A phase field model for rate-independent crack propagation: Robust algorithmic implementation based on operator splits

C. Miehe, F. Welschinger, M. Hofacker, Thermodynamically-consistent phase field models of fracture: Variational principles and multi-field fe implementations, International Journal for Numerical Methods in Engineering DOI: 10.1002/nme.2861. Griffith, 1921, The phenomena of rupture and flow in solids, Philosophical Transactions of the Royal Society London A, 221, 163, 10.1098/rsta.1921.0006 Irwin, 1958, Fracture, Vol. 6, 551 Francfort, 1998, Revisiting brittle fracture as an energy minimization problem, Journal of the Mechanics and Physics of Solids, 46, 1319, 10.1016/S0022-5096(98)00034-9 Bourdin, 2008 Dal Maso, 2002, A model for the quasistatic growth of brittle fractures: Existence and approximation results, Archive for Rational Mechanics and Analysis, 162, 101, 10.1007/s002050100187 Buliga, 1999, Energy minimizing brittle crack propagation, Journal of Elasticity, 52, 201, 10.1023/A:1007545213010 Bourdin, 2000, Numerical experiments in revisited brittle fracture, Journal of the Mechanics and Physics of Solids, 48, 797, 10.1016/S0022-5096(99)00028-9 Mumford, 1989, Optimal approximations by piecewise smooth functions and associated variational problems, Communications on Pure and Applied Mathematics, 42, 577, 10.1002/cpa.3160420503 Ambrosio, 1990, Approximation of functionals depending on jumps by elliptic functionals via γ-convergence, Communications on Pure and Applied Mathematics, 43, 999, 10.1002/cpa.3160430805 Dal Maso, 1993 Braides, 1998 Braides, 2002 Hakim, 2009, Laws of crack motion and phase-field models of fracture, Journal of the Mechanics and Physics of Solids, 57, 342, 10.1016/j.jmps.2008.10.012 Karma, 2001, Phase-field model of mode iii dynamic fracture, Physical Review Letters, 92 Eastgate, 2002, Fracture in mode i using a conserved phase-field model, Physical Review E, 65, 10.1103/PhysRevE.65.036117 Belytschko, 2003, Dynamic crack propagation based on loss of hyperbolicity and a new discontinuous enrichment, International Journal for Numerical Methods in Engineering, 58, 1873, 10.1002/nme.941 Song, 2009, Cracking node method for dynamic fracture with finite elements, International Journal for Numerical Methods in Engineering, 77, 360, 10.1002/nme.2415 Gürses, 2009, A computational framework of three-dimensional configurational-force-driven brittle crack propagation, Computer Methods in Applied Mechanics and Engineering, 198, 1413, 10.1016/j.cma.2008.12.028 Miehe, 2007, A robust algorithm for configurational-force-driven brittle crack propagation with r-adaptive mesh alignment, International Journal for Numerical Methods in Engineering, 72, 127, 10.1002/nme.1999 Miehe, 2007, A computational framework of configurational-force-driven brittle fracture based on incremental energy minimization, International Journal of Fracture, 145, 245, 10.1007/s10704-007-9078-1 Capriz, 1989 Mariano, 2001, Multifield theories in mechanics of solids, Advances in Applied Mechanics, 38, 1, 10.1016/S0065-2156(02)80102-8 Frémond, 2002 Miehe, 1998, Comparison of two algorithms for the computation of fourth-order isotropic tensor functions, Computers & Structures, 66, 37, 10.1016/S0045-7949(97)00073-4 Miehe, 2001, Algorithms for computation of stresses and elasticity moduli in terms of Seth–Hill's family of generalized strain tensors, Communications in Numerical Methods in Engineering, 17, 337, 10.1002/cnm.404 Bittencourt, 1996, Quasi-automatic simulation of crack propagation for 2d lefm problems, Engineering Fracture Mechanics, 55, 321, 10.1016/0013-7944(95)00247-2 Miehe, 1995, Discontinuous and continuous damage evolution in Ogden-type large-strain elastic materials, European Journal of Mechanics A / Solids, 14, 697