Models of adhesive contact between rough elastic solids

Adhesion of rough elastic solids is considered. Roughness is simulated by the Winkler–Fuss nonlinear elastic layer, which can be stretched. Mechanical properties of the layer are determined by statistical theories of adhesive contact between nominally flat rough surfaces. The contact of solids is described by the nonlinear boundary integral equations with non-monotonic operators, whose solutions determine reduction of effective thickness of the rough layer, nominal contact stresses, nominal contact regions and relation between applied force and approach of solids. The theoretical background and numerical implementation of the models are given. Both a full model and its simplified version are analyzed.