Applied Mathematics and Mechanics

, Volume 31, Issue 5, pp 623–634

# Analysis of a quasistatic contact problem with adhesion and nonlocal friction for viscoelastic materials

• Arezki Touzaline
Article

## Abstract

A mathematical model is established to describe a contact problem between a deformable body and a foundation. The contact is bilateral and modelled with a nonlocal friction law, in which adhesion is taken into account. Evolution of the bonding field is described by a first-order differential equation. The materials behavior is modelled with a nonlinear viscoelastic constitutive law. A variational formulation of the mechanical problem is derived, and the existence and uniqueness of the weak solution can be proven if the coefficient of friction is sufficiently small. The proof is based on arguments of time-dependent variational inequalities, differential equations, and the Banach fixed-point theorem.

## Key words

viscoelastic materials adhesion nonlocal friction fixed point weak solution

O343.3

## 2000 Mathematics Subject Classification

47J20 49J40 74M10 74M15

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