Analysis of the Behavior of Heterogeneous Media with Significantly Differing Physical Properties with Allowance for the Effective Dimension of the Space and Generalized Derivative Formalism

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Analysis of the Behavior of Heterogeneous Media with Significantly Differing Physical Properties with Allowance for the Effective Dimension of the Space and Generalized Derivative Formalism. / Mishin, A. V.; Fomin, V. M.

In: Mechanics of Solids, Vol. 57, No. 8, 2022, p. 2005-2019.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{fa0e2ed0886f453e96844c1e4fd72de8,

title = "Analysis of the Behavior of Heterogeneous Media with Significantly Differing Physical Properties with Allowance for the Effective Dimension of the Space and Generalized Derivative Formalism",

abstract = "The effective coefficients of linear elasticity theory are obtained and analyzed with the aim to analytically describe heterogeneous media. This is done for an arbitrary dimension of the space under consideration and taking into account the generalized derivative formalism. The effective coefficients and their derivatives are explored for the presence of a carrier phase and a structural phase transition (percolation properties) over the entire range of volumetric concentration. Based on the analysis carried out, a comparison is made with the results of existing approaches and with the available data on colloids, suspensions, and granular media.",

keywords = "heterogeneous medium, microstructure, space dimension, stochastic model, structural phase transition",

author = "Mishin, {A. V.} and Fomin, {V. M.}",

note = "Публикация для корректировки.",

year = "2022",

doi = "10.3103/S0025654422080210",

language = "English",

volume = "57",

pages = "2005--2019",

journal = "Mechanics of Solids",

issn = "1934-7936",

publisher = "Pleiades Publishing",

number = "8",

}

RIS

TY - JOUR

T1 - Analysis of the Behavior of Heterogeneous Media with Significantly Differing Physical Properties with Allowance for the Effective Dimension of the Space and Generalized Derivative Formalism

AU - Mishin, A. V.

AU - Fomin, V. M.

N1 - Публикация для корректировки.

PY - 2022

Y1 - 2022

N2 - The effective coefficients of linear elasticity theory are obtained and analyzed with the aim to analytically describe heterogeneous media. This is done for an arbitrary dimension of the space under consideration and taking into account the generalized derivative formalism. The effective coefficients and their derivatives are explored for the presence of a carrier phase and a structural phase transition (percolation properties) over the entire range of volumetric concentration. Based on the analysis carried out, a comparison is made with the results of existing approaches and with the available data on colloids, suspensions, and granular media.

AB - The effective coefficients of linear elasticity theory are obtained and analyzed with the aim to analytically describe heterogeneous media. This is done for an arbitrary dimension of the space under consideration and taking into account the generalized derivative formalism. The effective coefficients and their derivatives are explored for the presence of a carrier phase and a structural phase transition (percolation properties) over the entire range of volumetric concentration. Based on the analysis carried out, a comparison is made with the results of existing approaches and with the available data on colloids, suspensions, and granular media.

KW - heterogeneous medium

KW - microstructure

KW - space dimension

KW - stochastic model

KW - structural phase transition

UR - https://www.mendeley.com/catalogue/c9907f2b-9cfc-3c7e-b695-8a3a7a214b3c/

U2 - 10.3103/S0025654422080210

DO - 10.3103/S0025654422080210

M3 - Article

VL - 57

SP - 2005

EP - 2019

JO - Mechanics of Solids

JF - Mechanics of Solids

SN - 1934-7936

IS - 8

ER -

ID: 55694403