Estimating area of inclusions in anisotropic plates from boundary data

TL;DR

This paper develops a method to estimate the size of inclusions in anisotropic elastic plates using boundary measurements, providing bounds based on measurable quantities related to boundary forces and displacements.

Contribution

It introduces a constructive approach to estimate the area of inclusions in anisotropic plates from boundary data, extending inverse problem techniques to complex elastic materials.

Findings

Provides upper and lower bounds for inclusion area

Uses boundary measurements of displacement and forces

Applicable to non-homogeneous anisotropic materials

Abstract

We consider the inverse problem of determining the possible presence of an inclusion in a thin plate by boundary measurements. The plate is made by non-homogeneous linearly elastic material belonging to a general class of anisotropy. The inclusion is made by different elastic material. Under some a priori assumptions on the unknown inclusion, we prove constructive upper and lower estimates of the area of the unknown defect in terms of an easily expressed quantity related to work, which is given in terms of measurements of a couple field applied at the boundary and of the induced transversal displacement and its normal derivative taken at the boundary of the plate.