A numerical assessment of phase-field models for fracture

Abstract

We first give a concise description of phase-field models for the brittle and the cohesive approach to fracture. For brittle fracture we will address issues like the impact of the internal length scale parameter and the degradation function that are prominent in the model, and whether the functional that describes the smeared crack approaches that of the discrete crack in the limiting case that the internal length scale parameter vanishes. By an example we will show that this Γ-convergence is not necessarily attained numerically. For cohesive fracture the crack opening must be explicitly available as input for the cohesive traction-relative displacement relation. The resulting three-field problem can be solved properly on structured meshes when using a balanced interpolation of the field variables: displacements, phase field, and crack opening. A patch test shows that this does not necessarily extend to unstructured meshes.