Homogenization of a Nonstationary Model of Linear Theory of Elasticity with Account for Temporal Correlation of Phases in a Heterogeneous Structure

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Homogenization of a Nonstationary Model of Linear Theory of Elasticity with Account for Temporal Correlation of Phases in a Heterogeneous Structure. / Mishin, A. V.

в: Journal of Applied and Industrial Mathematics, Том 19, № 1, 7, 2025, стр. 67-76.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

BibTeX

@article{5d4118fd85ef47e8b457091de4836252,

title = "Homogenization of a Nonstationary Model of Linear Theory of Elasticity with Account for Temporal Correlation of Phases in a Heterogeneous Structure",

abstract = "The paper presents the homogenization of the nonstationary model of the linear theory ofelasticity by the method of conditional moments, as a result of which the effective coefficients ofthe linear theory of elasticity and the effective density are obtained. As a result of performingoperations, the obtained effective coefficients depend on the scales of phase correlation in time andspace and are interdependent. The occurrence of correlation scales is a consequence of calculatingthe integrals containing the Green{\textquoteright}s function (the solution for the operator of the nonstationarymodel of the linear theory of elasticity) and the correlation function of the structure in time andspace. The effective density is investigated.",

keywords = "Fourier transform, Green{\textquoteright}s function, conditional averaging, correlation function, heterogeneous medium, microstructure, structural phase transition, ГЕТЕРОГЕННАЯ СРЕДА, МИКРОСТРУКТУРА, ФУНКЦИЯ ГРИНА, УСЛОВНОЕ ОСРЕДНЕНИЕ, КОРРЕЛЯЦИОННАЯ ФУНКЦИЯ, ПРЕОБРАЗОВАНИЕ ФУРЬЕ, СТРУКТУРНЫЙ ФАЗОВЫЙ ПЕРЕХОД",

author = "Mishin, {A. V.}",

note = "Mishin A.V. Homogenization of a Nonstationary Model of Linear Theory of Elasticity with Account for Temporal Correlation of Phases in a Heterogeneous Structure // Journal of Applied and Industrial Mathematics. – 2025. – Vol. 19. - No. 1. – P. 67-76. – DOI 10.1134/S1990478925010077. – EDN ZQFPRX. This work was supported by ongoing institutional funding. No additional grants to carry out or direct this particular research were obtained.",

year = "2025",

doi = "10.1134/S1990478925010077",

language = "English",

volume = "19",

pages = "67--76",

journal = "Journal of Applied and Industrial Mathematics",

issn = "1990-4789",

publisher = "Maik Nauka-Interperiodica Publishing",

number = "1",

}

RIS

TY - JOUR

T1 - Homogenization of a Nonstationary Model of Linear Theory of Elasticity with Account for Temporal Correlation of Phases in a Heterogeneous Structure

AU - Mishin, A. V.

N1 - Mishin A.V. Homogenization of a Nonstationary Model of Linear Theory of Elasticity with Account for Temporal Correlation of Phases in a Heterogeneous Structure // Journal of Applied and Industrial Mathematics. – 2025. – Vol. 19. - No. 1. – P. 67-76. – DOI 10.1134/S1990478925010077. – EDN ZQFPRX. This work was supported by ongoing institutional funding. No additional grants to carry out or direct this particular research were obtained.

PY - 2025

Y1 - 2025

N2 - The paper presents the homogenization of the nonstationary model of the linear theory ofelasticity by the method of conditional moments, as a result of which the effective coefficients ofthe linear theory of elasticity and the effective density are obtained. As a result of performingoperations, the obtained effective coefficients depend on the scales of phase correlation in time andspace and are interdependent. The occurrence of correlation scales is a consequence of calculatingthe integrals containing the Green’s function (the solution for the operator of the nonstationarymodel of the linear theory of elasticity) and the correlation function of the structure in time andspace. The effective density is investigated.

AB - The paper presents the homogenization of the nonstationary model of the linear theory ofelasticity by the method of conditional moments, as a result of which the effective coefficients ofthe linear theory of elasticity and the effective density are obtained. As a result of performingoperations, the obtained effective coefficients depend on the scales of phase correlation in time andspace and are interdependent. The occurrence of correlation scales is a consequence of calculatingthe integrals containing the Green’s function (the solution for the operator of the nonstationarymodel of the linear theory of elasticity) and the correlation function of the structure in time andspace. The effective density is investigated.

KW - Fourier transform

KW - Green’s function

KW - conditional averaging

KW - correlation function

KW - heterogeneous medium

KW - microstructure

KW - structural phase transition

KW - ГЕТЕРОГЕННАЯ СРЕДА

KW - МИКРОСТРУКТУРА

KW - ФУНКЦИЯ ГРИНА

KW - УСЛОВНОЕ ОСРЕДНЕНИЕ

KW - КОРРЕЛЯЦИОННАЯ ФУНКЦИЯ

KW - ПРЕОБРАЗОВАНИЕ ФУРЬЕ

KW - СТРУКТУРНЫЙ ФАЗОВЫЙ ПЕРЕХОД

UR - https://www.scopus.com/pages/publications/105020675849

UR - https://www.elibrary.ru/item.asp?id=83155452

UR - https://www.elibrary.ru/item.asp?id=82970829

UR - https://www.mendeley.com/catalogue/f4bdf726-da99-389a-8cf8-793b33ef9e57/

U2 - 10.1134/S1990478925010077

DO - 10.1134/S1990478925010077

M3 - Article

VL - 19

SP - 67

EP - 76

JO - Journal of Applied and Industrial Mathematics

JF - Journal of Applied and Industrial Mathematics

SN - 1990-4789

IS - 1

M1 - 7

ER -

ID: 72127234