Bloch wave spectral analysis in the class of generalized Hashin-Shtrikman micro-structures

TL;DR

This paper introduces a spectral approach using Bloch waves to analyze homogenization in a broad class of non-periodic Hashin-Shtrikman micro-structures, extending spectral methods beyond periodic settings.

Contribution

It develops a spectral representation of homogenized coefficients for non-periodic Hashin-Shtrikman micro-structures, expanding Bloch wave analysis to non-commutative, non-periodic micro-structures.

Findings

Established classical homogenization results for generalized Hashin-Shtrikman structures.

Provided spectral representation of homogenized coefficients.

Extended Bloch spectral analysis to non-periodic, non-commutative micro-structures.

Abstract

In this paper, we use spectral methods by introducing the Bloch waves to study the homogenization process in the non-periodic class of generalized Hashin-Shtrikman micro-structures \cite[page no. 281]{T}, which incorporates both translation and dilation with a family of scales, including one subclass of laminates. We establish the classical homogenization result with providing the spectral representation of the homogenized coefficients. It offers a new lead towards extending the Bloch spectral analysis in the non-periodic, non-commutative class of micro-structures.