Nonlinear Neutral Inclusions: Assemblages of Coated Ellipsoids

TL;DR

This paper investigates the design of nonlinear neutral inclusions, specifically assemblages of coated ellipsoids, that do not disturb the external electric or thermal fields in a matrix, extending classical neutral inclusion concepts.

Contribution

It introduces methods for constructing nonlinear neutral inclusions from coated ellipsoids, expanding the classical theory of neutral inclusions to nonlinear materials.

Findings

Assemblages of coated ellipsoids can be designed as nonlinear neutral inclusions.

The study generalizes the Hashin coated sphere construction to nonlinear and ellipsoidal geometries.

The constructed inclusions do not disturb the external field in the matrix.

Abstract

The problem of determining nonlinear neutral inclusions in (electrical or thermal)conductivity is considered. Neutral inclusions, inserted in a matrix containing a uniform applied electric field, do not disturb the field outside the inclusions. The well known Hashin coated sphere construction is an example of a neutral inclusion. In this paper, we consider the problem of constructing neutral inclusions from nonlinear materials. In particular, we discuss assemblages of coated ellipsoids.