The paper focuses on the quantitative characterization of the microstructure of a two-dimensional heterogeneous solid with circular inhomogeneities that may vary from perfectly periodic arrangement to completely random one. This characterization is linked to the calculation of the effective conductivity of the material. The partially disordered system of disks is generated in the framework of the representative unit cell model using Metropolis algorithm. The orientation order metrics are taken as the structural parameters providing a quantitative measure of disorder, and their variation caused by the gradual disordering of the periodic system is assessed. The effective conductivity of the heterogeneous solid with partially disordered microstructure is evaluated by the multipole expansion method. It is shown that effective conductivity cannot be fully characterized by only one orientation order metric, and the required additional ones are identified.

该论文侧重于具有圆形不均匀性的二维非均质固体的微观结构的定量表征，圆形不均匀性可能从完全周期性排列到完全随机排列。这种表征与材料有效电导率的计算有关。使用 Metropolis 算法在代表性晶胞模型的框架中生成部分无序的磁盘系统。将取向顺序度量作为提供无序定量度量的结构参数，并评估由周期系统逐渐无序引起的它们的变化。具有部分无序微观结构的异质固体的有效电导率通过多极膨胀法进行评估。