Numerical Improvement of the Discrete Element Method applied to Shear of Granular Media

Details Numerical Improvement of the Discrete Element Method applied to Shear of Granular Media Numerical Improvement of the Discrete Element Method applied to Shear of Granular Media

2007-09-24

arxiv.org/abs/0709.3716v1

Physics

Condensed Matter

Materials Science

16 page, 10 figures, submitted to Acta Mechanica, Special Issue to Honour J.D Goddard

Scientific paper

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.

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