An energy-preserving Discrete Element Method for elastodynamics∗

Laurent Monasse; Christian Mariotti

ESAIM: Mathematical Modelling and Numerical Analysis (2012)

  • Volume: 46, Issue: 6, page 1527-1553
  • ISSN: 0764-583X

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.

How to cite

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Monasse, Laurent, and Mariotti, Christian. "An energy-preserving Discrete Element Method for elastodynamics∗." ESAIM: Mathematical Modelling and Numerical Analysis 46.6 (2012): 1527-1553. <http://eudml.org/doc/276378>.

@article{Monasse2012,
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.},
author = {Monasse, Laurent, Mariotti, Christian},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Solids; elasticity; discrete element method; Hamiltonian; explicit time integration; solids},
language = {eng},
month = {6},
number = {6},
pages = {1527-1553},
publisher = {EDP Sciences},
title = {An energy-preserving Discrete Element Method for elastodynamics∗},
url = {http://eudml.org/doc/276378},
volume = {46},
year = {2012},
}

TY - JOUR
AU - Monasse, Laurent
AU - Mariotti, Christian
TI - An energy-preserving Discrete Element Method for elastodynamics∗
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2012/6//
PB - EDP Sciences
VL - 46
IS - 6
SP - 1527
EP - 1553
AB - 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.
LA - eng
KW - Solids; elasticity; discrete element method; Hamiltonian; explicit time integration; solids
UR - http://eudml.org/doc/276378
ER -

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