Anisotropic mesh adaptation for the generalized Ambrosio-Tortorelli functional with application to brittle fracture

06/2016

Anisotropic mesh adaptation for the generalized Ambrosio-Tortorelli functional with application to brittle fracture

Tuesday 16th February 2016

Micheletti, S.; Perotto, S.; Signorini, M.

Quasi-static crack propagation in brittle materials is modeled via the Ambrosio-Tortorelli approximation [7]. 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 [8], 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.