Application of methods of the mechanics of heterogeneous media to describe dispersion processes in an electromagnetic field

1989 ◽  
Vol 29 (4) ◽  
pp. 583-587
Author(s):  
S. Yu. Arutyunov ◽  
I. N. Dorokhov ◽  
V. V. Kafarov ◽  
V. G. Korniichuk ◽  
V. P. Solov'ev
Keyword(s):  
Electromagnetic Field ◽  
Heterogeneous Media ◽  
Mechanics Of Heterogeneous Media

Micromechanics of Random Heterogeneous Materials: New Background, Opportunities and Prospects

2016 ◽  
Author(s):  
Valeriy A. Buryachenko
Keyword(s):  
Integral Equations ◽  
Heterogeneous Media ◽  
Effective Field ◽  
Local Fields ◽  
Homogeneous Field ◽  
Multi Scale ◽  
General Integral ◽  
Operator Form ◽  
Mechanics Of Heterogeneous Media ◽  
Improved Accuracy

One considers a linear heterogeneous media (e.g. filtration in porous media, composite materials, CMs, nanocomposites, peristatic CMs, and rough contacted surfaces). The idea of the effective field hypothesis (EFH, H1, see for references and details [1], [2]) dates back to Mossotti (1850) who pioneered the introduction of the effective field concept as a local homogeneous field acting on the inclusions and differing from the applied macroscopic one. It is proved that a concept of the EFH (even if this term is not mentioned) is a (first) background of all four groups of analytical methods in physics and mechanics of heterogeneous media (model methods, perturbation methods, self-consistent methods, and variational ones, see for refs. [1]). An operator form of the general integral equations (GIEs) is obtained which connects the driving fields and fluxes in a point being considered. Either the volume integral equations or boundary ones are used for these GIEs, new concept of the interface polarisation tensors are introduced. New GIEs present in fact the new (second) background (which does not use the EFH) of multi-scale analysis offering the opportunities for a fundamental jump in multiscale research of random heterogeneous media with drastically improved accuracy of local field estimations (with possible change of sign of predicted local fields).

General Integral Equations and Bounds of the Effective Moduli of Random Structure Composites

2017 ◽  
Author(s):  
Valeriy A. Buryachenko
Keyword(s):  
Heterogeneous Media ◽  
Effective Field ◽  
Local Fields ◽  
Upper And Lower Bounds ◽  
Homogeneous Field ◽  
Random Structure ◽  
Variational Functional ◽  
General Integral ◽  
Mechanics Of Heterogeneous Media ◽  
The Difference

One considers a linear elastic random structure composite material (CM) with a homogeneous matrix. The idea of the effective field hypothesis (EFH, H1) dates back to Faraday, Poisson, Mossotti, Clausius, and Maxwell (1830–1870, see for references and details [1], [2]) who pioneered the introduction of the effective field concept as a local homogeneous field acting on the inclusions and differing from the applied macroscopic one. It is proved that a concept of the EFH (even if this term is not mentioned) is a (first) background of all four groups of analytical methods in physics and mechanics of heterogeneous media (model methods, perturbation methods, self-consistent methods, and variational ones, see for refs. [1]). New GIEs essentially define the new (second) background (which does not use the EFH) of multiscale analysis offering the opportunities for a fundamental jump in multiscale research of random heterogeneous media with drastically improved accuracy of local field estimations (with possible change of sign of predicted local fields). Estimates of the Hashin-Shtrikman (H-S) type are developed by extremizing of the classical variational functional involving either a classical GIE [1] or a new one. In the classical approach by Willis (1977), the H-S functional is extremized in the class of trial functions with a piece-wise constant polarisation tensors while in the current work we consider more general class of trial functions with a piece-wise constant effective fields. One demonstrates a better quality of proposed bounds, that is assessed from the difference between the upper and lower bounds for the concrete numerical examples.

New Background of Micromechanics of Random Heterogeneous Media: Opportunities and Prospects

2015 ◽  
Author(s):  
Valeriy A. Buryachenko
Keyword(s):  
Multiscale Analysis ◽  
Perturbation Methods ◽  
Heterogeneous Media ◽  
Effective Field ◽  
Local Fields ◽  
Homogeneous Field ◽  
General Integral ◽  
Operator Form ◽  
Mechanics Of Heterogeneous Media ◽  
Improved Accuracy

One considers a linear heterogeneous media (e.g. filtration in porous media, composite materials, CMs, nanocomposites, peristatic CMs, and rough contacted surfaces). The idea of the effective field hypothesis (EFH, H1, see for references and details [1], [2]) dates back to Mossotti (1850) who pioneered the introduction of the effective field concept as a local homogeneous field acting on the inclusions and differing from the applied macroscopic one. It is proved that a concept of the EFH (even if this term is not mentioned) is a (first) background of all four groups of analytical methods in physics and mechanics of heterogeneous media (model methods, perturbation methods, self-consistent methods, and variational ones, see for refs. [1]). An operator form of the general integral equations (GIEs) is obtained which connects the driving fields and fluxes in a point being considered. New GIEs present in fact the new (second) background (which does not use the EFH) of multiscale analysis offering the opportunities for a fundamental jump in multiscale research of random heterogeneous media with drastically improved accuracy of local field estimations (with possible change of sign of predicted local fields).

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