Mathematical modeling of elasticity properties in the mechanics of composite materials
Čebyševskij sbornik, Tome 21 (2020) no. 3, pp. 262-271 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

This paper presents an overview of mathematical models that allow us to determine the effective elastic characteristics of various types of composite materials. The most well-known models are considered: virial decomposition, self-matching method, correlation approximation, and singular approximation. Models with a layered structure and matrix systems with a regular structure are considered.
Mots-clés : composites
Keywords: mathematical models, modeling, plasticity, strength, elasticity.
@article{CHEB_2020_21_3_a21,
     author = {I. K. Arkhipov and V. I. Abramova and A. E. Gvozdev and O. V. Kuzovleva},
     title = {Mathematical modeling of elasticity properties in the mechanics of composite materials},
     journal = {\v{C}eby\v{s}evskij sbornik},
     pages = {262--271},
     year = {2020},
     volume = {21},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHEB_2020_21_3_a21/}
}
TY  - JOUR
AU  - I. K. Arkhipov
AU  - V. I. Abramova
AU  - A. E. Gvozdev
AU  - O. V. Kuzovleva
TI  - Mathematical modeling of elasticity properties in the mechanics of composite materials
JO  - Čebyševskij sbornik
PY  - 2020
SP  - 262
EP  - 271
VL  - 21
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/CHEB_2020_21_3_a21/
LA  - ru
ID  - CHEB_2020_21_3_a21
ER  - 
%0 Journal Article
%A I. K. Arkhipov
%A V. I. Abramova
%A A. E. Gvozdev
%A O. V. Kuzovleva
%T Mathematical modeling of elasticity properties in the mechanics of composite materials
%J Čebyševskij sbornik
%D 2020
%P 262-271
%V 21
%N 3
%U http://geodesic.mathdoc.fr/item/CHEB_2020_21_3_a21/
%G ru
%F CHEB_2020_21_3_a21
I. K. Arkhipov; V. I. Abramova; A. E. Gvozdev; O. V. Kuzovleva. Mathematical modeling of elasticity properties in the mechanics of composite materials. Čebyševskij sbornik, Tome 21 (2020) no. 3, pp. 262-271. http://geodesic.mathdoc.fr/item/CHEB_2020_21_3_a21/

[1] Krivoglaz M. A., Cherevko A.S., “About elastic modules of a solid mixture”, Metal Physics and metal science, 8:2 (1959), 161–164

[2] Kanaun S. K., “Self-consistent field Method in the problem of effective properties of an elastic composite”, Applied mechanics and technical physics, 1975, no. 4, 194

[3] Shermergor T. D., Theory of elasticity of micro-homogeneous media, Nauka, M., 1977, 399 pp.

[4] Arkhipov I. K., Tolokonnikov L. A., “Effective relations between stresses and deformations in the correlation theory of elastic-plastic deformations”, Izvestiya AN SSSR. Solid mechanics, 2 (1984), 196–200 | MR

[5] Arkhipov I. K., Gerlein O. V., “Correlation characteristics of the plastic stiffness of a chaotically reinforced composite”, News of universities. Mathematics, 1982:7, 66–70

[6] Fokin A. G., Shermergor T. D., “Calculation of effective elastic modules of composite materials taking into account multiparticle interactions”, Applied mechanics and technical physics, 1969, no. 1, 51 | Zbl

[7] Livshits I. M., Rosenzweig L. N., “On the theory of elastic properties of polycrystals”, Journal of experimental and theoretical physics, 11:1946, 967

[8] Fokin A. G., Shermergor T. D., “Statistical description of the elastic field of layered materials”, Engineering and physical journal. Solid mechanics, 1968, no. 4, 93

[9] Fokin A. G., Shermergor T. D., “Effective elastic modulus of a composite composed of anisotropic layers”, Mechanics of polymers, 1975, no. 3, 408

[10] Yeh R. H. T., “Variational principles of elastic moduli of composite materials”, J. App. Phys., 1970, no. 8, 3353 | DOI

[11] Yeh R. H. T., “Variational bounds of the elastic moduli of twophase materials”, J. App. Phys., 1971, no. 3, 1101 | DOI | MR