Sofonea, M. and Matei, A. (2012) Mathematical Models in Contact Mechanics (London Mathematical Society Lecture Note Series Book Vol. 398). Cambridge University Press, Cambridge.

has been cited by the following article:

• TITLE: Numerical Analysis of a Sliding Frictional Contact Problem with Normal Compliance and Unilateral Contact

  AUTHORS: Yahyeh Souleiman, Mikaël Barboteu

  KEYWORDS: Viscoelastic Material, Sliding Frictional Contact, Normal Compliance, Unilateral Constraint, Memory Term, Variational Approximation, Finite Element, Error Estimate, Numerical Simulations

  JOURNAL NAME: Open Journal of Modelling and Simulation, Vol.9 No.4, October 18, 2021

  ABSTRACT: This paper represents a continuation of [1] and [2]. Here, we consider the numerical analysis of a non-trivial frictional contact problem in a form of a system of evolution nonlinear partial differential equations. The model describes the equilibrium of a viscoelastic body in sliding contact with a moving foundation. The contact is modeled with a multivalued normal compliance condition with memory term restricted by a unilateral constraint and is associated with a sliding version of Coulomb’s law of dry friction. After a description of the model and some assumptions, we derive a variational formulation of the problem, which consists of a system coupling a variational inequality for the displacement field and a nonlinear equation for the stress field. Then, we introduce a fully discrete scheme for the numerical approximation of the sliding contact problem. Under certain solution regularity assumptions, we derive an optimal order error estimate and we provide numerical validation of this result by considering some numerical simulations in the study of a two-dimensional problem.