On the signorini frictionless contact problem for linear viscoelastic materials

Abstract

We consider a mathematical model which describes the contact between a deformable body and an obstacle, the so-called foundation. The body is assumed to have a linear viscoelastic behavior that we model with the Kelvin-Voigt constitutive law. The contact is frictionless and is modeled with the well-known Signorini condition in the form with a zero gap function. We derive a weak formulation of the model and prove an existence and uniqueness result of the solution. The proof is based on a regularization method involving normal compliance frictionless contact conditions followed by compactness and lower semicontinuity arguments. We also prove that the solution of the problem converges to the solution of the corresponding elastic problem, as the viscosity tensor converges to zero.

Keywords:

• Viscoelastic material
• Frictionless contact
• Signorini condition
• Normal compliance
• Weak solution
• Approach to elasticity

AMS Subject Classification:

• 74M15
• 35J85
• 75D05

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Notes

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