Estimating the effective conductivity for ellipse-inclusion model with Kapitza thermal resistance

Van-Luat Nguyen

doi:10.1051/epjam/2021010

Abstract

The ellipse assemblage model with imperfect interface has quite complex microstructure, that can be considered an extension of the circle assemblage model with imperfect interfaces. The paper introduces an approximate method for computing the effective conductivity of isotropic composites with imperfect interfaces in two-dimensional space. Based on the coated-ellipse assemblage model and the equivalent inclusion approximation, one can determine the effective thermal conductivity of the composites. The polarization approximation is given in an explicit form (PEK) and this method will be applied to calculate the effective conductivity of the composite with Kapitza thermal resistance model. The PEK result will have compared with the Fast Fourier Transform (FFT) simulation and Hashin-strikman bounds (HS).

Highlights

Due to limited available information about the materials as well as the complexity of microstructure, the determination of macroscopic moduli of composite materials is not simple
The Fast Fourier Transform (FFT) results in a special case r =1, a1 = a2 = R which were compared with results of Monchiet [15] for square model with one circle inclusion in the unit cell (Fig. 2), the unit cell having the dimension L = 1 along each space directions containing inclusion with the dimensionless radius R varies from 0.1 to 0.5
The paper has presented a solution for effective conductivity of the coated-ellipse assemblage model with imperfect interfaces, the effective conductivity of isotropic multiphase composites with imperfect interfaces can be determined with two different approaches

Summary

Introduction

Due to limited available information about the materials as well as the complexity of microstructure, the determination of macroscopic moduli of composite materials is not simple. Determination of macroscopic properties of composite materials from the properties of the component materials and their microstructure (homogenization) is the subject of many studies in recent decades. The objective of this research part is to present the methods (approximateanalytic and numerical simulation), which determine macroscopic properties of composite materials with.

The ellipse inclusion with interfacial thermal resistance

Application and comparison

Conclusion