  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.
