The problem of reconstruction and quantitative characterization of the microstructure of random composites, as a fundamental problem of material sciences, has been a subject of a considerable amount of literature. Thus far, previous studies used for the reconstruction either statistical microstructure descriptors or the overall property of real material. This paper makes a major contribution to research on reconstruction by formulating a procedure to recover the microstructure that produces the same effective thermal conductivity as the real composite material. In particular, our goal is to find a binary representation of ‘replacement’ microstructure that, being a two-phase statistically isotropic medium, produces minimal disagreement with the experimental data. Such a binary microstructure is invariant with respect to the conductivity of fluid occupying the porous space. Thus, in some sense, the paper is an extension of the concept proposed by Łydżba et al. (2018), who showed, in the framework of analytical homogenization, that any isotropic microstructure can be represented by randomly oriented spheroids of certain distribution over the aspect ratios. The efficiency of our methodology was illustrated by examples including Wiener and Hashin-Shtrikman bounds as well as the microstructure created by the system of non-overlapping disks. Finally, we use our algorithm to construct the ‘replacement’ microstructure for the real porous medium, i.e., medium sand. The main advantage of the digital representation of ‘replacement’ microstructure over the analytical one, is that it can be further used in computational modeling as well as in 3D printing applications.

随机复合材料微观结构的重构和定量表征问题作为材料科学的一个基本问题，一直是大量文献的主题。到目前为止，以前的研究用于重建统计微观结构描述符或真实材料的整体特性。本文通过制定程序来恢复产生与真实复合材料相同的有效热导率的微观结构，对重建研究做出了重大贡献。特别是，我们的目标是找到“替代”微观结构的二进制表示，它是一种两相统计各向同性介质，与实验数据产生最小的分歧。这种二元微结构对于占据多孔空间的流体的电导率是不变的。因此，在某种意义上，这篇论文是 Łydżba 等人提出的概念的延伸。（2018 年），他在分析均质化的框架中表明，任何各向同性的微观结构都可以由在纵横比上具有一定分布的随机取向的球体表示。我们的方法的效率通过包括 Wiener 和 Hashin-Shtrikman 界以及由非重叠磁盘系统创建的微观结构的示例来说明。最后，我们使用我们的算法为真正的多孔介质（即介质砂）构建“替代”微观结构。“替代”微观结构的数字表示相对于分析表示的主要优势，