Statistical characteristics of structural stochastic stress and strain fields in polydisperse heterogeneous solid media

• Stochastic boundary value problem solution was obtained in elastoplastic case.
• Statistical characteristics of stress fields in phases of composite were determined.
• Microstructure of composites is described with high-order correlation functions.
• Results for porous polydisperse composites with elastoplastic matrix were obtained.
• The automated programming algorithms were developed in Wolfram Mathematica.

The aim of this research is to develop the mechanisms of calculation of stress and strain fields’ statistical characteristics in components of heterogeneous solid media in dependence on variation of internal and external parameters in elastoplastic case.Analytical expressions for statistical characteristics of structural fields, such as mean values and dispersions, are formed using solution of stochastic boundary value problems and structural multipoint correlation functions. The boundary value problems have been solved in elastoplastic case in the second approximation with the Green’s functions method. The multipoint correlation functions up to fifth order have been built for synthesized 3D material microstructure RVE models with polydisperse spherical inclusions.New analytical expressions and numerical results for statistical characteristics in components of elastoplastic heterogeneous solids with different types of structural parameters and properties of the phases have been obtained for simple shear state of strain. Numerical results are presented for porous composites with different inclusions volume fraction in case of simple shear state of strain.