Size estimates for nanoplates

TL;DR

This paper develops quantitative bounds for estimating the size of an inclusion within an elastic nanoplate using boundary measurements, aiding defect detection in nanomaterials.

Contribution

It introduces a method to estimate the size of an unknown elastic inclusion in a nanoplate based on boundary data, under specific assumptions.

Findings

Provides upper and lower bounds for inclusion area

Relates boundary work to inclusion size

Applicable to elastic isotropic nanoplates

Abstract

We consider the problem of determining, within an elastic isotropic nanoplate in bending, the possible presence of an inclusion made of different elastic material. Under suitable a priori assumptions on the unknown inclusion, we provide quantitative upper and lower estimates for the area of the unknown defect in terms of the works exerted by the boundary data when the inclusion is present or absent.