An Asymptotic Expansion for Perturbations in the Displacement Field due to the Presence of Thin Interfaces

TL;DR

This paper develops a rigorous asymptotic expansion for displacement fields caused by thin elastic inhomogeneities with variable thickness, using layer potential techniques, and relates measurements to object shape.

Contribution

It introduces a new asymptotic expansion method for thin inhomogeneities with non-uniform thickness in elasticity problems, extending layer potential techniques.

Findings

Derived a rigorous asymptotic expansion for displacement fields

Established a relationship between measurements and object shape

Extended layer potential techniques to variable thickness inhomogeneities

Abstract

We derive an asymptotic expansion for two-dimensional displacement field associated to thin elastic inhomogeneities having no uniform thickness. Our derivation is rigorous and based on layer potential techniques. We extend these techniques to determine a relationship between traction-displacement measurements and the shape of the object.