  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.
