Abstract

This chapter reveals certain aspects of theoretical statistical approach to studying mechanical behavior of randomly reinforced composite materials, particularly focusing on microstructural characterization and methods of description of stress and strain fields in components of material. Mechanical properties of microstructural components are defined with conventional phenomenological equations and criteria while the effective properties of composite and characteristics of microscopic deformation fields are computed using the solutions of stochastic boundary value problems (SBVPs). Microstructural description is based on a concept of the representative volume elements (RVE) and is implemented with the correlation functions of the second and higher orders. Statistical moments of microstructural fields are used as the characteristic of deformation and fracture processes and analytically connect the microstructural correlation functions with the SBVP solution. Using the Green’s functions these solutions have been obtained in elastic and elastoplastic formulations. The numerical calculations for a case study of porous composites with different microstructural properties were obtained for various loading conditions. Some milestones of emerging and development of the described methods are also addressed.

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