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Journal of Convex Analysis 24 (2017), No. 1, 001--017
Copyright Heldermann Verlag 2017

Quasistatic Viscoplasticity with Polynomial Growth Condition and with Frictional Contact

Lukasz Glen
Faculty of Mathematics and Information Sciences, Warsaw University of Technology, ul. Koszykowa 75, 00-662 Warsaw, Poland

We consider a problem in the inelastic deformation theory. There is a body consisted of a viscoplastic material, which is deformed in a quasistatic process i.e. the movement varies slowly. Additionally we assume that the body has a contact with a rigid foundation: the body moves on the foundation with a friction modelled by a dissipative potential. Together with an inelastic constitutive function, it gives a problem that involves two monotone operators: one acting on the body, other acting on its boundary. We prove existence and uniqueness of a solution to this problem where inelastic constitutive function has a polynomial growth at infinity.

Keywords: Inelastic deformation theory, viscoplasticity, friction, frictional contact, sum of monotone operators.

MSC: 74C10

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