Phase-field modeling of crack branching and deflection in heterogeneous media

This contribution presents a diffuse framework for modeling cracks in heterogeneous media. Interfaces are depicted by static phase-fields. This concept allows the use of non-conforming meshes. Another phase-field is used to describe the crack evolution in a regularized manner. The interface modeling implements two combined approaches. Firstly, a method from the literature is extended where the interface is incorporated by a local reduction of the fracture toughness. Secondly, variations of the elastic properties across the interface are enabled by approximating the abrupt change between two adjacent subdomains using a hyperbolic tangent function, which alters the elastic material parameters accordingly. The approach is validated qualitatively by means of crack patterns and quantitatively with respect to critical energy release rates with fundamental analytical results from Linear Elastic Fracture Mechanics, where a crack impinges an arbitrarily oriented interface and either branches, gets deflected or experiences no interfacial influence. The model is particularly relevant for phase-field analyses in heterogeneous, possibly complex-shaped solids, where cohesive failure in the constituent materials as well as adhesive failure at interfaces and its quantification play a role.