A continuum phase field model for fracture

Abstract

A phase field model based on a regularized version of the variational formulation of brittle fracture is introduced. The influences of the regularization parameter that controls the interface width between broken and undamaged material and of the mobility constant of the evolution equation are studied in finite element simulations. A generalized Eshelby tensor is derived and analyzed for mode I loading in order to evaluate the energy release rate of the diffuse phase field cracks. The numerical implementation is performed with finite elements and an implicit time integration scheme. The configurational forces are computed in a postprocessing step after the coupled problem of mechanical balance equations and the evolution equation is solved. Some of the numerical results are compared to analytical results from classical Griffith theory.