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An energy-preserving Discrete Element Method for elastodynamics∗

Published online by Cambridge University Press:  13 June 2012

Laurent Monasse  and
Christian Mariotti
Laurent Monasse
Affiliation:
Université Paris-Est, CERMICS 6 et 8 avenue Blaise Pascal, Cité Descartes – Champs-sur-Marne 77455 Marne-la-Vallée Cedex 2, France. monassel@cermics.enpc.fr CEA DAM DIF, 91297 Arpajon, France; laurent.monasse@cea.fr; christian.mariotti@cea.fr
Christian Mariotti
Affiliation:
CEA DAM DIF, 91297 Arpajon, France; laurent.monasse@cea.fr; christian.mariotti@cea.fr

Abstract

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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.

Keywords

Solidselasticitydiscrete element methodHamiltonianexplicit time integration

Information

Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 46 , Issue 6 , November 2012 , pp. 1527 - 1553
Copyright
© EDP Sciences, SMAI, 2012

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