Eshelby's method for unidirectional periodic composites

Abstract

Open boundary conditions are always used to investigate the effective properties of composites. In this paper, Eshelby's transformation field method is developed to deal with the effective responses of the unidirectional periodic composites having an open boundary. In this method, Hermite polynomials are chosen to cope with the open boundary conditions of the perturbation fields induced by inclusions. The transformation fields are introduced in the composite system to meet the interface conditions between the complex structure inclusions and the matrix. As an example, the formulas of Eshelby's method are derived for calculating the effective responses of the 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 the unidirectional periodic composites having complex geometric inclusions.