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Paper details
Number 1 - March 2002
Volume 12 - 2002
Analysis of a viscoelastic antiplane contact problem with slip-dependent friction
Thierry-Vincent Hoarau-Mantel, Andaluzia Matei
Abstract
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.
Keywords
antiplane problem, slip-dependent friction law, viscoelastic law