Numerical Analysis of Contact Between Elastic Bodies in the Presence of Thin Coating and Nonlinear Winkler Surface Layers

We consider the problem of unilateral contact through a nonlinear Winkler surface layer of a massive elastic body and a composite body consisting of a thin coating in the form of a Timoshenko-type shell and a massive elastic base connected with the coating via the other nonlinear Winkler layer. We present a weak formulation of this problem in the form of a nonlinear variational equation. To solve this equation, we propose a parallel Robin-type domain decomposition method that reduces the original contact problem to the iterative solution of independent linear variational equations corresponding to elasticity problems for massive bodies and a problem of the Timoshenko-type shell theory for the thin coating. With the help of finite element approximations, the developed method is used to study the contact between two massive elastic bodies with surface groove in the presence of a thin coating and the nonlinear Winkler-type surface layers. We analyze the dependence of the contact and interface stresses on the height of the coating and the Winkler layer parameter. The results obtained for the coatings modeled using the Timoshenko-type shell theory and the classical elasticity theory are compared.