Method of successive approximations in stochastic elastic boundary value problem for structurally heterogenous materials

This work is connected with microstress and microstrain fields determination problem in matrix composites with randomly located inclusions. Stochastic structure of the composites is described with set of correlation functions. The boundary problem is reduced to integral–differential equation in pulsations of displacements. Solution of the problem is searched in the second approximation with Green function method. Analytical expressions for statistical characteristic of stress and strain fields are obtained. Numerical results for average quantities for the simple shear macroscopic state of strain are presented.

Three-dimensional random structures synthesis. Higher-order correlation functions for random structures. Solution method of stochastic boundary value problem of elasticity theory in higher-orders approximation. Analytical expressions for structural stresses and strains correlations in second-order approximation. Statistical characteristics for simple shear and uniaxial tension states of strain in case of porous composite.