Eshelby's method for unidirectional periodic composites

TL;DR

This paper extends Eshelby's transformation field method to analyze the effective properties of unidirectional periodic composites with open boundaries, using Hermite polynomials and interface conditions, validated by comparison with exact solutions.

Contribution

The paper develops a novel approach combining Eshelby's method with Hermite polynomials to handle open boundary conditions in complex unidirectional composites.

Findings

Method accurately estimates effective responses of dielectric composites.

Validation shows good agreement with exact dilute limit solutions.

Approach effectively handles complex geometric inclusions with open boundaries.

Abstract

Open boundary conditions are always used in investigating the effective properties of composites. In this paper, Eshelby's transformation field method is developed to deal with the effective response of unidirectional periodic composites having an open boundary. In the method, Hermite polynomials are used to cope with the open boundary conditions of the perturbation fields induced by the inclusions. The transformation fields are introduced in the composite system to meet the interface conditions between complex structure inclusions and matrix. As an example, Eshelby's method is used to estimate the effective responses of two-dimensional unidirectional periodic dielectric composites having an open boundary. The validity is verified by comparing the effective responses calculated by the method with the exact solutions of dilute limit. It is shown that the method is valid to solve the open boundary problem of unidirectional periodic composites having complex geometric inclusions.