Nonlocal and Nonlinear Friction Laws and Variational Principles for Contact Problems in Elasticity

Abstract

The use of the classical Coulomb law of friction in the formulation of contact problems in elasticity leads to both physical and mathematical difficulties; the former arises from the fact that this law provides a poor model of frictional stresses at points on metallic surfaces in contact, and the latter is due to the fact that the existence of solutions of the governing equations can be proved only for very special situations. In the present paper, nonclassical friction laws are proposed in an attempt to overcome both of these difficulties. We consider a class of contact problems involving the equilibrium of linearly elastic bodies in contact on surfaces on which nonlocal and nonlinear friction laws are assumed to hold. The physics of friction between metallic bodies in contact is discussed and arguments in support of the theory are presented. Variational principles for boundary-value problems in elasticity in which such nonlinear nonlocal laws hold are then developed. A brief discussion of the questions of existence and uniqueness of solutions to the nonlocal and nonlinear problems is given.

Modélisation et résolution du problème de contact mécanique et son application dans un contexte multi-physiques /

“…:"""": : Afin de généraliser cette modélisation et de la rendre plus proche de la réalité, la microstructure de la zone de contact peut être prise en compte par une approche non locale et non linéaire [2] Ceci peut provoquer des instabilités ou des oscillations numériques lors d'une résolution numérique. Néanmoins, ce travail ne s'intéresse pas au choix de la loi du contact méca-nique frottant, mais plutôt à la résolution du problème dans le cas où cette loi est non différentiable.…”

Effect of the Material Parameters on Layered Viscoelastic Frictional Contact Systems

“…According to Oden and Pires [21], the nonlinear relation between the frictional stress and the relative tangential displacement throughout the contact interface can be represented as…”

“…The welding, shearing, and ploughing theory is the basis for the nonclassical friction laws. Nonclassical nonlocal-nonlinear friction models are developed by many researchers, among of them Oden and Pires [21,22].…”

Constitutive equation for friction with rotational and orthotropic anisotropy

“…First, let the elastic-sliding velocity be given by (6) where fn and ft are the normal component and tangential component, respectively, of the traction vector f applied to a unit area of contact surface, i.e.…”