Multipoint stochastic approach to localization of microscale elastic behavior of random heterogeneous media

• Approach for localization of mechanical behavior in random media is presented. • Multipoint correlation functions are used for characterization of morphology. • The developed formulations are independent of meshing of geometrical models. • Application is demonstrated on case studies of bicontinuous heterogeneous RVEs. • The method is suitable for analysis of materials with complex microstructure. 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.