Numerical Improvement of the Discrete Element Method applied to Shear of Granular Media

TL;DR

This paper analyzes the integration step bounds in the Discrete Element Method for granular media, revealing that smaller steps are needed for convergence and proposing an alternative frictional force computation method.

Contribution

It provides a detailed analysis of integration step limits in DEM and introduces an alternative approach that maintains convergence with larger steps.

Findings

Upper limits for integration steps are smaller than commonly used.

The kinetic energy decay analysis helps determine proper step sizes.

An alternative frictional force method converges with larger steps.

Abstract

We present a detailed analysis of the bounds on the integration step in Discrete Element Method (DEM) for simulating collisions and shearing of granular assemblies. We show that, in the numerical scheme, the upper limit for the integration step, usually taken from the average time $t_c$ of one contact, is in fact not sufficiently small to guarantee numerical convergence of the system during relaxation. In particular, we study in detail how the kinetic energy decays during the relaxation stage and compute the correct upper limits for the integration step, which are significantly smaller than the ones commonly used. In addition, we introduce an alternative approach, based on simple relations to compute the frictional forces, that converges even for integration steps above the upper limit.