Eshelby's method for unidirectional periodic composites

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.