MATHEMATICS

An approach for constructing refined generalized models of composite durability in extreme conditions based on the modern kinetic theory of strength

E. L. Gusev^ab, V. N. Bakulin<sup>c

a</sup> Institute of Oil and Gas Problems of the Federal Research Center "Yakut Scientific Center of the Siberian Branch of the Russian Academy of Sciences", Yakutsk, Russia
^b Institute of Mathematics and Informatics, North-Eastern Federal University, Yakutsk, Russia
^c Institute of Applied Mechanics of Russian Academy of Sciences, Moscow, Russia

Abstract: An approach is proposed for constructing refined generalized models of the durability of composites under extreme conditions based on the modern kinetic theory of strength. Within the framework of variational formulations, effective methods for predicting the defining characteristics (residual life, strength, reliability, durability) of composites under extreme environmental conditions are proposed and developed. Based on conducted research, a method is developed for matching the defining parameters of physical models at the microscopic level with the corresponding defining parameters of mathematical models at the macroscopic level. As a result, we solve the problem of restoring the parameters of physical and chemical processes occurring at the microscopic level and leading to destructive changes in composites and deterioration of their characteristics over time.

Keywords: kinetic theory of strength, composite materials, variational formulation, prediction methods, physical and mathematical models, extreme factors, residual life, durability.

UDC: 51-72:517.977.5:519.873

Presented: B. N. Chetverushkin
Received: 01.08.2024
Revised: 08.10.2024
Accepted: 28.10.2024

DOI: 10.31857/S2686954324060065

 English version: Doklady Mathematics, 2024, 110:3, 480–485

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