Error Controlled Adaptive Multiscale Method for Fracture in Polycrystalline Materials

A lack of separation of scales is the major hurdle hampering predictive and computationally tractable simulations of fracture over multiple scales. In this thesis an adaptive multiscale method is presented in an attempt to address this challenge. This method is set in the context of FE2 Feyel and Chaboche [2000] for which computational homogenisation breaks down upon loss of material stability (softening). The lack of scale separation due to the coalescence of microscopic cracks in a certain zone is tackled by a full discretisation of the microstructure in this zone. Polycrystalline materials are considered with cohesive cracks along the grain boundaries as a model problem. Adaptive mesh refinement of the coarse region and adaptive initiation and growth of fully resolved regions are performed based on discretisation error and homogenisation error criteria, respectively. In order to follow sharp snap-backs in load-displacement paths, a local arc-length technique is developed for the adaptive multiscale method. The results are validated against direct numerical simulation