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

作     者：Yahyeh Souleiman Mikaël Barboteu Yahyeh Souleiman;Mikaël Barboteu

作者机构：Mathematics and Computer Science Laboratory Campus Balbala University of Djibouti Balbala Djibouti Mathematics and Physics Laboratory University of Perpignan Perpignan France 

出 版 物：《Open Journal of Modelling and Simulation》 (建模与仿真（英文）)

年 卷 期：2021年第9卷第4期

页      面：391-406页

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

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

摘      要：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.