ABSTRACT
Two-dimensional assemblies of disks, with a uniform distribution of diameters between a/2 and a, are enclosed in a periodic rectangular cell, the size of which might change in response to externally applied stress. Particles are moved as in standard molecular dynamics methods, as introduced, e.g., by in Cundall & Strack (1979). If h denotes the normal deflection (apparent interpenetration) in a contact, −h being the distance between grain surfaces when h < 0, the static normal force between two neighboring grains, counted positively when repulsive, is the sum of an elastic part N e = KN hY (h) and a cohesive term N c. N c is equal to constant −F0 if particles touch (h > 0), varies linearly with distance −h when they are apart, and vanishes beyond a maximum interaction distance D0:
(H is the Heaviside step function). Tangential elastic forces T e incrementally relate to tangential relative displacements KT , and are limited by the Coulomb
condition T e ≤µN e, involving the friction coefficientµ. Such contact laws are summarized on Figure 1. A viscous normal force is also introduced to speed up the approach to equilibrium states. In addition, we implemented rolling resistance (RR), with the model introduced by Tordesillas & Stuart (2002), involving a rolling friction coefficient µr which sets the maximum rolling moment in a contact at µrN e (µr should be of the order of µl, with l some typical asperity size on particle surfaces).
