Error Controlled Adaptive Multiscale Method For Fracture Modelling in Polycrystalline materials

In this paper an adaptive multiscale method is presented in an attempt to address the lack of separation of
scales in simulation of fracture. This method is set in the context of FE2 [20] 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.