Homogenization of a nonstationary model of linear theory of elasticity with account for temporal correlation of phases in a heterogeneous structure

A. V. Mishin<sup>ab

a</sup> Novosibirsk State University, Novosibirsk, 630090 Russia
^b Khristianovich Institute of Theoretical and Applied Mechanics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090 Russia

Abstract: The paper presents the homogenization of the nonstationary model of the linear theory of elasticity by the method of conditional moments, as a result of which the effective coefficients of the linear theory of elasticity and the effective density are obtained. As a result of performing operations, the obtained effective coefficients depend on the scales of phase correlation in time and space and are interdependent. The occurrence of correlation scales is a consequence of calculating the integrals containing the Green’s function (the solution for the operator of the nonstationary model of the linear theory of elasticity) and the correlation function of the structure in time and space. The effective density is investigated.

Keywords: heterogeneous medium, microstructure, Green’s function, conditional averaging, correlation function, Fourier transform, structural phase transition.

UDC: 539.3

Received: 27.10.2024
Revised: 15.04.2025
Accepted: 24.04.2025

DOI: 10.33048/SIBJIM.2025.28.103

 English version: Journal of Applied and Industrial Mathematics, 2025, 19:1, 67–76