@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",
}