Few problems with regularized Coulomb law

Abstract

The main idea is to present some problems where the friction obeys to regularized Coulomb law. Mathematically, it is usual that the friction law is supposed to be the Coulomb law which is controlled by a function "sign" with discontinuity at the origin. In reality, friction phenomenon corresponds to an average continuous behavior. From a modelling point of view, the simplest way to get this continuity is to regularize friction law. Obviously, friction problems become more complicated due to the fact that the friction law exhibits two phases of behavior. Solving problems with this friction law could bring some special results. To present them, the problems considered in this paper are related to the bending of two beams in contact under a certain pressure and to the transversal strain of an elastic thin strip in contact with a rigid body. For these two problems, analytical solutions are presented and also some finite element simulations for comparison.