From molecular dynamics and particle simulations towards constitutive relations for continuum theory

A challenge of today‖s research is the realistic simulation of disordered atomistic systems or particulate and granular materials like sand, powders, ceramics or composites, which consist of many millions of atoms/particles. The inhomogeneous fine-structure of such materials makes it very difficult to treat these with continuum methods, which typically assume homogeneity and scale separation. As an alternative, particle based methods can be straightforwardly applied, since they intrinsically take the fine-structure into account. The ultimate challenge is to find constitutive relations for continuum theory from these particle-based simulations. In this chapter, a particle simulation approach, the so-called discrete elementmethod (DEM), as related to molecular dynamics (MD) methods, is introduced and applied to the simulation of many-particle systems. The examples (clustering in granular gases, and bi-axial as well as cylindrical shearing of dense packings) illustrate the micro-macro transition towards continuum theory.