Multiscale solution of the mechanical contact between coated knee prosthesis and bone

A macroscopic mathematical model for bone-prosthesis contact conditions based on asymptotic homogenization is proposed which allows to take into account roughness properties of the prosthesis (in this case a special coating layer) on the micro level. We propose to decouple the macro- and micro-problems. The construction of the macroscopic contact law is done by fitting our various numerical FE-simulations of the contact in the coating layer under considering of some phenomenological models. The model parameters for the macroscopic contact conditions can be calculated in advance and additional iterations between micro-macro levels are not required. Starting with a frictionless micro contact problem with a rough interface one can get the macro-problem containing friction. The proposed macro model is applied to a knee-prosthesis system. The corresponding numerical results will be discussed.