On constitutive assumptions in phase field approaches to brittle fracture

Constitutive assumptions involved in phase field models of fracture in order to capture the behavior of cracks on the (smeared) continuum level are critically reviewed and several improvements are suggested. While some of the deficiencies of existing models are connected to the variational structure of respective phase field approaches, non-variational approaches are shown to allow for greater flexibility towards constitutive assumptions needed for a realistic representation of cracks. Benefits of the latter are illustrated by numerical examples.