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首页> 外文期刊>Journal of Physics, D. Applied Physics: A Europhysics Journal >Conductivity calculation for a two-phase composite with spheroidal inclusions
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Conductivity calculation for a two-phase composite with spheroidal inclusions

机译：球状夹杂物的两相复合材料的电导率计算

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摘要

An analytical solution is presented for the electrical conductivity of a material composed of spheroidal particles embedded in a matrix. The particles are arranged on a simple-cubic lattice with their axes of rotation aligned with one of the lattice vectors. In this arrangement, there are two independent components of the conductivity tensor; one for the electric field applied parallel to the rotation axis of the spheroids and one for the electric field applied perpendicular to this axis. Both components are calculated using a method in which each particle is replaced by a singular multipole source which gives rise to the electric potential in the interstitial domain. This potential can readily be written as a sum of spherical harmonics but, in order to treat spheroidal particles, it is necessary to transform the solution into one in terms of spheroidal harmonics. The calculation of the matrix elements required for this transformation is described and the solution for each component of the conductivity tensor is given in analytic form. Results are presented for various values of particle aspect ratio, volume fraction and conductivity ratio between the two phases. Very good agreement is observed with experimental data and the results of an independent calculation.
机译：提出了一种分析解决方案，用于解决由嵌入基体中的球形颗粒组成的材料的电导率问题。粒子排列在单立方晶格上，其旋转轴与晶格矢量之一对齐。在这种布置中，电导率张量有两个独立的分量。一个用于平行于球体的旋转轴施加的电场，另一个用于垂直于该球体的旋转轴施加的电场。使用一种方法来计算两个分量，其中每个粒子都被单个多极源替换，该单个多极源会在间隙域中产生电势。该电势可以很容易地写成球谐函数的总和，但是，为了处理球体颗粒，有必要根据球谐函数将解转换为一个。描述了此转换所需的矩阵元素的计算，并以解析形式给出了电导率张量的每个分量的解。给出了两相之间颗粒长宽比，体积分数和电导率的各种值的结果。观察到与实验数据和独立计算结果非常一致。

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