DEVELOPMENT OF A CONTINUUM REPRESENTATION OF A DISCRETE GRANULAR MEDIUM

Abstract eng:
The discrete element method (DEM) has become a popular tool for understanding granular mechanics. A central theme of DEM research to apply micromechanical concepts to improve constitutive relationships for continuum models. In particular, recent work has been directed at micro-polar models that account for an independent rotation field. Such models have applications for capturing important mechanism associated with localization and provide an avenue for formulating mathematically well-posed problems for materials subject to instability. A key step in applying micromechanics is the homogenization of the discrete quantities describing the granular media to equivalent continuum quantities. In this paper we discuss this process from that standpoint of homogenizing the equilibrium equations for the DEM by application of a smoothing function in a manner similar to the weighted residual method. The process results in equations of equilibrium for a Cosserat continuum and the associated boundary conditions from which well-known relationships between contact forces and continuum stress is recovered. The deformation measures that are conjugate to stress variables are considered in detail.

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