ABSTRACT
The unilateral feature of contact evoked previously means that the gap between contactor bodies is non negative. Since we consider only dry systems, the reaction force is positive and when the contact vanishes, it is equal to zero. This is summarized by the so-called velocity Signorini condition
where the index n denotes the normal component of the various quantities: u the relative velocity between bodies in contact and r the local contact force. For explicit method the normal force is usually proportional to the penetration between two particles. Here there is no bilateral conditions.The dry frictional law is the Coulomb’s one for which the basic features are:The friction force lies in the Coulomb’s cone (||rt || ≤µrn, µ friction coefficient), and if the sliding relative velocity is not equal to zero, its direction is opposed to the friction force (||rt || =µrn). We can summarize previous explanations by the following relation:
The velocity Signorini condition does not provide enough information when collisions occur. For rigid bodies we also need to adopt a collision law based on the Newton restitution law, u+n =−enu−n , realistic for collection of spheres and extended to multicontact systems (Moreau 1994). To solve our contact problem we can use a classical non linear Gauss-Seidel algorithm (Jean 1999) or a Conjugate Projected Gradient one (Renouf and Alart 2004a). To face long CPU-time of 2D and 3D simulations, previous algorithms benefit of parallel versions (Renouf et al 2004; Renouf and Alart 2004b).
