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Quasistatic viscoelastic contact with friction and wear diffusion. (English) Zbl 1180.74046
Summary: We consider a quasistatic problem of frictional contact between a deformable body and a moving foundation. The material is assumed to have nonlinear viscoelastic behavior. The contact is modeled with normal compliance and the associated law of dry friction. The wear takes place on a part of the contact surface and its rate is described by the Archard differential condition. The main novelty in the model is the diffusion of the wear particles over the potential contact surface. Such phenomena arise in orthopaedic biomechanics where the wear debris diffuse and influence the properties of joint prosthesis and implants. We derive a weak formulation of the model which is given by a coupled system with an evolutionary variational inequality and a nonlinear evolutionary variational equation. We prove that, under a smallness assumption on some of the data, there exists a unique weak solution for the model.

MSC:
74M15 Contact in solid mechanics
74M10 Friction in solid mechanics
74D10 Nonlinear constitutive equations for materials with memory
74H20 Existence of solutions of dynamical problems in solid mechanics
74H25 Uniqueness of solutions of dynamical problems in solid mechanics
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