Contact models leading to variational–hemivariational inequalities

A frictional contact model, under the small deformations hypothesis, for static processes is considered. We model the behavior of the material by a constitutive law using the subdifferential of a proper, convex and lower semicontinuous function. The contact is described with a boundary condition involving Clarkeʼs generalized gradient. Our study focuses on the weak solvability of the model. Based on a fixed point theorem for set-valued mappings, we prove the existence of at least one weak solution. The uniqueness, the boundedness and the stability of the weak solution are also discussed; the investigation is based on arguments in the theory of variational–hemivariational inequalities. Finally, we present several examples of constitutive laws and friction laws for which our theoretical results are valid.