Noneuclidean structure of internal stress in continuum
Dalʹnevostočnyj matematičeskij žurnal, Tome 2 (2001) no. 2, pp. 29-44 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

It is shown that the choice in determination of internal stress in continuum is defined by the noneuclidean geometric objects charactirizing defects of internal material structure.
@article{DVMG_2001_2_2_a2,
     author = {M. A. Guzev and V. P. Myasnikov},
     title = {Noneuclidean structure of internal stress in continuum},
     journal = {Dalʹnevosto\v{c}nyj matemati\v{c}eskij \v{z}urnal},
     pages = {29--44},
     year = {2001},
     volume = {2},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DVMG_2001_2_2_a2/}
}
TY  - JOUR
AU  - M. A. Guzev
AU  - V. P. Myasnikov
TI  - Noneuclidean structure of internal stress in continuum
JO  - Dalʹnevostočnyj matematičeskij žurnal
PY  - 2001
SP  - 29
EP  - 44
VL  - 2
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/DVMG_2001_2_2_a2/
LA  - ru
ID  - DVMG_2001_2_2_a2
ER  - 
%0 Journal Article
%A M. A. Guzev
%A V. P. Myasnikov
%T Noneuclidean structure of internal stress in continuum
%J Dalʹnevostočnyj matematičeskij žurnal
%D 2001
%P 29-44
%V 2
%N 2
%U http://geodesic.mathdoc.fr/item/DVMG_2001_2_2_a2/
%G ru
%F DVMG_2001_2_2_a2
M. A. Guzev; V. P. Myasnikov. Noneuclidean structure of internal stress in continuum. Dalʹnevostočnyj matematičeskij žurnal, Tome 2 (2001) no. 2, pp. 29-44. http://geodesic.mathdoc.fr/item/DVMG_2001_2_2_a2/

[1] S. K. Godunov, E. I. Romenskii, Elementy mekhaniki sploshnoi sredy, Nauchnaya kniga, Novosibirsk, 1998, 268 pp.

[2] K. Kondo, “On the geometrical and physical foundations of the theory of yielding”, Proc. 2nd Japan Nat. Congr. Appl. Mech., Tokyo, 1953, 41–47 | MR

[3] B. A. Bilby, R. Bullough, E. Smith, “Continuos distributions of dislocations: a new application of the methods of non-Reimannian geometry”, Proc. Roy. Soc. A, 231, 1955, 263–273 | MR

[4] A. Kadich, D. Edelen, Kalibrovochnaya teoriya dislokatsii i disklinatsii, Mir, M., 1987, 168 pp. | MR

[5] Fizicheskaya mezomekhanika i kompyuternoe konstruirovanie materialov, v. 1, ed. V. E. Panin, Nauka, Novosibirsk, 1995, 297 pp.

[6] Fizicheskaya mezomekhanika i kompyuternoe konstruirovanie materialov, v. 2, ed. V. E. Panin, Nauka, Novosibirsk, 1995, 320 pp.

[7] V. P. Myasnikov, M. A. Guzev, “Neevklidova model deformirovaniya materialov na razlichnykh strukturnykh urovnyakh”, Fizicheskaya mezomekhanika, 3:1 (2000), 5–16

[8] G. N. Chernyshov, A. L. Popov, V. M. Kozintsev, I. I. Ponomarev, Ostatochnye napryazheniya v deformiruemykh tverdykh telakh, Nauka, M., 1996, 240 pp.

[9] L. D. Landau, E. M. Lifshits, Teoriya uprugosti, Nauka, M., 1987, 248 pp. | MR | Zbl

[10] N. I. Ostrosablin, “Ob uravneniyakh Beltrami-Michella i operatore Sen-Venana”, Dinamika sploshnoi sredy. Sbornik nauchnykh trudov, 116 (2000), 211–217, Novosibirsk | MR | Zbl

[11] L. D. Landau, E. M. Lifshits, Teoriya polya, Nauka, M., 1988, 512 pp. | MR

[12] B. A. Dubrovin, S. P. Novikov, L. T. Fomenko, Sovremennaya geometriya: Metody i prilozheniya, Nauka, M., 1986, 760 pp. | MR