Numerical homogenisation based on asymptotic theory and model reduction for coupled elastic-viscoplastic damage

This article deals with damage computation of heterogeneous structures containing locally periodic micro-structures. Such heterogeneous structure is extremely expensive to simulate using classical finite element methods, as the level of discretisation required to capture the micro-structural effects is too fine. The simulation time becomes even higher when dealing with highly non-linear material behaviour, e.g. damage, plasticity and such others. Therefore, a multi-scale strategy is proposed here that facilitates the simulation of non-linear heterogeneous material behaviour in a manner that is computationally feasible. Based on the asymptotic homogenisation theory, this multi-scale technique explores the micro–macro behaviour for elasto-(visco)plasticity coupled with damage. The theory inherently segregates the heterogeneous continua into a macroscopic homogeneous structure and an underlying heterogeneous microscopic periodic unit cell. Several heterogeneous structures have been simulated using the multi-scale method along with a one-dimensional verification with respect to a reference solution. Additionally, a reduced order modelling is used to prevent large memory requirement for storing micro-structural quantities of interest.