Asymptotic analysis of contact problems between an elastic material and thin-rigid plates

Abstract

We consider an elastic material in contact with a three-dimensional rigid plate of varying thickness. We suppose that a perfect adhesion occurs along thin zones disposed in a self-similar way on the interface between the two materials. We suppose that the elasticity coefficients in the plate depend on its thickness and tend to infinity as this thickness tends to zero. We derive the effective material properties using Γ-convergence methods.

Keywords:

• elastic material
• thin-rigid plate
• contact problems
• Γ-convergence

AMS Subject Classifications::

• 35B40
• 74Q05