ANALYSIS OF STOCHASTIC PROCESSES OF DEFORMATION AND DESTRUCTION IN MODERN COMPOSITES WITH RANDOM STRUCTURES BASED ON MULTIPOINT APPROXIMATIONS OF THE SOLUTION TO ELASTIC BOUNDARY-VALUE PROBLEMS
DOI:
Keywords:
composites, multi-point approach, moment functions, stochastic boundary value problem, stress and strain fields, statistical characteristics, fracture probability, random microstructure, fracture criteria, deformation processesAbstract
The project aim is to use new multi-point approximations of solutions of boundary value problems of the mechanics of composites with a random structure for the analysis of stochastic processes of structural deformation and fracture of composites, modeling of micro- and macroscale failures.The analytical expressions for multi-point correlation functions of the first and second order stress and strain fields were derived in the components of the composite represented as homogeneous media. The restoration method of the distribution laws of structural stresses was developed to allow calculating the probability of a failure on two scale levels - structural and macroscopic, based on microstructural correlation functions of deformation fields, using actual geometry of the internal structure of the material. The relation between the probability of a failure at the micro and macro levels was established.Three-dimensional models of the internal structure of polydisperse textured matrix composites with elliptic inclusions were developed. The values of the structural correlation functions of higher orders were obtained for them. Approximating analytical expressions for structural correlation functions were calculated.The developed method is used for numerical calculation of the correlation functions of the fields in the elastic and elastic-plastic cases under various loading conditions.
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