Stability under lamination and polycrystalline effective conductivity

TL;DR

This paper proves the stability under lamination of certain effective conductivity matrices in polycrystals, enhancing the understanding of their G-closure and providing improved bounds in three-dimensional cases.

Contribution

It establishes the stability under lamination for a specific set of matrices related to polycrystal conductivities, advancing the theoretical framework of effective medium approximations.

Findings

Proves stability under lamination for a class of matrices

Provides the best known inner bounds on the G-closure of 3D polycrystals

Connects stability results with previous constructions for effective conductivities

Abstract

We prove the stability under lamination of a set of real, symmetric 3$\times$3 matrices that can be viewed as a subset of the effective conductivities of a polycrystal. Constructed in a companion paper, such set in combination with several previous constructions provides the best inner bound known so far on the $G$-closure of a three dimensional polycrystal.