Abstract
We consider quasistatic evolution of a viscoelastic boby which is in bilateral frictional contact with a rigid foundation. We derive two variational formulations for the problem:the primal formulation in terms of the displacements and the dual formulation in terms of the stress field. We prove the existence of a unique solution to each one and establish the equivalence between the two variational formulations. We also prove the continuous dependence of the solution on the friction yield limit.
Highlights
We investigate a model for the process of quasistatic frictional contact between a viscoelastic body and a rigid foundation
This work is a continuation of [15, 16] where related problems were investigated, but there only the primal formulations, in terms of the displacements, were considered
A viscoelastic body occupies the domain Q and has surface r that is partitioned into three disjoint measurable parts rv, rN and r c such that meas r D > 0
Summary
We investigate a model for the process of quasistatic frictional contact between a viscoelastic body and a rigid foundation. The classical formulation of the model consists of a system of evolution equations with a frictional boundary condition on the contact surface Since, generally, such problems do not have classical solutions, we reformulate the model as a variational inequality for the displacements. Since such problems do not have classical solutions, we reformulate the model as a variational inequality for the displacements
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