Effective properties of composites with open boundary conditions

Abstract: A primitive problem of predicting the effective properties of composites is open boundary conditions. In this paper, Eshelby's transformation field method is developed to solve the open boundary problem of two-phase composites having arbitrary inclusion geometry. The transformation fields are introduced in the composite system to cope with the complicated interface boundary-value problem of the composite. Furthermore, the open boundary problem is solved by Hermite polynomial, which is used to express the transformation fields and the perturbation fields. As an example, the formulas of Eshelby's method are derived for calculating the effective dielectric property of two-dimensional isotropic dielectric composites having open boundary conditions. The validity of the method is verified by comparing the effective responses estimated by the method with the exact solutions of dilute limit. The results show that the method is valid to solve the open boundary problem of composites having complex geometric inclusions.