A viscoelastic frictionless contact problem with adhesion

Abstract

We consider a model for the quasistatic, bilateral, adhesive and frictionless contact between a viscoelastic body and a rigid foundation. The adhesion process on the contact surface is modeled by a surface internal variable, the bonding field, and the tangential shear due to the bonding field is included. The problem is formulated as a coupled system of a variational equality for the displacements and an integro-differential equation for the bonding field. The existence of a unique weak solution for the problem is established by construction of an appropriate mapping which is shown to be a contraction on a Hilbert space. We also consider the problem describing the bilateral contact between two viscoelastic bodies, and establish similar results.

Keywords:

• Adhesion
• Quasistatic process
• Bilateral frictionless contact
• Viscoelastic material
• Existence and uniqueness
• Monotone operator
• Fixed point

AMS Subject Classification:

• 74M15
• 74F99
• 74G25

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Notes

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