An asymptotic expansion for perturbations in the displacement field due to the presence of thin interfaces

Abstract

We rigorously derive an asymptotic expansion for two-dimensional displacement field associated with thin elastic inclusion having no uniform thickness. Our approach is based on layer potential techniques through integral representation formulas of the fields. We extend these techniques to determine a relationship between traction–displacement measurements and the shape of the thin inclusion.

Keywords:

• Thin inhomogeneities
• small perturbations
• Lamé system
• asymptotic expansions
• boundary integral method

AMS Subject Classifications:

• 35B30
• 35C20
• 31B10

Notes

No potential conflict of interest was reported by the authors.