On the Treatment of inelastic materials within an ALE‐formulation of rolling contact

Abstract

For the FEM analysis of elastic rolling contact problems Arbitrary Lagrangian-Eulerian (ALE) methods are the state of the art. These methods allow mesh refinements concentrated on the contact region and offer a time independent formulation of the stationary rolling contact. The relative-kinematic description of rolling thereby leads to a relative motion between the finite element mesh and the material points. Thus for the treatment of inelastic material behavior convective terms have to be considered. In contrast to a pure Lagrangian description the history of the material particles is not determined directly. Therefore the internal variables have to be transported on streamlines of the particles through the fixed finite element mesh. This contribution treats the convection of the inelastic variables by the solution of the advection equation. The integration of this equation is performed by a time-discontinuous Galerkin formulation.