Analysis of a frictionless contact problem for elastic-viscoplastic materials

Abstract

We consider a dynamic frictionless contact problem for elastic-viscoplastic materials with damage. The contact is modelled with normal compliance condition. The adhesion of the contact surfaces is considered and is modelled with a surface variable, the bonding field whose evolution is described by a first order differential equation. We derive variational formulation for the model and prove an existence and uniqueness result of the weak solution. The proof is based on arguments of nonlinear evolution equations with monotone operators, a classical existence and uniqueness result on parabolic inequalities, differential equations and fixed-point arguments.

A Dynamic Problem of Frictionless Contact for Elastic-Thermo-Viscoplastic Materials With Damage

“…The novelty in all the above papers is the introduction of an absolute temperature θ. Then In this paper we extend a part of the results in [27,35] to more general contact conditions for elastic-thermo-viscoplastic materials.…”

“…Analysis of models for adhesive contact can be found in [9,10], and recently in the monograph [?]. We refer the reader to the extensive bibliography on the subject in [30,33,35,36]. The novelty in all the above papers is the introduction of an absolute temperature θ.…”

A frictionless contact problem for elastic-visco-plastic materials with adhesion and thermal effects

“…The contact condition (2.11) was used in various papers, see e.g. [6,7,26,29]. Condition (2.12) represents the adhesive contact condition on the tangential plane, in which p τ is a given function and R τ is the truncation operator given by…”

“…The adhesive contact between deformable bodies, when a glue is added to prevent relative motion of the surfaces, has received recently increased attention in the mathematical literature. Analysis of models for adhesive contact can be found in [23,25,26] and recently in the monographs [21]. In these papers, the bonding field, denoted by β , it describes the point wise fractional density of adhesion of active bonds on the contact surface, and some times referred to as the intensity of adhesion.…”

A frictionless contact problem for elastic-viscoplastic materials with adhesion and thermal effects

“…The adhesive contact between deformable bodies, when a glue is added to prevent relative motion of the surfaces, has received recently increased attention in the mathematical liter-ature. Analysis of models for adhesive contact can be found in [23,25,26] and recently in the monographs [21]. In these papers, the bonding field, denoted by β , it describes the point wise fractional density of adhesion of active bonds on the contact surface, and some times referred to as the intensity of adhesion.…”