Size estimates for fat inclusions in an isotropic Reissner-Mindlin plate

TL;DR

This paper develops a method to estimate the size of an elastic inclusion in an isotropic Reissner-Mindlin plate using boundary measurements, providing bounds based on deformation work.

Contribution

It introduces a novel inverse problem approach for size estimation of inclusions in thick plates modeled by Reissner-Mindlin theory, with constructive bounds derived from boundary data.

Findings

Provides upper and lower bounds for inclusion size

Applicable to plates with Lipschitz boundary

Uses deformation work as a key scalar quantity

Abstract

In this paper we consider the inverse problem of determining, within an elastic isotropic thick plate modelled by the Reissner-Mindlin theory, the possible presence of an inclusion made of a different elastic material. Under some a priori assumptions on the inclusion, we deduce constructive upper and lower estimates of the area of the inclusion in terms of a scalar quantity related to the work developed in deforming the plate by applying simultaneously a couple field and a transverse force field at the boundary of the plate. The approach allows to consider plates with boundary of Lipschitz class.