## AIMR Math Group Seminar #6

Date : August 24th (Thu.) 16:30-

Place：3C, AIMR Main Bldg., Katahira campus, Tohoku University

Speaker**： **Dominik KRENGEL

Title: Numerically exact computation of static friction

Abstract**： **

Static (Coulomb-) friction in granular materials has eﬀects beyond purely static assemblies: Also in sheared materials with ﬁnite velocity, the energy dissipation and the formation of regions where the position of the grains is constrained with respect to each other(”rigid clusters”) is actuated by static friction. The implementation of viscous (i.e. velocity-proportional) friction, where the relative tangential force at the contact vanishes with the tangential velocity is computationally simple. The implementation of Coulomb friction is algorithmically much more demanding: For zero tangential contact velocity, the tantential inter-particle force can be ﬁnite, so that it compensates tangential motion or forces between neighboring particles. While viscous friction is an energy dissipation mechanism, Coulomb friction is a constraint which may yield a ﬁnite, constraint force where the particles are ﬁxed to each other in tangential direction, so that no energy dissipation results. In some of the ﬁrst papers on the discrete element method, Cundall and Strack established a computation method of the tangential force where the increments are chosen proportional to the sliding velocity (or distance per timestep). While it is only a model, which replaces the constraint force from Coulomb friction with a parameter dependent force which may act like a degree of freedom (it is able to store elastic energy, a feat impossible for Coulomb friction) it is nevertheless suﬃcient to allow the formation of heaps on ﬂat surfaces. Recently, the authors have proposed a computation method which generalizes the numerically exact computation of Coulomb friction for onedimensionaly moving chains of particles to higher dimensions and arbitrary particle conﬁgurations.