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1 International Journal of Applied Mathematics and Computer Science

1 2002

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Analysis of a Viscoelastic Antiplane Contact Problem With Slip-Dependent Friction

Hoarau-Mantel T. V., Matei A.

International Journal of Applied Mathematics and Computer Science

2002

Vol. 12, no 1

51-58

We study a mathematical problem modelling the antiplane shear deformation of a viscoelastic body in frictional contact with a rigid foundation. The contact is bilateral and is modelled with a slip-dependent friction law. We present the classical formulation for the antiplane problem and write the corresponding variational formulation. Then we establish the existence of a unique weak solution to the model, by using the Banach fixed-point theorem and classical results for elliptic variational inequalities. Finally, we prove that the solution converges to the solution of the corresponding elastic problem as the viscosity converges to zero.