On coated inclusions neutral to bulk strain fields in two dimensions

TL;DR

This paper investigates the conditions under which coated inclusions in two-dimensional isotropic elastic materials remain neutral to uniform bulk fields, revealing that such inclusions must be concentric disks under specific elastic conditions.

Contribution

It proves that coated inclusions neutral to bulk fields in 2D isotropic elasticity must be concentric disks, extending understanding of neutral inclusion configurations.

Findings

Neutral inclusions are concentric disks under certain elastic conditions.

The shape of the core and shell must be concentric disks for neutrality.

The result applies to isotropic elastic materials with specific shear and bulk moduli.

Abstract

The neutral inclusion problem in two dimensional isotropic elasticity is considered. The neutral inclusion, when inserted in a matrix having a uniform applied field, does not disturb the field outside the inclusion. The inclusion consists of the core and shell of arbitrary shapes, and their elasticity tensors are isotropic. We show that if the coated inclusion is neutral to a uniform bulk field, then the core and shell must be concentric disks, provided that the shear and bulk moduli satisfy certain conditions.