On the use of coarse-graining to bridge the discrete and continuum descriptions of granular materials

Surface and volume coupling methods are reformulated for concurrent multi-scale modeling of granular materials. Based on a micro-macro transition technique called ``coarse-graining'' [1], we derive homogenization operators in more generalized forms than those reported in the literature. For surface coupling [2], coarse graining allows distributing the coupling forces beyond the finite elements that the particles are locally coupled with, namely, from contact points to their neighboring integration points. For volume coupling [3], coarse-graining is applied to enrich the homogenization/localization operations on particle-scale quantities, thereby offering a non-local coupling approach. The generalized coupling terms contain one user-defined parameter, namely, the coarse-graining width, setting a length scale for the “coarse-grained” fields.
The benefits of coarse-graining in surface and volume coupling are exemplified by modeling particle-cantilever interaction and wave propagation between discrete particles and continuum bodies. We show that the CG-enriched new formulation removes high-frequency/short-wavelength numerical oscillations and gives more physical predictions in the example of particle-cantilever interaction, compared with the conventional formulation using finite element basis functions. In the wave propagation example, the numerical dissipation, which is a known artifact of the volume coupling method, is reduced with an optimal coarse-graining width. In particular, the benefit of coarse-graining appears to be significant when the waveforms become increasingly complex and contain high frequency contents.