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.
Highlights
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
A more general contact condition, called the normal compliance condition restricted by unilateral constraint introduced in [11], models the contact with an elastic-rigid foundation
The aim of this paper is to study the numerical analysis of the contact problem with a sliding version of Coulomb’s law of dry friction for rate-type viscoplastic materials within the framework of the Mathematical Theory of Contact Mechanics
Summary
The modeling and the analysis of frictional contact problems represent important topics both in Engineering Sciences and Applied Mathematics, see for in-. The contact law with normal compliance and unilateral constraint was associated with a sliding version of Coulomb’s law of dry friction Both the material constitutive law of the body and the frictional contact model is characterized by memory terms in order to take into account physical relaxation behaviors. The mathematical model is based on a viscoelastic constitutive law with a long memory, contact conditions combining normal compliance, memory term, unilateral constraint and a frictional sliding version of Coulomb’s law. This nonstandard mathematical model can be formulated by a history-dependent quasi-variational inequality for the displacement field.
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