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. | Vietnam Journal of Mechanics, VAST, Vol. 38, No. 4 (2016), pp. 239 – 248 DOI: EQUIVALENT-INCLUSION APPROACH FOR THE CONDUCTIVITY OF ISOTROPIC MATRIX COMPOSITES WITH ANISOTROPIC INCLUSIONS Do Quoc Hoang1,2,∗ , Pham Duc Chinh2,3 , Tran Anh Binh1,2 1 National University of Civil Engineering, Hanoi, Vietnam 2 Graduate University of Science and Technology, VAST, Hanoi, Vietnam 3 Institute of Mechanics, VAST, Hanoi, Vietnam ∗ E-mail: hoangdq@ Received August 15, 2015 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. Keywords: Isotropic multicomponent material, disorderly oriented anisotropic inclusions, effective conductivity, matrix composite, equivalent inclusion. 1. INTRODUCTION Theoretical determination of effective properties of multicomponent materials generally is difficult because of their complex microstructure and the random distribution of inclusions. The most rigorous approach is to to construct upper and lower bounds on the possible values of the effective properties, [1–3]. The bounds containing the properties and volume fractions of the component materials are not very useful in the case of high contrast of matrix-inclusion properties. The numerical methods [4–9], such as finite element one, fast
