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The Generalized Derivative and Its Use in the Analysis of the Microstructure of a Heterogeneous Medium. / Mishin, A. V.
в: Journal of Applied and Industrial Mathematics, Том 15, № 4, 11.2021, стр. 631-646.Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
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TY - JOUR
T1 - The Generalized Derivative and Its Use in the Analysis of the Microstructure of a Heterogeneous Medium
AU - Mishin, A. V.
N1 - Funding Information: The author was supported by the Ministry of Education and Science of Russian Federation (project no. 075–15–2020–781). Publisher Copyright: © 2021, Pleiades Publishing, Ltd.
PY - 2021/11
Y1 - 2021/11
N2 - We provide some analytical account of the influence of the internal boundaries ofa heterogeneous medium on the propagation of an elastic stress field through it. The generalizedderivative serves as the mathematical concept displaying the microstructure of a heterogeneoussystem. Using the generalized derivative we modify the operator in the initial model of linearelasticity. The Green’s function (built on the operator) displays the microstructural features of thesystem. We use the method of conditional moments to obtain the effective coefficients of elasticitywhich are included in the averaged equations and describing the elastic properties ofa heterogeneous medium. This approach leads to the integrals containing the modified averagedGreen’s function and the correlation function of the structure geometry. Using these terms, weintegrally take into account the microstructure of the system in the final effective elasticitycoefficients.
AB - We provide some analytical account of the influence of the internal boundaries ofa heterogeneous medium on the propagation of an elastic stress field through it. The generalizedderivative serves as the mathematical concept displaying the microstructure of a heterogeneoussystem. Using the generalized derivative we modify the operator in the initial model of linearelasticity. The Green’s function (built on the operator) displays the microstructural features of thesystem. We use the method of conditional moments to obtain the effective coefficients of elasticitywhich are included in the averaged equations and describing the elastic properties ofa heterogeneous medium. This approach leads to the integrals containing the modified averagedGreen’s function and the correlation function of the structure geometry. Using these terms, weintegrally take into account the microstructure of the system in the final effective elasticitycoefficients.
KW - averaging
KW - generalized derivative
KW - Green’s function
KW - heterogeneous medium
KW - microstructure
KW - stochastic model
UR - http://www.scopus.com/inward/record.url?scp=85133974269&partnerID=8YFLogxK
UR - https://www.mendeley.com/catalogue/b5258294-7496-3cea-a37c-76b2b0e7d970/
U2 - 10.1134/S1990478921040074
DO - 10.1134/S1990478921040074
M3 - Article
AN - SCOPUS:85133974269
VL - 15
SP - 631
EP - 646
JO - Journal of Applied and Industrial Mathematics
JF - Journal of Applied and Industrial Mathematics
SN - 1990-4789
IS - 4
ER -
ID: 36686877