The paper is devoted to the method of evaluation of local mechanical state in microscale components of random heterogeneous media taking into account their morphological features. According to the proposed approach, a representative volume element (RVE) of heterogeneous medium can be considered as a system of random interacting components with distinguishable properties. In this case, internal mechanical response to the load applied to an RVE can be expressed via continuous distributions of microscale stress and strain fields. The novelty of this work is connected with the methodology of restoration of parameters of these distributions using the solutions of the stochastic boundary value problems (SBVPs) that consider multipoint statistical correlations between different points within RVE, in contrast to the traditionally widely used two-point correlations. This allow to obtain more accurate results for the problems of localization of mechanical behavior for materials with complex random microstructure. The computational techniques, which are essential for numerical implementation of the developed approach, are described. The case studies connected with analysis of local stress and strain fields distributions in random bicontinuous media with interpenetrating phases are investigated using the developed approach and verified with the finite element analysis.

考虑到其形态特征，本文致力于评估随机异质介质的微尺度成分中的局部机械状态的方法。根据提出的方法，可以将异质介质的代表性体积元素（RVE）视为具有可区分属性的随机相互作用成分的系统。在这种情况下，可以通过微尺度应力和应变场的连续分布来表达对施加到RVE的载荷的内部机械响应。这项工作的新颖性与使用考虑了RVE中不同点之间的多点统计相关性的随机边界值问题（SBVP）的解决方案来恢复这些分布的参数的方法有关，与传统上广泛使用的两点相关法相反。对于复杂的随机微观结构的材料，这可以为机械行为的局部化问题获得更准确的结果。描述了对于所开发方法的数值实施必不可少的计算技术。使用开发的方法对与互穿相的随机双连续介质中局部应力和应变场分布进行分析的案例研究进行了比较，并通过有限元分析进行了验证。