Computational Homogenization of Confined Frictional Granular Matter

Multiscale modeling and computation of confined granular media opens a novel way of simulating and understanding the complicated behavior of granular structures. Phenomenological continuum approaches are often not capable of reproducing distinguishing features of granular media, like, e.g., the breaking and forming of particle contacts. Alternatively, a multiscale homogenization procedure, based on a discrete element method, allows to capture such distinguishing features. The present manuscript deals with the variationally based computational homogenization and simulation of granular media, whereby the macroscopic impact of inter-particle friction defines the overall focal point. To bridge the gap between both scales, we apply the concept of a representative volume element, essentially linking both scales through variational considerations. As the beneficial outcome of the variational approach, the Piola stress is derived from the overall macroscopic energy density