Methods of Stochastic Mechanics for Characterization of Deformation in Randomly Reinforced Composite Materials

  • Mikhail A. Tashkinov
Part of the Engineering Materials book series (ENG.MAT.)


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.


Microstructural characterisation Stochastic boundary value problem Correlation functions Randomly reinforced composites Stochastic modeling Statistical characteristics Stress and strain fields 



This work was supported by the Russian Foundation for Basic Research (project 14-01-96024) and grant of the President of Russian Federation for state support of young Russian scientists (MK-5172.2015.1).


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© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.The Laboratory of Mechanics of Perspective Structural and Functional MaterialsPerm National Research Polytechnic UniversityPermRussia

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