Asymptotic derivation of quasistatic frictional contact models with wear for elastic rods

The aim of this paper is to derive mathematical models for the bending–stretching of an elastic rod in contact with a moving foundation, when the resulting wear is taken into account. The process is assumed to be quasistatic, the contact is modeled with normal compliance and the evolution of the wear function is described with Archard’s law. To derive the models we start with the corresponding 3D problem, introduce a change of variable together with the scaling of the unknowns and then we use arguments of asymptotic analysis to obtain error estimates and a convergence result to the limit model.