The effective properties of the fiber-reinforced composite materials with fibers of circle cross section are investigated. The novel estimation for the effective coefficient of thermal conductivity refining the classical Maxwell formula is derived. The method of asymptotic homogenization is used. For an analytical solution of the periodically repeated cell problem the Schwarz alternating process (SAP) was employed. Convergence of this method was proved by S. Mikhlin, S. Sobolev, V. Mityushev. Unfortunately, the rate of the convergence is often slow, especially for nondilute high-contrast composite materials. For improving this drawback we used Pade approximations for various forms of SAP solutions with the following additive matching of obtained expressions. As a result, the solutions in our paper are obtained in a fairly simple and convenient form. They can be used even for a volume fraction of inclusion very near the physically possible maximum value as well as for high-contrast composite constituents. The results are confirmed by comparison with known numerical and asymptotic results.

中文翻译：

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圆形截面纤维增强复合材料的麦克斯韦公式的改进。第二部分：使用 Padé 近似

研究了具有圆形截面纤维的纤维增强复合材料的有效性能。推导出了改进经典麦克斯韦公式的有效导热系数的新估计。使用渐近均质化的方法。对于周期性重复单元问题的解析解，采用了 Schwarz 交替过程 (SAP)。S. Mikhlin、S. Sobolev、V. Mityushev 证明了该方法的收敛性。不幸的是，收敛速度通常很慢，特别是对于非稀释的高对比度复合材料。为了改善这个缺点，我们对各种形式的 SAP 解决方案使用了 Pade 近似，并对获得的表达式进行了以下加法匹配。因此，我们论文中的解决方案是以相当简单和方便的形式获得的。它们甚至可以用于非常接近物理可能最大值的体积分数以及高对比度复合成分。通过与已知的数值和渐近结果进行比较来确认结果。