Abstract. Many effective medium approximations for effective conductivity are elaborated for matrix composites made from isotropic continuous matrix and isotropic inclusions associated with simple shapes such as circles or spheres, . . . In this paper, we focus specially on the effective conductivity of the isotropic composites containing the disorderly oriented anisotropic inclusions. We aim to replace those inhomogeneities by simple equivalent circular (spherical) isotropic inclusions with modified conductivities. Available simple approximations for the equivalent circular (spherical)-inclusion media then can be used to estimate the effective conductivity of the original composite. The equivalentinclusion approach agrees well with numerical extended finite elements results.

Abstract. Three-point correlation bounds are constructed on effective conductivity of unidirectional composites, which are isotropic in the transverse plane. The bounds contain, in addition to the properties and volume proportions of the component materials, three-point correlation parameters describing the micro-geometry of a composite, and are tighter those obtained in [1]. The bounds, applied to some disordered and periodic composites, keep inside the numerical homogenization results obtained by Fast Fourier method.

A novel approach to predict the effective elastic moduli of matrix composites made from non-circular inclusions embedded in a continuous matrix is proposed. In this approach, those inhomogeneities are substituted by simple equivalent circular-inclusions with modified elastic properties obtained from comparing the dilute solution results. Available simple approximations for the equivalent circular-inclusion medium then can be used to estimate the effective elastic moduli of the original composite. Robustness of proposed approach is demonstrated through the numerical examples with elliptic inclusions.

No abstract

A simple method is introduced for computing the effective conductivity of isotropic composite with imperfect interface. Based on the doubly-coated circle assemblage model, one can determine the effective thermal conductivity of the composite. The application of this model to the composite with imperfect interface of the Kapitza's type is proposed. The results obtained were compared with the FFT simulation and the equivalent inclusion approximation in 2D show the effectiveness of the methods.