  We propose a new discrete element method supporting general polyhedral
meshes. The method can be understood as a lowest-order discontinuous Galerkin
method parametrized by the continuous mechanical parameters (Young's modulus
and Poisson's ratio). We consider quasi-static and dynamic elasto-plasticity,
and in the latter situation, a pseudo-energy conserving time-integration method
is employed. The computational cost of the time-stepping method is moderate
since it is explicit and used with a naturally diagonal mass matrix. Numerical
examples are presented to illustrate the robustness and versatility of the
method for quasi-static and dynamic elasto-plastic evolutions.
