Frictionless contact problem with adhesion and finite penetration for elastic materials

Arezki Touzaline¹

¹ Laboratoire de Systèmes Dynamiques Faculté de Mathématiques, USTHB BP 32 El Alia Bab-Ezzouar, 16111, Algeria

Annales Polonici Mathematici, Tome 98 (2010) no. 1, pp. 23-38.

Résumé

The paper deals with the problem of quasistatic frictionless contact between an elastic body and a foundation. The elasticity operator is assumed to vanish for zero strain, to be Lipschitz continuous and strictly monotone with respect to the strain as well as Lebesgue measurable on the domain occupied by the body. The contact is modelled by normal compliance in such a way that the penetration is limited and restricted to unilateral contraints. In this problem we take into account adhesion which is modelled by a surface variable, the bonding field, whose evolution is described by a first-order differential equation. We derive a variational formulation of the mechanical problem and we establish an existence and uniqueness result by using arguments of time-dependent variational inequalities, differential equations and the Banach fixed-point theorem. Moreover, using compactness properties we study a regularized problem which has a unique solution and we obtain the solution of the original model by passing to the limit as the regularization parameter converges to zero.

Détail

DOI : 10.4064/ap98-1-2

Keywords: paper deals problem quasistatic frictionless contact between elastic body foundation elasticity operator assumed vanish zero strain lipschitz continuous strictly monotone respect strain lebesgue measurable domain occupied body contact modelled normal compliance penetration limited restricted unilateral contraints problem account adhesion which modelled surface variable bonding field whose evolution described first order differential equation derive variational formulation mechanical problem establish existence uniqueness result using arguments time dependent variational inequalities differential equations banach fixed point theorem moreover using compactness properties study regularized problem which has unique solution obtain solution original model passing limit regularization parameter converges zero