Application of higher‐order strain gradient theories in the phase‐field modelling of fracture mechanics

Abstract

AbstractThe simulation of crack propagation has always been a challenging task from a computational point of view. In the past, many mathematical and mechanical assumptions had to be taken into account to successfully simulate this process. The problem of tracking the sharp crack surface was among the first issues which was alleviated by the introduction of phase‐field models. The appearance of stress singularities near the crack tip in the classical continuum mechanics theory is considered to be another source of problem which makes the selection of proper mesh sizes for numerical models very cumbersome, and leads to unphysical results. In the presence of a singularity, the crack propagation starts earlier in problems with a finer discretization which is only natural considering that the strain energy density is higher and increases faster for smaller mesh sizes. Likewise, a loading which normally could not cause a crack to nucleate or propagate inside a structure, will do so in the numerical simulation due to over‐estimated stresses. Therefore, it stands to reason that removing this singular field from the results is a very crucial step in achieving physically meaningful results. The goal of the current contribution is twofold: first, existing models are shown to exhibit a singular stress behavior, and second, a possible remedy is proposed based on the application of higher‐order strain gradients.