Homogenization and Multi-Scale Approaches for Contact Problems

Abstract

The use of finite element analysis tools enables investigations of the contact behaviour of rough surfaces on micro-mechanical level. Such analysis incorporates enhanced physical modelling and can replace classical statistical methods based on simplified analytical models. It will lead to homogenized constitutive models for contact which can be employed in macroscopic contact numerical simulations. Depending on the surface roughness these homogenization process can be employed on several scales and then leads to macrosscopic constitutive equations which incoprorate the behaviour of different scales. Here the main aspect is to show that use of computational tools will lead to constitutive equations which describe the mechanical behaviour within the contact zone. As one example, the macroscopic constitutive equation for the approach of two rough surfaces is derived based on statistical numerical simulations taking into account the micro-structure of a rough surface. Another example describes a multi-scale approach for the characterization of the frictional behaviour of elastomere materials. Special attenteion is given to the development of a methods based on scale seperation and homogenization. It is applied to rubber materials being in contact with rough road surfaces.