Micromorphic continuum stress measures calculated from three-dimensional ellipsoidal discrete element simulations on granular media

The objective of the paper is to demonstrate the calculation of micromorphic continuum stress measures based directly on three-dimensional (3D) ellipsoidal discrete element (DE) simulations over representative volume elements (RVE) within the DE domain representing granular media. We will demonstrate these calculations for two simulations: (1) pile penetration, and (2) cavity expansion. All calculations are assumed to be performed in the current configuration with respect to a large deformation micromorphic continuum mechanics analysis. The micromorphic continuum stresses include the unsymmetric third order couple stress tensor mijk, symmetric second order micro-stress tensor sij , and unsymmetric second order Cauchy stress tensor σij . The DE continuum stress measure due to Christoffersen et al. (1981) and Rothenburg & Selvadurai (1981), is used as the symmetric “micro-element” stress tensor σ ij for micromorphic continuum mechanics (Eringen & Suhubi 1964). The balance equations solved are the balance of linear and angular momenta for the DE simulations, whereas the micromorphic continuum stress measures are only used to interpret the DE simulation results, at the moment.