A unified phase-field theory for the mechanics of damage and quasi-brittle failure

Journal of the Mechanics and Physics of Solids - Tập 103 - Trang 72-99 - 2017
Jian‐Ying Wu1
1State Key Laboratory of Subtropical Building Science, South China University of Technology, 510641 Guangzhou, China

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Alicandro, 1999, Free-discontinuitiy problems via functionals involving the l1-norm of the gradient and their approximations, Interf. Free Bound., 1, 17, 10.4171/IFB/2

Ambati, 2015, A review on phase-field models for brittle fracture and a new fast hybrid formulation, Comput. Mech., 55, 383, 10.1007/s00466-014-1109-y

Ambrosio, 2000

Amor, 2009, Regularized formulation of the variational brittle fracture with unilateral contact: numerical experiments, J. Mech. Phys. Solids, 57, 1209, 10.1016/j.jmps.2009.04.011

Aranson, 2000, Continuum field description of crack propagation, Phys. Rev. Lett., 85, 118, 10.1103/PhysRevLett.85.118

Balay, 2016, PETSc Users Manual

Borden, 2014, A higher-order phase-field model for brittle fracture: formulation and analysis within the isogeometric analysis framework, Comput. Methods Appl. Mech. Engrg., 273, 100, 10.1016/j.cma.2014.01.016

de Borst, 2016, Gradient damage vs phase-field approaches for fracture: similarities and differences, Comput. Methods Appl. Mech. Engrg., 10.1016/j.cma.2016.05.015

Bourdin, 2000, Numerical experiments in revisited brittle fracture, J. Mech. Phys. Solids, 48, 797, 10.1016/S0022-5096(99)00028-9

Bourdin, 2008

Bourdin, 2011, A time-discrete model for dynamic fracture based on crack regularization, Int. J. Frac., 168, 133, 10.1007/s10704-010-9562-x

Bourdin, 2014, Morphogenesis and propagation of complex cracks induced by thermal shocks, Phys. Rev. Lett., 112, 014301, 10.1103/PhysRevLett.112.014301

Braides, 1999, Variational formulation of softening phenomena in fracture mechanics: the one-dimensional case, Arch. Ration. Mech. Anal., 146, 23, 10.1007/s002050050135

Conti, 2015, Phase field approximation of cohesive fracture models, Annales de l’Institut Henri Poincare (C) Non Linear Anal., 33, 1033, 10.1016/j.anihpc.2015.02.001

Cornelissen, 1986, Experimental determination of crack softening characteristics of normalweight and lightweight concrete, Heron, 31, 45

Dumstorff, 2007, Crack propagation criteria in the framework of x-fem-based structural analyses, Int. J. Numer. Anal. Methods Geomech., 31, 239, 10.1002/nag.560

Farrell, 2016, Linear and nonlinear solvers for variational phase-field models of brittle fracture, Int. J. Numer. Meth. Eng.

Focardi, 2017, Numerical insight of a variational smeared approach to cohesive fracture, J. Mech. Phys. Solids, 98, 156, 10.1016/j.jmps.2016.09.003

Francfort, 1998, Revisting brittle fracture as an energy minimization problem, J. Mech. Phys. Solids, 46, 1319, 10.1016/S0022-5096(98)00034-9

Frémond, 1996, Damage, gradient of damage and principle of virtual power, int. J. Solids Struct., 33, 1083, 10.1016/0020-7683(95)00074-7

Geuzaine, 2009, Gmsh: a three-dimensional finite element mesh generator with built-in pre- and post-processing facilities, Int. J. Numer. Eng., 79(11), 1309, 10.1002/nme.2579

Hakim, 2009, Laws of crack motion and phase-field models of fracture, J. Mech. Phys. Solids, 57, 342, 10.1016/j.jmps.2008.10.012

Hofacker, 2013, A phase field model of dynamic fracture: robust field updates for the analysis of complex crack patterns, Int. J. Numer. Eng., 93, 276, 10.1002/nme.4387

Jirásek, 2002, Computational resolution of strong discontinuities

Jirásek, 1998, Analysis of rotating crack model, J. Eng. Mech. ASCE, 124, 842, 10.1061/(ASCE)0733-9399(1998)124:8(842)

Karma, 2001, Phase-field model of mode iii dynamic fracture, Phys. Rev. Lett., 87, 118, 10.1103/PhysRevLett.87.045501

Kuhn, 2010, A continuum phase field model for fracture, Eng. Fract. Mech., 77, 3625, 10.1016/j.engfracmech.2010.08.009

Kuhn, 2015, On degradation functions in phase field fracture models, Comput. Mater. Sci., 108, 374, 10.1016/j.commatsci.2015.05.034

Landau, 1980

Li, 2016, Gradient damage modeling of brittle fracture in an explicit dynamics context, Int. J. Numer. Meth. Eng., 10.1002/nme.5262

Lorentz, 2011, Gradient damage models: towards full-scale computations, Comput. Methods Appl. Mech. Eng., 200, 1927, 10.1016/j.cma.2010.06.025

May, 2015, A numerical assessment of phase-field models for brittle and cohesive fracture: G-convergence and stress oscillations, Eur. J. Mech. A Solids, 52, 72, 10.1016/j.euromechsol.2015.02.002

Miehe, 2015, Phase field modeling of fracture in multi-physics problems. part i. balance of crack surface and failure criteria for brittle crack propagation in thermo-elastic solids, Comput. Methods Appl. Mech. Eng., 294, 449, 10.1016/j.cma.2014.11.016

Miehe, 2010, Thermodynamically consistent phase-field models of fracture: variational principles and multi-field fe implementations, Int. J. Numer. Meth. Eng., 83, 1273, 10.1002/nme.2861

Negri, 1999, The anisotropy introduced by the mesh in the finite element approximation of the mumford-shah functional, Numer. Funct. Anal. Optim., 20, 957, 10.1080/01630569908816934

Ngo, 1967, Finite element analysis of reinforced concrete beams, ACI J., 64, 152

Peerlings, 1996, Gradient-enhanced damage for quasi-brittle materials, Int. J. Numer. Methods Eng., 39, 3391, 10.1002/(SICI)1097-0207(19961015)39:19<3391::AID-NME7>3.0.CO;2-D

Pham, 2011, Gradient damage models and their use to approximate brittle fracture, Int. J. Dam. Mech., 20, 618, 10.1177/1056789510386852

Pijaudier-Cabot, 1987, Nonlocal damage theory, J. Eng. Mech. ASCE, 113, 1512, 10.1061/(ASCE)0733-9399(1987)113:10(1512)

Rashid, 1968, Analysis of prestressed concrete pressure vessels, Nucl. Eng. Des., 7, 334, 10.1016/0029-5493(68)90066-6

Rots, 1988

Sicsic, 2013, From gradient damage laws to griffith’s theory of crack propagation, J. Elastic., 113, 55, 10.1007/s10659-012-9410-5

Simó, 1987, Strain- and stress-based continuum damage models. i: formulation; ii: computational aspects, Int. J. Solids Struct., 23, 821, 10.1016/0020-7683(87)90083-7

Spatschek, 2011, Phase field modeling of crack propagation, Philos. Mag., 9, 75, 10.1080/14786431003773015

Unger, 2007, Modelling of cohesive crack growth in concrete structures with the extended finite element method, Comput. Methods Appl. Mech. Eng., 196, 4087, 10.1016/j.cma.2007.03.023

Verhoosel, 2013, A phase-field model for cohesive fracture, Int. J. Numer. Meth. Engng., 96, 43, 10.1002/nme.4553

Vignollet, 2014, Phase-field models for brittle and cohesive fracture, Meccanica, 49, 2587, 10.1007/s11012-013-9862-0

Winkler, 2001

Wu, 2011, Unified analysis of enriched finite elements for modeling cohesive cracks, Comput. Methods Appl. Mech. Eng., 200, 3031, 10.1016/j.cma.2011.05.008

Wu, 2013, Strain localization in elastoplastic damage solids, 497

Zamani, 2012, Cohesive and non-cohesive fracture by higher-order enrichment of xfem, Int. J. Numer. Meth. Eng., 90, 452, 10.1002/nme.3329