Multiscale Statistical Model of Progressive Failure in Random Heterogeneous Media

  • Mikhail TashkinovEmail author
Conference paper
Part of the Lecture Notes in Mechanical Engineering book series (LNME)


The analysis of mechanical behavior of structurally heterogeneous media keeps bringing up challenges due to development of new multiphase materials. Many theoretical and experimental studies had proven that microstructural features of heterogeneous materials significantly influence distributions of local stress and strain fields as well as processes of failure initiation and propagation. Thus, it is necessary to take into account multi-particle interactions of the components and contribution of each of them to the effective strength characteristics. One of the directions in the micromechanics of materials with random structure is related to the methods and tools of statistical analysis. They consider the representative volume element (RVE) of a material as a random system and allow to take into account interactions within the particles and to investigate distributions of stress and strain fields in each phase of material from the analytical point of view. Within such framework, the failure probability can be assessed on the basis of the statistical representation of the failure criteria. This work presents the approach for restoration of distribution of stress and strain fields in representative volume element of heterogeneous media and its constituents. The techniques for estimation of parameters of distribution laws are described. The statistical model of progressive failure is presented and illustrated with some numerical results and comparisons for particular case studies.


Micromechanics Composites Statistical methods Integral equations Failure 



This work was supported by the Grant of the President of Russian Federation for state support of young Russian scientists (MK-2395.2017.1) and by the Russian Foundation for Basic Research (project 16-01-00327_a).


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© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.Perm National Research Polytechnic UniversityPermRussia

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