An energy-preserving Discrete Element Method for elastodynamics

Details An energy-preserving Discrete Element Method for elastodynamics An energy-preserving Discrete Element Method for elastodynamics

2009-07-13

arxiv.org/abs/0907.2202v2

Mathematics

Numerical Analysis

27 pages, 7 figures

Scientific paper

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.

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