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Analysis of a contact adhesive problem with normal compliance and nonlocal friction

100%

Touzaline A.

tom 104

nr 2

175-188

The paper deals with the problem of a quasistatic frictional contact between a nonlinear elastic body and a deformable foundation. The contact is modelled by a normal compliance condition in such a way that the penetration is restricted with a unilateral constraint and associated to the nonlocal friction law with adhesion. The evolution of the bonding field is described by a first-order differential equation. We establish a variational formulation of the mechanical problem and prove an existence and uniqueness result under a smallness assumption on the friction coefficient by using arguments of time-dependent variational inequalities, differential equations and the Banach fixed-point theorem.

A study of a unilateral and adhesive contact problem with normal compliance

100%

Touzaline A.

2014

tom 41

nr 4

385-402

The aim of this paper is to study a quasistatic unilateral contact problem between an elastic body and a foundation. The constitutive law is nonlinear and the contact is modelled with a normal compliance condition associated to a unilateral constraint and Coulomb's friction law. The adhesion between contact surfaces is taken into account and is modelled with a surface variable, the bonding field, whose evolution is described by a first-order differential equation. We establish a variational formulation of the mechanical problem and prove an existence and uniqueness result in the case where the friction coefficient is small enough. The technique of proof is based on time-dependent variational inequalities, differential equations and the Banach fixed-point theorem. We also study a penalized and regularized problem which admits at least one solution and prove its convergence to the solution of the model when the penalization and regularization parameter tends to zero.