Shapovalova M. Evaluation of the limiting state of a two-component material with spherical inclusions and predicting the reliability of the structure by methods of computer and mathematical modeling

The dissertation substantiates the theoretical provisions and develops practical principles for improving the mathematical methods for assessing the strength and probabilistic characteristics of reliability of structural elements made of two-component material; the analysis of elastic parameters and limiting state is carried out taking into account the peculiarities of the microstructure. The object of the research is the deformation process of two-component materials with spherical inclusions. The subject of research is the probabilistic characteristics of the elastic parameters of the limiting state as a yield surface at various concentrations of the internal components of the material; statistical forecast of the reliability of structures made of two-component materials. The theoretical basis of the dissertation is the following methods: image processing (filtering, segmentation, normalization, and object recognition); mechanics of a rigid deformable-body; theory of probability and stochastic processes The calculation of the SSS of statistically equivalent microstructures was carried out within the framework of the finite element method. In this work, a new computational approach based on the Monte Carlo method has been developed for assessing the probabilistic parameters of the limiting state of the material under study, based on the analysis of statistically equivalent microstructures. The approach allows predicting the residual life of structural elements and determining their possible characteristics. Algorithms (based on methods of computer image processing) have been developed for the automated determination of the probabilistic characteristics of the size, spatial distribution, and concentration of spherical inclusions of a two-component material. This makes it possible to determine the density functions of the distribution of the radii of the inclusions depending on their concentration for the synthesis of statistically equivalent structures. The regularities of the influence of the concentration of inclusions on the distribution density functions (and their parameters) of the components of the stiffness tensor of the material under study have been established. The concentration dependences of the mathematical expectation, dispersion, and confidence intervals of the yield points in compression and tension for cast iron (microstructures of the ShG2-ShG12 type) have been established.