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
re nement 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