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

2016 ◽  
Vol 38 (4) ◽  
pp. 239-248 ◽  
Author(s):  
Do Quoc Hoang ◽  
Pham Duc Chinh ◽  
Tran Anh Binh
Keyword(s):  
Finite Elements ◽  
Effective Conductivity ◽  
Spherical Inclusion ◽  
Effective Medium ◽  
Matrix Composites ◽  
Isotropic Matrix ◽  
Equivalent Inclusion

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 equivalent-inclusion 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

2018 ◽  
Vol 37 (14) ◽  
pp. 968-980
Author(s):  
Trung Kien Nguyen ◽  
Duc Chinh Pham ◽  
Quoc Hoang Do
Keyword(s):  
Experimental Data ◽  
Effective Medium ◽  
Matrix Composites ◽  
Conductivity Data ◽  
Isotropic Matrix ◽  
Equivalent Inclusion ◽  
Circular Fiber ◽  
Experimental Reference ◽  
Fibrous Fillers

The construction starts from certain typical effective medium approximations for conductivity of idealistic isotropic matrix composites with randomly oriented inclusions of perfect spherical, platelet, and circular fiber forms, which obey Hashin–Shtrikman bounds over all the ranges of volume proportions of the component materials. Equivalent inclusion approach is then developed to account for possible diversions, such as non-idealistic geometric forms of the inhomogeneities, imperfect matrix-inclusion contacts, filler dispersions, and when the particular values of the fillers’ properties are unspecified, using available numerical or experimental reference conductivity data for particular composites. Illustrating applications involving experimental data from the literature show the usefulness of the approach.

A Spherical Inclusion with Inhomogeneous Interface in Conduction

2003 ◽  
Vol 19 (1) ◽  
pp. 1-8
Author(s):  
T. Chen ◽  
C. H. Hsieh ◽  
P. C. Chuang
Keyword(s):  
Infinite Number ◽  
Effective Conductivity ◽  
Spherical Inclusion ◽  
Cone Angle ◽  
Imperfect Interface ◽  
Infinite Matrix ◽  
Algebraic Equations ◽  
Legendre Series ◽  
Linear Set ◽  
The Matrix

ABSTRACTA series solution is presented for a spherical inclusion embedded in an infinite matrix under a remotely applied uniform intensity. Particularly, the interface between the inclusion and the matrix is considered to be inhomegeneously bonded. We examine the axisymmetric case in which the interface parameter varies with the cone angle θ. Two kinds of imperfect interfaces are considered: an imperfect interface which models a thin interphase of low conductivity and an imperfect interface which models a thin interphase of high conductivity. We show that, by expanding the solutions of terms of Legendre polynomials, the field solution is governed by a linear set of algebraic equations with an infinite number of unknowns. The key step of the formulation relies on algebraic identities between coefficients of products of Legendre series. Some numerical illustrations are presented to show the correctness of the presented procedures. Further, solutions of the boundary-value problem are employed to estimate the effective conductivity tensor of a composite consisting of dispersions of spherical inclusions with equal size. The effective conductivity solely depends on one particular constant among an infinite number of unknowns.

Anisotropic effective conductivity in fractured rocks by explicit effective medium methods

2014 ◽  
Vol 62 (6) ◽  
pp. 1297-1314 ◽  
Author(s):  
Pål Naeverlid Saevik ◽  
Morten Jakobsen ◽  
Martha Lien ◽  
Inga Berre
Keyword(s):  
Fractured Rocks ◽  
Effective Conductivity ◽  
Effective Medium

scholarly journals FREQUENCY DEPENDENT EFFECTIVE CONDUCTIVITY OF TWO-DIMENSIONAL METAL–DIELECTRIC COMPOSITES

2005 ◽  
Vol 16 (06) ◽  
pp. 991-998 ◽  
Author(s):  
LOTFI ZEKRI
Keyword(s):  
Lattice Model ◽  
Effective Conductivity ◽  
System Size ◽  
Effective Medium ◽  
Two Dimensional ◽  
Metal Insulator ◽  
Frequency Dependent ◽  
Low Frequencies

We analyze a random resistor–inductor–capacitor (RLC) lattice model of two-dimensional metal–insulator composites. The results are compared with Bruggeman's and Landauer's Effective Medium Approximations where a discrepancy was observed for some frequency zones. Such a discrepancy is mainly caused by the strong conductivity fluctuations. Indeed, a two-branches distribution is observed for low frequencies. We show also by increasing the system size that at pc the so-called Drude peak vanishes; it increases for vanishing losses.

Two-Ellipsoidal Inhomogeneities by the Equivalent Inclusion Method

1975 ◽  
Vol 42 (4) ◽  
pp. 847-852 ◽  
Author(s):  
Z. A. Moschovidis ◽  
T. Mura
Keyword(s):  
Computer Program ◽  
Strain Field ◽  
Applied Strain ◽  
Stress And Strain ◽  
Isotropic Matrix ◽  
Equivalent Inclusion Method ◽  
Inclusion Method ◽  
Equivalent Inclusion ◽  
The Matrix ◽  
Final Stress

The problem of two ellipsoidal inhomogeneities in an infinitely extended isotropic matrix is treated by the equivalent inclusion method. The matrix is subjected to an applied strain field in the form of a polynomial of degree M in the position coordinates xi. The final stress and strain states are calculated for two isotropic ellipsoidal inhomogeneities both in the interior and the exterior (in the matrix) by using a computer program developed. The method can be extended to more than two inhomogeneities.

scholarly journals Effective conductivity of isotropic composite with Kapitza thermal resistance

2018 ◽  
Author(s):  
Kien Trung Nguyen ◽  
Luat Van Nguyen ◽  
Chinh Duc Pham
Keyword(s):  
Thermal Conductivity ◽  
Thermal Resistance ◽  
Effective Thermal Conductivity ◽  
Effective Conductivity ◽  
Imperfect Interface ◽  
Simple Method ◽  
Isotropic Composite ◽  
Equivalent Inclusion

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.

Sign in / Sign up

Export Citation Format

Share Document