Nonlinear Neutral Inclusions: Assemblages of Spheres

TL;DR

This paper explores the construction of nonlinear neutral inclusions, specifically assemblages of coated spheres and disks, that do not disturb a uniform electric field outside the inclusion, extending classical linear results.

Contribution

It introduces methods for creating nonlinear neutral inclusions from assemblages of coated spheres and disks, expanding the understanding of neutral inclusions in nonlinear materials.

Findings

Assemblages of coated spheres can be constructed as nonlinear neutral inclusions.

Assemblages of coated disks in two dimensions are also analyzed for neutrality.

The study extends classical linear neutral inclusion concepts to nonlinear materials.

Abstract

If a neutral inclusion is inserted in a matrix containing a uniform applied electric field, it does not disturb the field outside the inclusion. The well known Hashin coated sphere is an example of a neutral coated inclusion. In this paper, we consider the problem of constructing neutral inclusions from nonlinear materials. In particular, we discuss assemblages of coated spheres and the two-dimensional analogous problem of assemblages of coated disks.