Abstract

This talk will discuss two new approaches to obtaining contact forces in stiff grain systems. Typical discrete element methods (DEM) use an elastic contact law to infer interparticle forces through apparent overlaps.  While some practitioners view these overlap forces merely as a penalty in order to achieve a desired rigid-grain response, these forces actually encompass the mechanics of the grain elasticity and add important physics to the process even for stiff static packings.  For example, without the elastic physics, rigid-grain models such as contact dynamics (CD) can suffer from issues such as force indeterminacy which sometimes affects the way the packing flows dynamically.   In the first part of this talk, we will discuss a modification to CD for hard grains which still assumes the grains are rigid but guarantees the forces found by the solver are the ones that are compatible with a chosen elastic contact law—- that is, the forces obtained could have come from adding a small displacement to the grains and applying one’s desired force model (e.g. Hertz, Hooke) to the overlaps.  This resolves the indeterminacy problem of CD while maintaining the benefits of CD such as the larger time-step that CD offers over DEM . In the second part, we discuss a new DEM contact model for grains made from anisotropic elastic material, such as crystalline solids. The contact law we obtain is remarkably accurate when compared with exact finite-element solutions, for a wide range of materials and surface geometries.  We showcase two application examples based on real materials where elastic anisotropy of the particles induces noticeable effects on macroscopic behavior. For example, we demonstrate the ability to engineer tunable vibrational band gaps in a stack of grains by merely rotating the constituent spherical particles.