Constitutive Relations and Computer Simulation of Granular Material

The main research subject in the continuum approach of dense granular materials is the derivation of constitutive relations needed for closure. These relations have been derived using many kinds of model. The brief outlines of these models, simulation results for mechanical fields using these relations and the experimental verifications are presented. There are not so many as these studies explain correctly the detailed behaviors of granular materials. It would be necessary to verify the simulation results based on these models by direct comparison with the experimental data performed under the same conditions as the calculation. The reason for the lack of simulation results to describe behaviors of dense granular materials is the difficulty in calculating the mechanical fields in which statics and dynamics are simultaneously involved under real-life boundary values using these constitutive relations. We describe briefly our constitutive equations based on the mechanical data of dense granular materials obtained by distinct element method calculation and show the simulation results of real flow fields (granular collapse and heap) using our constitutive equations by the smoothed particle hydrodynamics (SPH) method and the verification by the direct comparison with experimental data presented in a previous paper. It seems that a Lagrangian approach, e.g. the SPH method, is a simple and reliable method for the calculation of dense granular materials using these complicated constitutive relations under real-life boundary conditions.