Towards Multiscale Computation of Confined Granular Media

Contact Forces, Stresses and Tangent Operators

Abstract

The present work is focused on the computational simulation of granular media on different scales. On the microscopic level, we suggest a discrete element method to evaluate inter-particle contact forces. On the macroscopic level, we utilize the finite element method to determine stress distributions in a continuum sense. To bridge the gap between both scales, we apply the concept of a representative volume element, essentially linking both scales through the Taylor assumption and Hills' theorem. The governing equations on both scales will be presented with a particular focus on the consistent linearization of the nonlinear response on the material point level. The latter essentially allows for the use of the highly efficient Newton Raphson scheme which ensures quadratic convergence of the iterative solution process. We first elaborate the influence of the size of the representative volume element in terms of a contact normal density function and statistical error bar analyzes. Then we demonstrate the features of our multiscale algorithm in terms of the classical slope stability benchmark problem.