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

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Phase field modelling of anisotropic crack propagation (2017, methodology): “Note that the similar idea of this method can be found in the work by Frémond and Nedjar (1996); Pham et al. (2011); Miehe et al. (2015).”
A phase‐field model for chemo‐mechanical induced fracture in lithium‐ion battery electrode particles (2016, methodology): “Following [61], the irreversible evolution of the crack phase field is driven by a global constitutive evolution equation of regularized crack surface d dt l.d/„ ƒ‚ … evolution of cracks D 1 l Z B0 Œ.1 d/H Pd Pd dV„ ƒ‚ … constitutive crack driving power > 0: (3) Here, Pd is a viscous crack resistanc”
Phase‐field modeling of ductile fracture at finite strains: A robust variational‐based numerical implementation of a gradient‐extended theory by micromorphic regularization (2017, background): “[90] with local irreversibility and elastic domain.”
On penalization in variational phase-field models of brittle fracture (2018, background): “extended to ductile (elasto-plastic) fracture [27, 28, 29, 30, 31, 32, 33], fracture in films [34, 35], shells [36, 37, 38, 39], fracture under thermal loading [40, 41, 42], hydraulic fracture [43, 44, 45, 46, 47, 48], fracture in porous media [49, 50, 51], anisotropic fracture [52, 53, 54, 55, 56, ”