Dual formulation of a quasistatic viscoelastic contact problem with tresca's friction law

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.

Keywords:

• Quasistatic bilateral frictional contact
• ; Viscoelastic constitutive law
• Dual problem
• Fixed point
• Tresca'a law of friction

AMS:

• 74M10
• 35585
• 74D10
• 74M15

^*Corresponding author.

^*Corresponding author.

Notes

^*Corresponding author.