Equivalent-inclusion approach for the conductivity of isotropic matrix composites with anisotropic inclusions

Abstract

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.

Equivalent inclusion approach and approximations for conductivity of isotropic matrix composites with sphere-like, platelet, and fibrous fillers

“…Equivalent inclusion approach has been applied to suspensions of randomly oriented anisotropic inclusions. 38…”

“…A common particular feature of equivalent inclusion PAs (equations (23) and (24), (26) and (27), and (29) and (30) is that the exact value c I of the inclusions is not required, while the respective equivalent inclusion conductivity truec¯I is found from the reference experimental effective conductivity crefeff at vIref, and then the approximation is used to predict c eff at a range of v I beyond vIref (the idea is similar to that when we use the equivalent inclusion conductivity truec¯I constructed from dilute solution reference in Hoang et al. 38 and Pham and Tran 39 and Do et al. 29 – as introduced in the first part of this section for the approximation outside the range vI≪1).…”

“…Equivalent inclusion approach has been applied to suspensions of randomly oriented anisotropic inclusions. 38 Equivalent inclusion approach has been used in Pham and Tran 39 to make equivalent inclusion conductivity c I for suspensions of coated spherical (circular) inclusions, in which the spherical (circular) core of conductivity c I2 is embedded in a spherical (circular) shell of conductivity c I1 , and their relative volume propor-…”

Effective medium approximation for conductivity of coated-inclusion composites with anisotropic coating

“…A widely recognized observation is that the effective behavior of a matrix-inclusion composites depends on the coating shells (interface or chemical reaction layer). Over several decades, determining the thermal gradient and flux fields in the layers has become a interesting subject for numerous theoretical [1][2][3][4][5][6][7][8][9].…”

Polarization versus Mori-Tanaka approximations for effective conductivity of isotropic composites

“…Hence various approximate formulae have been developed to estimate the effective properties, from the simplest volume arithmetic and harmonic averages to the more-advanced effective medium approximations (EMA) [1,2]. One of the most notable EMAs applied to matrix composites is the Mori-Tanaka one, which has been used widely in applications [3][4][5][6]. Likes many other EMAs, the Mori-Tanaka approximation has been derived from the field equations using analytical dilute solution results for ellipsoidal inclusions suspended in a major matrix.…”