## Abstract

We consider a mathematical model which describes the quasistatic contact between a viscoplastic body and a foundation. The material’s behavior is modelled with a rate-type constitutive law with internal state variable. The contact is frictionless and is modelled with normal compliance, unilateral constraint and memory term.

We present the classical formulation of the problem, list the assumptions on the data and derive a variational formulation of the model. Then we prove its unique weak solvability. The proof is based on arguments of history-dependent quasivariational inequalities.

We also study the dependence of the solution with respect to the data and prove a convergence result.

## Authors

Mircea **Sofonea**

(Laboratoire de Mathématiques et Physique, Université de Perpignan)

Flavius **Patrulescu**

(Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy)

Anca **Farcaş**

(Babeş-Bolyai University Faculty of Mathematics and Computer Sciences)

## Keywords

## Cite this paper as:

M. Sofonea, F. Pătrulescu, A. Farcaş,* A viscoplastic contact problem with normal compliance, unilateral constraint and memory term*, Appl. Math. Opt., vol. 62 (2014), pp. 175-198

## About this paper

##### Journal

Applied Mathematics and Optimization

##### Publisher Name

Springer US, New York, NY

##### Print ISSN

0095-4616

##### Online ISSN

1432-0606

## MR

3175193

## ZBL

1297.74086

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