Solving Normal Cone Inclusion Problems in Contact Mechanics by Iterative Methods

Abstract

In this paper we show how inclusions originating from set-valued force laws can be written as non-linear equations for finite-dimensional second order dynamical systems. We express the set-valued force laws as subdifferentials of the indicator function to a given convex set C, apply the augmented Lagrangian and arrive at a proximal point problem which is solved by Jacobi or Gauss Seidel like iterative schemes. This proceed provides a simple unified access to frictional contact problems in dynamics and can be used either in event-driven or time-stepping simulation approaches.