Abstract

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.

Author information

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Lukasz Gleń

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

lukasz.glen@poczta.fm

Keywords

  • Inelastic deformation theory
  • viscoplasticity
  • friction
  • frictional contact
  • sum of monotone operators

Mathematics Subject Classification

74C10

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Suggested citation

L. Gleń. “Quasistatic Viscoplasticity with Polynomial Growth Condition and with Frictional Contact.” Journal of Convex Analysis 24 (2017), No. 1, 1–17. https://doi.org/10.68381/jca24001

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Published by Heldermann Verlag, 2017. Rights now held by Banach Press LLC.