in Engineering, 1994, 37(2): 229–256
CrossRef
Google scholar
|
[71] |
Wells G N, Sluys L. A new method for modelling cohesive cracks using finite elements. International Journal for Numerical Methods in Engineering, 2001, 50(12): 2667–2682
CrossRef
Google scholar
|
[72] |
Rabczuk T, Akkermann J, Eibl J. A numerical model for reinforced concrete structures. International Journal of Solids and Structures, 2005, 42(5–6): 1327–1354
CrossRef
Google scholar
|
[73] |
Rabczuk T, Belytschko T. Cracking particles: A simplified meshfree method for arbitrary evolving cracks. International Journal for Numerical Methods in Engineering, 2004, 61(13): 2316–2343
CrossRef
Google scholar
|
[74] |
Hrennikoff A. Solution of problems of elasticity by the framework method. Journal of Applied Mechanics, 1941, 8(4): 169–175
|
[75] |
Schlangen E, van Mier J. Simple lattice model for numerical simulation of fracture of concrete materials and structures. Materials and Structures, 1992, 25(9): 534–542
CrossRef
Google scholar
|
[76] |
Schlangen E, Garboczi E. Fracture simulations of concrete using lattice models: Computational aspects. Engineering Fracture Mechanics, 1997, 57(2–3): 319–332
CrossRef
Google scholar
|
[77] |
Lilliu G, van Mier J G M. 3D lattice type fracture model for concrete. Engineering Fracture Mechanics, 2003, 70(7–8): 927–941
CrossRef
Google scholar
|
[78] |
Cusatis G, Pelessone D, Mencarelli A. Lattice discrete particle model (LDPM) for failure behavior of concrete. I: Theory. Cement and Concrete Composites, 2011, 33(9): 881–890
CrossRef
Google scholar
|
[79] |
Cusatis G, Mencarelli A, Pelessone D, Baylot J. Lattice discrete particle model (LDPM) for failure behavior of concrete. II: Calibration and validation. Cement and Concrete Composites, 2011, 33(9): 891–905
CrossRef
Google scholar
|
[80] |
Cusatis G, Bažant Z P, Cedolin L. Confinement-shear lattice model for concrete damage in tension and compression: I. Theory. Journal of Engineering Mechanics, 2003, 129(12): 1439–1448
CrossRef
Google scholar
|
[81] |
Cusatis G, Bažant Z P, Cedolin L. Confinement-shear lattice model for concrete damage in tension and compression: II. Computation and validation. Journal of Engineering Mechanics, 2003, 129(12): 1449–1458
CrossRef
Google scholar
|
[82] |
Cusatis G, Bažant Z P, Cedolin L. Confinement-shear lattice CSL model for fracture propagation in concrete. Computer Methods in Applied Mechanics and Engineering, 2006, 195(52): 7154–7171
CrossRef
Google scholar
|
[83] |
Pelessone D. Discrete Particle Method, Technical Report. Engineering and Software System Solutions, Inc., 2005
|
[84] |
Menetrey P, Willam K. Triaxial failure criterion for concrete and its generalization. Structural Journal, 1995, 92(3): 311–318
|
[85] |
Grassl P, Lundgren K, Gylltoft K. Concrete in compression: A plasticity theory with a novel hardening law. International Journal of Solids and Structures, 2002, 39(20): 5205–5223
CrossRef
Google scholar
|
[86] |
Papanikolaou V K, Kappos A J. Confinement-sensitive plasticity constitutive model for concrete in triaxial compression. International Journal of Solids and Structures, 2007, 44(21): 7021–7048
CrossRef
Google scholar
|
[87] |
Červenka J, Papanikolaou V K. Three dimensional combined fracture-plastic material model for concrete. International Journal of Plasticity, 2008, 24(12): 2192–2220
CrossRef
Google scholar
|
[88] |
Folino P, Etse G. Performance dependent model for normal and high strength concretes. International Journal of Solids and Structures, 2012, 49(5): 701–719
CrossRef
Google scholar
|
[89] |
Ortiz M. A constitutive theory for the inelastic behavior of concrete. Mechanics of Materials, 1985, 4(1): 67–93
CrossRef
Google scholar
|
[90] |
Carol I, Rizzi E, Willam K. 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
CrossRef
Google scholar
|
[91] |
Tao X, Phillips D V. A simplified isotropic damage model for concrete under bi-axial stress states. Cement and Concrete Composites, 2005, 27(6): 716–726
CrossRef
Google scholar
|
[92] |
Voyiadjis G Z, Kattan P I. A comparative study of damage variables in continuum damage mechanics. International Journal of Damage Mechanics, 2009, 18(4): 315–340
CrossRef
Google scholar
|
[93] |
Jason L, Huerta A, Pijaudier-Cabot G, Ghavamian S. 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
CrossRef
Google scholar
|
[94] |
Grassl P, Jirásek M. Damage-plastic model for concrete failure. International Journal of Solids and Structures, 2006, 43(22–23): 7166–7196
CrossRef
Google scholar
|
[95] |
Nguyen G D, Korsunsky A M. 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
CrossRef
Google scholar
|
[96] |
Nguyen G D, Houlsby G T. 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
CrossRef
Google scholar
|
[97] |
Voyiadjis G Z, Taqieddin Z N, Kattan P I. Anisotropic damage-plasticity model for concrete. International Journal of Plasticity, 2008, 24(10): 1946–1965
CrossRef
Google scholar
|
[98] |
Grassl P. On a damage-plasticity approach to model concrete failure. Proceedings of the Institution of Civil Engineers, 2009, 162(em4): 221–231
|
[99] |
Sánchez P, Huespe A, Oliver J, Diaz G, Sonzogni V. 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
CrossRef
Google scholar
|
[100] |
Hofstetter B V 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
CrossRef
Google scholar
|
[101] |
Oliver J, Huespe A E, Samaniego E, Chaves E. 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
CrossRef
Google scholar
|
[102] |
Tailhan J, Rossi P, Dal Pont S. 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] |
Abu Al-Rub R K, Kim S M. Computational applications of a coupled plasticity-damage constitutive model for simulating plain concrete fracture. Engineering Fracture Mechanics, 2010, 77(10): 1577–1603
CrossRef
Google scholar
|
[104] |
Bažant Z P, Gambarova P G. Crack shear in concrete: Crack band microplane model. Journal of Structural Engineering, 1984, 110(9): 2015–2035
CrossRef
Google scholar
|
[105] |
Bažant Z P, Xiang Y, Prat P C. Microplane model for concrete. I: Stress-strain boundaries and finite strain. Journal of Engineering Mechanics, 1996, 122(3): 245–254
CrossRef
Google scholar
|
[106] |
Bažant Z P, Oh B H. Microplane Model for Fracture Analysis of Concrete Structures, Technical Report. Northwestern University, Technological Institute, 1983
|
[107] |
Ožbolt J, Li Y, Kožar I. Microplane model for concrete with relaxed kinematic constraint. International Journal of Solids and Structures, 2001, 38(16): 2683–2711
CrossRef
Google scholar
|
[108] |
Yang Z, Su X, Chen J F, Liu G. Monte Carlo simulation of complex cohesive fracture in random heterogeneous quasi-brittle materials. International Journal of Solids and Structures, 2009, 46(17): 3222–3234
CrossRef
Google scholar
|
[109] |
Su X, Yang Z, Liu G. 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
CrossRef
Google scholar
|
[110] |
Teng J, Zhu W, Tang C. Mesomechanical model for concrete. Part II: Applications. Magazine of Concrete Research, 2004, 56(6): 331–345
CrossRef
Google scholar
|
[111] |
Zhu H, Zhou S, Yan Z, Ju W, Chen Q. 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
CrossRef
Google scholar
|
[112] |
Caballero A, L’opez C, Carol I. 3D meso-structural analysis of concrete specimens under uniaxial tension. Computer Methods in Applied Mechanics and Engineering, 2006, 195(52): 7182–7195
CrossRef
Google scholar
|
[113] |
Trias D, Costa J, Fiedler B, Hobbiebrunken T, Hurtado J E. 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
CrossRef
Google scholar
|
[114] |
Al-Ostaz A, Diwakar A, Alzebdeh K I. Statistical model for characterizing random microstructure of inclusion-matrix composites. Journal of Materials Science, 2007, 42(16): 7016–7030
CrossRef
Google scholar
|
[115] |
Ren W, Yang Z, Sharma R, Zhang C, Withers P J. Two-dimensional X-ray CT image based meso-scale fracture modelling of concrete. Engineering Fracture Mechanics, 2015, 133: 24–39
CrossRef
Google scholar
|
[116] |
Huang Y, Yang Z, Ren W, Liu G, Zhang C. 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
CrossRef
Google scholar
|
[117] |
Du X, Jin L, Ma G. Numerical modeling tensile failure behavior of concrete at mesoscale using extended finite element method. International Journal of Damage Mechanics, 2014, 23(7): 872–898
CrossRef
Google scholar
|
[118] |
Zemskov S V, Jonkers H M, Vermolen F J. A mathematical model for bacterial self-healing of cracks in concrete. Journal of Intelligent Material Systems and Structures, 2014, 25(1): 4–12
CrossRef
Google scholar
|
[119] |
Zhou X, Hao H. Mesoscale modelling of concrete tensile failure mechanism at high strain rates. Computers & Structures, 2008, 86(21–22): 2013–2026
CrossRef
Google scholar
|
[120] |
Wang X, Yang Z, Yates J, Jivkov A, Zhang C. Monte Carlo simulations of mesoscale fracture modelling of concrete with random aggregates and pores. Construction & Building Materials, 2015, 75: 35–45
CrossRef
Google scholar
|
[121] |
Wang X, Yang Z, Jivkov A P. Monte Carlo simulations of mesoscale fracture of concrete with random aggregates and pores: A size effect study. Construction & Building Materials, 2015, 80: 262–272
CrossRef
Google scholar
|
[122] |
Wang X, Zhang M, Jivkov A P. 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
CrossRef
Google scholar
|
[123] |
Wang X, Jivkov A P. Combined numerical-statistical analyses of damage and failure of 2D and 3D mesoscale heterogeneous concrete. Mathematical Problems in Engineering, 2015, 2015: 1–12
CrossRef
Google scholar
|
[124] |
Koutsourelakis P S, Deodatis G. Simulation of multidimensional binary random fields with application to modeling of two-phase random media. Journal of Engineering Mechanics, 2006, 132(6): 619–631
CrossRef
Google scholar
|
[125] |
Xu X F, Graham-Brady L. 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
CrossRef
Google scholar
|
[126] |
Graham-Brady L, Xu X F. Stochastic morphological modeling of random multiphase materials. Journal of Applied Mechanics, 2008, 75(6): 061001
CrossRef
Google scholar
|
[127] |
Most T. 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] |
Bruggi M, Casciati S, Faravelli L. Cohesive crack propagation in a random elastic medium. Probabilistic Engineering Mechanics, 2008, 23(1): 23–35
CrossRef
Google scholar
|
[129] |
Yang Z, Xu X F. 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
CrossRef
Google scholar
|
[130] |
Grassl P, Grégoire D, Rojas Solano L, Pijaudier-Cabot G. 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
CrossRef
Google scholar
|
[131] |
Hamdia K M, Silani M, Zhuang X, He P, Rabczuk T. Stochastic analysis of the fracture toughness of polymeric nanoparticle composites using polynomial chaos expansions. International Journal of Fracture, 2017, 206(2): 215–227
CrossRef
Google scholar
|
[132] |
Hamdia K M, Zhuang X, He P, Rabczuk T. Fracture toughness of polymeric particle nanocomposites: Evaluation of models performance using Bayesian method. Composites Science and Technology, 2016, 126: 122–129
CrossRef
Google scholar
|
[133] |
Hamdia K M, Lahmer T, Nguyen-Thoi T, Rabczuk T. Predicting the fracture toughness of PNCS: A stochastic approach based on ann and anfis. Computational Materials Science, 2015, 102: 304–313
CrossRef
Google scholar
|
[134] |
Vu-Bac N, Lahmer T, Zhuang X, Nguyen-Thoi T, Rabczuk T. A software framework for probabilistic sensitivity analysis for computationally expensive models. Advances in Engineering Software, 2016, 100: 19–31
CrossRef
Google scholar
|
[135] |
Hamdia K M, Msekh M A, Silani M, Vu-Bac N, Zhuang X, Nguyen-Thoi T, Rabczuk T. Uncertainty quantification of the fracture properties of polymeric nanocomposites based on phase field modeling. Composite Structures, 2015, 133: 1177–1190
CrossRef
Google scholar
|
/
〈 | 〉 |