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

Miehe, 2010, Thermodynamically consistent phase-field models of fracture: Variational principles and multi-field FE implementations, Internat. J. Numer. Methods Engrg., 83, 1273, 10.1002/nme.2861 Miehe, 2010, A phase field model for rate-independent crack propagation: Robust algorithmic implementation based on operator splits, Comput. Methods Appl. Mech. Engrg., 199, 2765, 10.1016/j.cma.2010.04.011 Borden, 2012, A phase-field description of dynamic brittle fracture, Comput. Methods Appl. Mech. Engrg., 217–220, 77, 10.1016/j.cma.2012.01.008 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 Verhoosel, 2013, A phase-field model for cohesive fracture, Internat. J. Numer. Methods Engrg., 96, 43, 10.1002/nme.4553 Ambrosio, 1990, Approximation of functionals depending on jumps by elliptic functionals via Γ-convergence, Comm. Pure Appl. Math., 43, 999, 10.1002/cpa.3160430805 Ambrosio, 1992, On the approximation of free discontinuity problems, Boll. Unione Mat. Ital., 6-B, 105 Dal Maso, 1993 Braides, 2002 Braides, 1998 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 Karma, 2001, Phase-field model of mode III dynamic fracture, Phys. Rev. Lett., 87, 045501, 10.1103/PhysRevLett.87.045501 Eastgate, 2002, Fracture in mode I using a conserved phase-field model, Phys. Rev. E, 65, 036117, 10.1103/PhysRevE.65.036117 Kuhn, 2010, A continuum phase field model for fracture, Eng. Fract. Mech., 77, 3625, 10.1016/j.engfracmech.2010.08.009 Francfort, 1998, Revisiting brittle fracture as an energy minimization problem, J. Mech. Phys. Solids, 46, 1319, 10.1016/S0022-5096(98)00034-9 Bourdin, 2008 Capriz, 1989 Mariano, 2001, Multifield theories in mechanics of solids, Adv. Appl. Mech., 38, 1 Frémond, 2002 Miehe, 2011, A multi-field incremental variational framework for gradient-extended standard dissipative solids, J. Mech. Phys. Solids, 59, 898, 10.1016/j.jmps.2010.11.001 Frémond, 1996, Damage, gradient of damage, and principle of virtual power, Internat. J. Solids Structures, 33, 1083, 10.1016/0020-7683(95)00074-7 Peerlings, 1996, Gradient enhanced damage for quasi-brittle materials, Internat. J. Numer. Methods Engrg., 39, 3391, 10.1002/(SICI)1097-0207(19961015)39:19<3391::AID-NME7>3.0.CO;2-D Comi, 1999, Computational modelling of gradient-enhanced damage in quasi-brittle materials, Mech. Cohes.-Frict. Mater., 4, 17, 10.1002/(SICI)1099-1484(199901)4:1<17::AID-CFM55>3.0.CO;2-6 Comi, 2001, Fracture energy based bi-dissipative damage model for concrete, Internat. J. Solids Structures, 38, 6427, 10.1016/S0020-7683(01)00066-X Pham, 2011, Gradient damage models and their use to approximate brittle fracture, Int. J. Damage Mech., 20, 618, 10.1177/1056789510386852 Xu, 1993, Void nucleation by inclusion debonding in a crystal matrix, Modelling Simul. Mater. Sci. Eng., 1, 111, 10.1088/0965-0393/1/2/001 Ortiz, 1999, Finite-deformation irreversible cohesive elements for three-dimensional crack-propagation analysis, Internat. J. Numer. Methods Engrg., 44, 1267, 10.1002/(SICI)1097-0207(19990330)44:9<1267::AID-NME486>3.0.CO;2-7 Miehe, 2007, A robust algorithm for configurational-force-driven brittle crack propagation with R-adaptive mesh alignment, Internat. J. Numer. Methods Engrg., 72, 127, 10.1002/nme.1999 Gürses, 2009, A computational framework of three-dimensional configurational-force-driven brittle crack propagation, Comput. Methods Appl. Mech. Engrg., 198, 1413, 10.1016/j.cma.2008.12.028 Simo, 1993, An analysis of strong discontinuities induced by strain-softening in rate-independent inelastic solids, Comput. Mech., 12, 277, 10.1007/BF00372173 Oliver, 1996, Modelling strong discontinuities in solid mechanics via strain softening constitutive equations. Part 1: Fundamentals, Internat. J. Numer. Methods Engrg., 39, 3575, 10.1002/(SICI)1097-0207(19961115)39:21<3575::AID-NME65>3.0.CO;2-E Oliver, 1996, Modelling strong discontinuities in solid mechanics via strain softening constitutive equations. Part 2: Numerical simulation, Internat. J. Numer. Methods Engrg., 39, 3601, 10.1002/(SICI)1097-0207(19961115)39:21<3601::AID-NME64>3.0.CO;2-4 Linder, 2009, Finite elements with embedded branching, Finite Elem. Anal. Des., 45, 280, 10.1016/j.finel.2008.10.012 Moës, 1999, A finite element method for crack growth without remeshing, Internat. J. Numer. Methods Engrg., 46, 131, 10.1002/(SICI)1097-0207(19990910)46:1<131::AID-NME726>3.0.CO;2-J Wells, 2001, A new method for modelling cohesive cracks using finite elements, Internat. J. Numer. Methods Engrg., 50, 2667, 10.1002/nme.143 Gasser, 2005, Modeling 3D crack propagation in unreinforced concrete using pufem, Comput. Methods Appl. Mech. Engrg., 194, 2859, 10.1016/j.cma.2004.07.025 Belytschko, 2003, Dynamic crack propagation based on loss of hyperbolicity and a new discontinuous enrichment, Internat. J. Numer. Methods Engrg., 58, 1873, 10.1002/nme.941 Song, 2009, Cracking node method for dynamic fracture with finite elements, Internat. J. Numer. Methods Engrg., 77, 360, 10.1002/nme.2415 Protter, 1984 Benallal, 2007, Bifurcation and stability issues in gradient theories with softening, Modelling Simul. Mater. Sci. Eng., 15, S283, 10.1088/0965-0393/15/1/S22 Lu, 1975, Decomposition of the deformation and representation of the free energy function for isotropic thermoelastic solids, Internat. J. Solids Structures, 11, 927, 10.1016/0020-7683(75)90015-3 Miehe, 1995, Entropic thermoelasticity at finite strains. Aspects of the formulation and numerical implementation, Comput. Methods Appl. Mech. Engrg., 120, 243, 10.1016/0045-7825(94)00057-T Geyer, 1982, Experimental investigation of thermally induced interacting cracks in brittle solids, Internat. J. Solids Structures, 18, 349, 10.1016/0020-7683(82)90059-2 Sicsic, 2014, Initiation of a periodic array of cracks in the thermal shock problem: A gradient damage modeling, J. Mech. Phys. Solids, 256, 10.1016/j.jmps.2013.09.003 B. Bourdin, J. Marigo, C. Maurini, P. Sicsic, Morphogenesis and propagation of complex cracks induced by thermal shocks, ArXiv e-prints, 1 (2013) 1–5. Davidge, 1968, The strength of two-phase ceramic/glass materials, J. Mater. Sci., 3, 629, 10.1007/BF00757910