Time reversibility of the discrete element method

An algorithm is presented for discrete element method (DEM) simulations of energy-conserving systems of frictionless, spherical particles in a reversed-time frame. This algorithm is verified, within the limits of round-off error, through implementation in the LAMMPS code. Mechanisms for energy dissipation such as interparticle friction, damping, rotational resistance, particle crushing or bond breakage cannot be incorporated into this algorithm without causing time irreversibility. This theoretical development is applied to critical-state soil mechanics as an exemplar. It is shown that the convergence of soil samples, which differ only in terms of their initial void ratio, to the same critical state requires the presence of shear forces and frictional dissipation within the soil system.