Electron. J. Differential Equations, Vol. 2018 (2018), No. 107, pp. 1-19.

Model and analysis for quasistatic frictional contact of a 2D elastic bar

Mircea Sofonea, Meir Shillor

This article constructs and analyzes a mathematical model that describes the quasistatic evolution of a 2D elastic bar that may come in frictional contact with a deformable foundation. The model and the underlying mechanical assumptions are described in detail and so are the assumptions on the problem data. The variational formulation of the problem is derived and, since friction is taken into account, it is in the form of an evolutionary variational inequality for the displacement field. Existence of solutions for the problem is established by using arguments of evolutionary variational inequalities.

Submitted January 30, 2017. Published May 8, 2018.
Math Subject Classifications: 74M10, 74M15, 74K20, 58E35, 35Q74.
Key Words: 2D bar; frictional contact; normal compliance; weak solution; variational inequality.

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Mircea Sofonea
Laboratoire de Mathéematiques et Physique
University of Perpignan Via Domitia
52 Avenue Paul Alduy, 66860 Perpignan, France
email: sofonea@univ-perp.fr
Meir Shillor
Department of Mathematics and Statistics
Oakland University
Rochester, MI 48309, USA
email: shillor@oakland.edu

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