Abstract
This work is concerned with the study of a class of dynamic problems, coupling unilateral contact, adhesion and nonlocal friction for viscoelastic bodies of Kelvin-Voigt type. We consider a model for the dynamic frictional contact with reversible adhesion, where the coefficient of friction depends on the slip velocity and the evolution of the intensity of adhesion is nonlinear. A corresponding variational formulation is given as a system of coupled implicit variational inequalities, including a nonlinear parabolic inequality which describes the evolution, possibly reversible, of the adhesion field. An abstract problem is considered in order to study the approximation of variational solutions by a penalty method and also to analyse other problems including normal compliance laws. Based on incremental techniques together with a fixed point method, a general result is presented and is applied to show the existence and uniqueness of the penalized solutions. Using several estimates on the penalized solutions and some compactness arguments, one can obtain a variational solution of the initial problem.
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Cocou, M. (2013). Coupled Implicit Variational Inequalities and Dynamic Contact Interactions in Viscoelasticity. In: Stavroulakis, G. (eds) Recent Advances in Contact Mechanics. Lecture Notes in Applied and Computational Mechanics, vol 56. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33968-4_14
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DOI: https://doi.org/10.1007/978-3-642-33968-4_14
Publisher Name: Springer, Berlin, Heidelberg
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