Geodesic
An energy-preserving Discrete Element Method for elastodynamics
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 46 (2012) no. 6, pp. 1527-1553

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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.

DOI : 10.1051/m2an/2012015
Classification : 65Z05
Keywords: solids, elasticity, discrete element method, hamiltonian, explicit time integration 
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     author = {Monasse, Laurent and Mariotti, Christian},
     title = {An energy-preserving {Discrete} {Element} {Method} for elastodynamics},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {1527--1553},
     publisher = {EDP-Sciences},
     volume = {46},
     number = {6},
     year = {2012},
     doi = {10.1051/m2an/2012015},
     mrnumber = {2996339},
     zbl = {1267.74114},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an/2012015/}
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Monasse, Laurent; Mariotti, Christian. An energy-preserving Discrete Element Method for elastodynamics. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 46 (2012) no. 6, pp. 1527-1553. doi: 10.1051/m2an/2012015

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