| Issue |
ESAIM: M2AN
Volume 46, Number 6, November-December 2012
|
|
|---|---|---|
| Page(s) | 1527 - 1553 | |
| DOI | https://doi.org/10.1051/m2an/2012015 | |
| Published online | 13 June 2012 | |
An energy-preserving Discrete Element Method for elastodynamics∗
1
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
2
CEA DAM DIF, 91297
Arpajon,
France
laurent.monasse@cea.fr; christian.mariotti@cea.fr
Received: 4 January 2011
Revised: 9 January 2012
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.
Mathematics Subject Classification: 65Z05
Key words: Solids / elasticity / discrete element method / Hamiltonian / explicit time integration
© EDP Sciences, SMAI, 2012
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