Abstract
In this paper we present a model for quasistatic frictional contact between a thermoviscoelastic body and a moving foundation that involves wear of contacting surface and diffusion of wear debris. The damage effect is taken into account in the thermoviscoelastic constitutive law, its evolution is described by a parabolic inclusion with the homogeneous Neumann boundary condition. Contact is modeled with a normal compliance condition and is associated to a dry friction. The wear takes place on a part of the contact surface, when the wear debris surface density diffuse on the whole of the contact surface and is accompanied by frictional heat exchange. We derive a variational formulation of the problem and state that, under a smallness assumption on the problem data, there exists a unique weak solution for the model. The proof is based on elliptic variational inequalities, parabolic variational inequalities, first order evolution equations and fixed point arguments.
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Latreche, S., Selmani, L. A thermoviscoelastic contact problem with friction, damage and wear diffusion. Afr. Mat. 34, 58 (2023). https://doi.org/10.1007/s13370-023-01100-5
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DOI: https://doi.org/10.1007/s13370-023-01100-5