Material vs discretization length scales in plasticity imulations of solid foams

The stress-strain response of metal foams has attracted significant attention from the mechanics community due to the local collapse that individual cells experience. This collapse results in the development of strain localization bands, also known as crushing bands, which give rise to a random but localized accumulation of damage. Such experimental observations have been successfully simulated by using a strain gradient plasticity model that is numerically implemented through a cellular automaton; stochasticity was accounted for by allowing the initial yield stress of each mesh element to vary according to a Weibull distribution. In the present study new simulations, along the same lines, are performed in order to further understand not only the effect of microstructure on the stress-strain response of ordered and disordered foams, but also that of the mesh size of the simulation grid. It is found that there are no significant size effects in foams of low disorder, while such effects exist when a higher degree of structural disorder is considered.