A hierarchical model for cross-scale simulation of granular media

This paper presents a multiscale modeling framework for granular media based on a hierarchical cross-scale approach. The overall material is treated as a continuum on the macroscale and the corresponding boundary value problem is solved by finite element method (FEM). At each Gauss point of the FEM mesh, a discrete element assembly is embedded from which the material behavior is obtained for the global FEM computation. It is demonstrated that this technique may capture the salient macroscopic behavior of granular media in a natural manner, and meanwhile helps to bypass the conventional phenomenological nature of continuum modeling approaches. Moreover, the framework provides us with rich information on the particle level which can be closely correlated to the macroscopic material response and hence helps to shed lights on the cross-scaling understanding of granular media. Specific linkages between the microscopic origins and mechanisms and the macroscopic responses can be conveniently developed. As a demonstrative example, the strain localization of granular sand in biaxial compression test is investigated by the multiscale approach to showcase the above features