CONFIGURATIONS.FORCES IN A PHASE FIELD MODEL FOR FRACTURE

摘要

A phase field model based on a regularised version of the variational formulation of brittle fracture is introduced. The phase field parameter models the continuous change in stiffness between broken and undamaged material on a small lengthscale controlled by a regularisa-tion parameter. In order to evaluate the configurational forces acting on the diffuse phase field cracks, and to compare with the underlying sharp crack model, a generalised Eshelby stress tensor is derived and analysed in mode I loading. The numerical treatment is done with finite elements, utilising an implicit Euler scheme for the time integration of the Ginzburg-Landau evolution equation of the phase field parameter. The configurational forces associated with the generalised Eshelby stress tensor are computed in a postprocessing step, after the coupled problem of mechanical balance equations and the evolution equation has been solved. Examples show the relation between the initiation of crack growth and the configurational forces acting on the phase field cracks.