|Abstract:|| Quasi-static crack propagation in brittle materials is modeled via the
Ambrosio-Tortorelli approximation . The crack is modeled by a smooth
phase-field, defined on the whole computational domain. Since the crack
is confined to a thin layer, the employment of anisotropic adapted grids is
shown to be a really effective tool in containing computational costs. We
extend the error analysis in [3, 4, 5] to the generalized Ambrosio-Tortorelli functional introduced in , where a unified framework for several elasticity laws is dealt with as well as a non-convex fracture energy can be accommodated. After deriving an anisotropic a posteriori error estimator, we devise an algorithm which alternates optimization and mesh adaptation. Both anti-plane and plane-strain configurations are numerically checked.