A multiscale method for frictionless contact mechanics of rough surfaces

An efficient methodology is proposed for the analysis of frictionless contact between rough surfaces. The surface is described by parabolic asperities which deform according to Hertz Theory. The problem is solved considering interactions between elliptic contact zones. Such analysis provides interface laws that are incorporated into a macroscopic numerical model where contact surfaces are flat. This operation is done by means of Love solution for elastic half spaces and the penalty method. A numerical example of this multiscale method is presented to show its robustness. In comparison with a purely numerical model where roughness is explicitly described, the proposed strategy provides good results and saves a considerable amount of time. •A multi-scale analysis of a frictionless rough contact interface is performed.•Contact surfaces are described as a set of parabolic asperities.•Interface modelling considering that the asperities are interacting with each other.•Integration of the issued contact laws into a large-scale numerical model.•Good accuracy and a reduced computational time compared to a purely numerical model.