Numerical Analysis of a Sliding Frictional Contact Problem with Normal Compliance and Unilateral Contact ()
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.
Share and Cite:
Souleiman, Y. and Barboteu, M. (2021) Numerical Analysis of a Sliding Frictional Contact Problem with Normal Compliance and Unilateral Contact.
Open Journal of Modelling and Simulation,
9, 391-406. doi:
10.4236/ojmsi.2021.94025.