A quasistatic crack propagation model allowing for cohesive forces and crack reversibility

Abstract

While the classical theory of Griffith is the foundation of modern understanding of brittle fracture, it has a number of significant shortcomings: Griffith theory does not predict crack initiation and path and it suffers from the presence of unphysical stress singularities. In 1998, Francfort and Marigo presented an energy functional minimization method, where the crack (or its absence) as well as its path are part of the problem's solution. The energy functionals act on spaces of functions of bounded variations, where the cracks are related to the discontinuity sets of such functions. The new model presented here uses modified energy functionals to account for molecular interactions in the vicinity of crack tips, resulting in Barenblatt cohesive forces, such that the model becomes free of stress singularities. This is done in a physically consistent way using recently published concepts of Sinclair. Here, for the consistency of the model, it becomes necessary to allow for crack reversibility and to consider local minimizers of the energy functionals. The latter is achieved by introducing different time scales. The model is solved in its global as well as in its local version for a simple one-dimensional example, showing that local minimization is necessary to yield a physically reasonable result.