From DEM simulations towards a continuum theory of granular matter

One essential question in material sciences is how to bridge the gap between the microscopic picture and a macroscopic description. The former involves contact forces and deformations, whereas the latter concerns tensorial quantities like the stress or the velocity gradient. A two-dimensional shear-cell filled with disks of different sizes is examined by means of a ``microscopic'' discrete element method (DEM). Applying a consistent averaging formalism, one can obtain scalar- and vector-fields as well as classical tensorial macroscopic quantities like fabric, stress or velocity gradient and, in addition, micropolar quantities like curvature or couple-stress.