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

• Main Authors: Mircea Sofonea, Meir Shillor
• Format: Article
• Language: English
• Published: Texas State University 2018-05-01
• Series: Electronic Journal of Differential Equations
• Subjects: 2D bar; frictional contact; normal compliance; weak solution; variational inequality
• Online Access: http://ejde.math.txstate.edu/Volumes/2018/107/abstr.html

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.