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Asymptotic analysis of effective conductivity of composite materials with large rhombic fibers

机译：大菱形纤维复合材料有效电导率的渐近分析

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摘要

The effective heat conductivity of composite materials formed by a regular array of large rhombic fibers embedded in a matrix is studied. Analytical solution is obtained by means of asymptotic homogenization method and with some further asymptotic ap- proximations. The obtained results are equally applicable to determining different effective transport coefficients, such as dielectric constants, magnetic permeability, electric conductivity, etc. as the examples of the considered composite materials three possible limiting forms of two-component inhomogeneous structures with contacting inclusions are investigated. Obtained asymptotic results are discussed in relations to the known Dykhne formula.
机译：研究了由规则的大菱形纤维阵列嵌入基质形成的复合材料的有效导热率。借助渐近均化方法以及一些进一步的渐近近似来获得解析解。获得的结果同样适用于确定不同的有效传输系数，例如介电常数，磁导率，电导率等。以所考虑的复合材料为例，研究了具有接触夹杂物的两组分不均匀结构的三种可能的限制形式。讨论了与已知Dykhne公式有关的渐近结果。

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