Simulation of failure processes with the variational multiscale method

In the present contribution a multiscale method for the modeling an simulation of failure and crack propagation is presented. Thereby, the variational multiscale method initially introduced by Hughes provides the methodological multiscale framework. The basis of this method is a decomposition of the solution into coarse scale and fine scale contributions, the latter incorporating the local behaviour. The method involves the propagation of cracks at finite strains. A twoscale approach, macro-meso, is adopted and both scales are discretized with finite elements whereby certain locality assumptions are prescribed to the mesoscopic solution. At the fine scale an evolving mesostructure induced by crack propagation is taken into account. The multiscale framework implies naturally a refined discretization in the area of the crack tip. Nevertheless, when crack propagation is modelled, the crack direction should not depend on the discretization. To prevent constant remeshing a discretization with discontinuous elements at the fine scale is applied. The applicability of the method to simulate multiscale failure processes at finite strains is demonstrated by numerical examples.