An energy-preserving Discrete Element Method for elastodynamics

TL;DR

This paper introduces an energy-preserving Discrete Element Method for elastodynamics using polyhedral elements, ensuring stability and energy conservation in long-term simulations of large displacements.

Contribution

It develops a Hamiltonian-based DEM with symplectic integration for elastodynamics, ensuring energy preservation and stability over long simulations.

Findings

Conservation of energy demonstrated in numerical tests.

Method accurately models large displacements.

Stable long-term simulations achieved.

Abstract

We develop a Discrete Element Method (DEM) for elastodynamics using polyhedral elements. We show that for a given choice of forces and torques, we recover the equations of linear elastodynamics in small deformations. Furthermore, the torques and forces derive from a potential energy, and thus the global equation is an Hamiltonian dynamics. The use of an explicit symplectic time integration scheme allows us to recover conservation of energy, and thus stability over long time simulations. These theoretical results are illustrated by numerical simulations of test cases involving large displacements.