Broadening of damage in gradient models and phase- field models

Abstract

Gradient damage models have been reported to produce an unrealistic broadening of the damage zones in the later stages of material degradation. We analyse here this feature for gradient damage models with constant gradient activity (i.e. a constant characteristic length, that is, a constant diffusion parameter in the regularisation equation). We show that, even with such simple models, broadening can be controlled to a large extent with an appropiate choice of material parameters and a fine enough spatial discretisation. In fact, damage broadens due to the “crosswind” diffusion (i.e. diffusion perpendicular to the crack path) caused by the gradient activity. If the problem setup, loading conditions and material parameters are such that crack propagation is predominant over diffusion, then little broadening is observed. Broadening can be further avoided by using models with variable gradient activity. This refers both to gradient models with a damage-dependent, decreasing characteristic length and to phase-field approaches, which implicitly incorporate such a feature. These aspects will be discussed with some representative examples.