Weak solutions for contact models involving a class of generalized materials. (August 2023)

• Record Type: Journal Article
• Authors: Matei, Andaluzia
• Is Part Of: Nonlinear analysis. Volume 72(2023)
• Publication Date: 2023-08
• Subjects: Generalized materials -- Multi-contact boundary conditions -- Bipotential -- Lagrange multipliers -- Weak solutions -- Fixed points for set-valued maps; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2023.103863
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: We consider a contact model for a class of generalized materials whose behaviour is described by means of a bipotential. Using the theory of the bipotentials we deliver a weak formulation consisting of a system of three variational inequalities. The unknown is a triple having as components the displacement field, the Cauchy stress tensor and a Lagrange multiplier related to the friction force on the frictional contact zone. We investigate the existence of the weak solutions by using a fixed point theorem for set-valued mappings and a minimization technique.