Exact determination of the volume of an inclusion in a body having constant shear modulus

TL;DR

This paper presents an exact formula to determine the volume of an inclusion within an elastic body with constant shear modulus, based on boundary measurements mimicking an infinite medium.

Contribution

It introduces a novel exact formula for volume determination in elastic bodies with inclusions, under specific boundary conditions.

Findings

Derived an explicit formula for inclusion volume

Applicable when boundary conditions mimic an infinite medium

Relies on boundary measurements of displacement and traction

Abstract

We derive an exact formula for the volume fraction of an inclusion in a body when the inclusion and the body are linearly elastic materials with the same shear modulus. Our formula depends on an appropriate measurement of the displacement and traction around the boundary of the body. In particular, the boundary conditions around the boundary of the body must be such that they mimic the body being placed in an infinite medium with an appropriate displacement applied at infinity.