  We present a detailed analysis of the bounds on the integration step in
Discrete Element Method (DEM) for simulating collisions and shearing of
granular assemblies. We show that, in the numerical scheme, the upper limit for
the integration step, usually taken from the average time $t_c$ of one contact,
is in fact not sufficiently small to guarantee numerical convergence of the
system during relaxation. In particular, we study in detail how the kinetic
energy decays during the relaxation stage and compute the correct upper limits
for the integration step, which are significantly smaller than the ones
commonly used. In addition, we introduce an alternative approach, based on
simple relations to compute the frictional forces, that converges even for
integration steps above the upper limit.
