Analysis and Numerical Approximation of a Contact Problem Involving Nonlinear Hencky-Type Materials with Nonlocal Coulomb's Friction Law. (18th August 2019)

• Record Type: Journal Article
• Authors: Benkhira, EL-Hassan; Fakhar, Rachid; Mandyly, Youssef
• Is Part Of: Numerical functional analysis and optimization. Volume 40:Number 11(2019)
• Page Start: 1291
• Page End: 1314
• Publication Date: 2019-08-18
• Subjects: Augmented Lagrangian -- Coulomb's friction law -- Kačanov method -- nonlinear elastic constitutive Hencky's law -- Signorini's condition -- Uzawa block relaxation method; 35J87 -- 74C05 -- 49J40 -- 47J25 -- 74S05 -- 65N55 -- 37M05; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2019.1600546
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: A static frictional contact problem between an elasto-plastic body and a rigid foundation is considered. The material's behavior is described by the nonlinear elastic constitutive Hencky's law. The contact is modeled with the Signorini condition and a version of Coulomb's law in which the coefficient of friction depends on the slip. The existence of a weak solution is proved by using Schauder's fixed-point theorem combined with arguments of abstract variational inequalities. Afterward, a successive iteration technique, based on the Kačanov method, to solve the problem numerically is proposed, and its convergence is established. Then, to improve the conditioning of the iterative problem, an appropriate Augmented Lagrangian formulation is used and that will lead us to Uzawa block relaxation method in every iteration. Finally, numerical experiments of two-dimensional test problems are carried out to illustrate the performance of the proposed algorithm.