Phase‐field modeling and simulation of fracture in brittle materials with strongly anisotropic surface energy

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High-accuracy phase-field models for brittle fracture based on a new family of degradation functions (2017, background): “On the other hand, Li et al. (2015) point out that the incorporation of general anisotropic effects relating to the surface energy requires a formulation that is at least 4th order.”
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, ”
Phase field modelling of anisotropic crack propagation (2017, result): “Note that compared to the formulation proposed by Li et al. (2015), a standard finite element implementation is used herein.”
Crack nucleation in variational phase-field models of brittle fracture (2018, unknown): “They have been expended to account for dynamic eﬀects, ductile behavior [2, 71, 3], cohesive eﬀects [33, 32, 42], large deformations [4, 70, 14], or anisotropy [63], for instance.”