Standard
Representative Elementary Volume via Averaged Scalar Minkowski Functionals. / Andreeva, M. V.; Kalyuzhnyuk, A. V.; Krutko, V. V. et al.
Advanced Problem in Mechanics II - Proceedings of the 48th International Summer School-Conference “Advanced Problems in Mechanics”, 2020. ed. / D. A. Indeitsev; A. M. Krivtsov. 1. ed. Springer Science and Business Media Deutschland GmbH, 2022. p. 533-539 (Lecture Notes in Mechanical Engineering).
Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Research › peer-review
Harvard
Andreeva, MV, Kalyuzhnyuk, AV, Krutko, VV, Russkikh, NE
& Taimanov, IA 2022,
Representative Elementary Volume via Averaged Scalar Minkowski Functionals. in DA Indeitsev & AM Krivtsov (eds),
Advanced Problem in Mechanics II - Proceedings of the 48th International Summer School-Conference “Advanced Problems in Mechanics”, 2020. 1 edn, Lecture Notes in Mechanical Engineering, Springer Science and Business Media Deutschland GmbH, pp. 533-539, 48th International Conference on Advanced Problems in Mechanics, 2020, Virtual, Online,
21.06.2020.
https://doi.org/10.1007/978-3-030-92144-6_40APA
Andreeva, M. V., Kalyuzhnyuk, A. V., Krutko, V. V., Russkikh, N. E.
, & Taimanov, I. A. (2022).
Representative Elementary Volume via Averaged Scalar Minkowski Functionals. In D. A. Indeitsev, & A. M. Krivtsov (Eds.),
Advanced Problem in Mechanics II - Proceedings of the 48th International Summer School-Conference “Advanced Problems in Mechanics”, 2020 (1 ed., pp. 533-539). (Lecture Notes in Mechanical Engineering). Springer Science and Business Media Deutschland GmbH.
https://doi.org/10.1007/978-3-030-92144-6_40Vancouver
Andreeva MV, Kalyuzhnyuk AV, Krutko VV, Russkikh NE
, Taimanov IA.
Representative Elementary Volume via Averaged Scalar Minkowski Functionals. In Indeitsev DA, Krivtsov AM, editors, Advanced Problem in Mechanics II - Proceedings of the 48th International Summer School-Conference “Advanced Problems in Mechanics”, 2020. 1 ed. Springer Science and Business Media Deutschland GmbH. 2022. p. 533-539. (Lecture Notes in Mechanical Engineering). doi: 10.1007/978-3-030-92144-6_40
Author
Andreeva, M. V. ; Kalyuzhnyuk, A. V. ; Krutko, V. V. et al. /
Representative Elementary Volume via Averaged Scalar Minkowski Functionals. Advanced Problem in Mechanics II - Proceedings of the 48th International Summer School-Conference “Advanced Problems in Mechanics”, 2020. editor / D. A. Indeitsev ; A. M. Krivtsov. 1. ed. Springer Science and Business Media Deutschland GmbH, 2022. pp. 533-539 (Lecture Notes in Mechanical Engineering).
BibTeX
@inproceedings{c0467b1fed144ecc8332e5944a9b32d2,
title = "Representative Elementary Volume via Averaged Scalar Minkowski Functionals",
abstract = "Representative Elementary Volume (REV) at which the material properties do not vary with change in volume is an important quantity for making measurements or simulations which represent the whole. We discuss the geometrical method to evaluation of REV based on the quantities coming in the Steiner formula from convex geometry. For bodies in three-dimensional space this formula gives us four scalar functionals known as scalar Minkowski functionals. We demonstrate on certain samples that the values of such averaged functionals almost stabilize for cells for which the length of edges are greater than certain threshold value R. Therefore, from this point of view, it is reasonable to consider cubes of volume R3 as representative elementary volumes for certain physical parameters of porous medium.",
keywords = "Convex geometry, Minkowski functionals, Porous media, Representative elementary volume",
author = "Andreeva, {M. V.} and Kalyuzhnyuk, {A. V.} and Krutko, {V. V.} and Russkikh, {N. E.} and Taimanov, {I. A.}",
note = "Publisher Copyright: {\textcopyright} 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.; 48th International Conference on Advanced Problems in Mechanics, 2020 ; Conference date: 21-06-2020 Through 26-06-2020",
year = "2022",
doi = "10.1007/978-3-030-92144-6_40",
language = "English",
isbn = "978-3-030-92143-9",
series = "Lecture Notes in Mechanical Engineering",
publisher = "Springer Science and Business Media Deutschland GmbH",
pages = "533--539",
editor = "Indeitsev, {D. A.} and Krivtsov, {A. M.}",
booktitle = "Advanced Problem in Mechanics II - Proceedings of the 48th International Summer School-Conference “Advanced Problems in Mechanics”, 2020",
address = "Germany",
edition = "1",
}
RIS
TY - GEN
T1 - Representative Elementary Volume via Averaged Scalar Minkowski Functionals
AU - Andreeva, M. V.
AU - Kalyuzhnyuk, A. V.
AU - Krutko, V. V.
AU - Russkikh, N. E.
AU - Taimanov, I. A.
N1 - Publisher Copyright:
© 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.
PY - 2022
Y1 - 2022
N2 - Representative Elementary Volume (REV) at which the material properties do not vary with change in volume is an important quantity for making measurements or simulations which represent the whole. We discuss the geometrical method to evaluation of REV based on the quantities coming in the Steiner formula from convex geometry. For bodies in three-dimensional space this formula gives us four scalar functionals known as scalar Minkowski functionals. We demonstrate on certain samples that the values of such averaged functionals almost stabilize for cells for which the length of edges are greater than certain threshold value R. Therefore, from this point of view, it is reasonable to consider cubes of volume R3 as representative elementary volumes for certain physical parameters of porous medium.
AB - Representative Elementary Volume (REV) at which the material properties do not vary with change in volume is an important quantity for making measurements or simulations which represent the whole. We discuss the geometrical method to evaluation of REV based on the quantities coming in the Steiner formula from convex geometry. For bodies in three-dimensional space this formula gives us four scalar functionals known as scalar Minkowski functionals. We demonstrate on certain samples that the values of such averaged functionals almost stabilize for cells for which the length of edges are greater than certain threshold value R. Therefore, from this point of view, it is reasonable to consider cubes of volume R3 as representative elementary volumes for certain physical parameters of porous medium.
KW - Convex geometry
KW - Minkowski functionals
KW - Porous media
KW - Representative elementary volume
UR - http://www.scopus.com/inward/record.url?scp=85127114495&partnerID=8YFLogxK
UR - https://www.mendeley.com/catalogue/536645e9-d0f3-3a57-8e4e-f1bb05245e1f/
U2 - 10.1007/978-3-030-92144-6_40
DO - 10.1007/978-3-030-92144-6_40
M3 - Conference contribution
AN - SCOPUS:85127114495
SN - 978-3-030-92143-9
T3 - Lecture Notes in Mechanical Engineering
SP - 533
EP - 539
BT - Advanced Problem in Mechanics II - Proceedings of the 48th International Summer School-Conference “Advanced Problems in Mechanics”, 2020
A2 - Indeitsev, D. A.
A2 - Krivtsov, A. M.
PB - Springer Science and Business Media Deutschland GmbH
T2 - 48th International Conference on Advanced Problems in Mechanics, 2020
Y2 - 21 June 2020 through 26 June 2020
ER -
