Stochastic modelling of deformation process in elastoplastic composites with randomly located inclusions using high order correlation functions

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 microstructural parameters.Multiscale hierarchy of heterogeneous (composite) materials is investigated using the Repre- sentative Volume Element (RVE) concept when parameters of larger scale models are measured or calculated on a smaller scale. Fields of stress, strain and displacements are presented in the form of statistically homogeneous coordinate functions.Analytical expressions for statistical characteristics of structural fields, such as mean values and dispersions, are formed using solution of stochastic boundary value problems and contain structural multipoint correlation functions. The order of the required correlation functions is determined by the solution of stochastic boundary value problem. The boundary value problem is being reduced to inte- gral-differential equation in fluctuations of displacements. The second approximation of the problem solution is obtained. To determine relation between deformation in components and macroscopic de- formation, the iteration procedure was organized.New analytical expressions and numerical results for statistical characteristics of stress and strain fields in components of elastoplastic composite materials are derived with the second approxima- tion of the boundary value problem and correlation functions up to fifth order. 3D models of representa- tive volume of material microstructure with polydisperse ellipsoidal inclusions are synthesized; the mul- tipoint correlation functions up to fifth order have been obtained for them. Numerical results are obtained for porous composites with polydisperse ellipsoidal inclusions in simple shear state of strain for micro- structures with various inclusions volume fraction.