Geodesic
On the numerical investigations of stress-strain behavior of materials based on isotropic elasticity model for multimodulus media
Matematičeskoe modelirovanie, Tome 20 (2008) no. 4, pp. 117-127.

Voir la notice de l'article provenant de la source Math-Net.Ru

The paper deals with the multimodulus approach to problems of continuum mechanics. In the introduction we give a survey of promising multimodulus model developed by V.P.Myasnikov for the case of isotropic elasticity. We consider also the numerical finite-element approximations to the multimodulus equilibrium state equations which in fact form the sophisticated Lame system. By means of that model a set of test problems was solved. The test simulations were carried out for structural objects consisting of such multimodulus materials as steel, concrete, ceramics and soil. The results are presented in the final part of the article. The effect of different moduli in tension and compression on the strain intensity is discussed. 
@article{MM_2008_20_4_a9,
     author = {V. A. Gasilov and M. V. Golovin},
     title = {On the numerical investigations of stress-strain behavior of materials based on isotropic elasticity model for multimodulus media},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {117--127},
     publisher = {mathdoc},
     volume = {20},
     number = {4},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2008_20_4_a9/}
}
TY  - JOUR
AU  - V. A. Gasilov
AU  - M. V. Golovin
TI  - On the numerical investigations of stress-strain behavior of materials based on isotropic elasticity model for multimodulus media
JO  - Matematičeskoe modelirovanie
PY  - 2008
SP  - 117
EP  - 127
VL  - 20
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MM_2008_20_4_a9/
LA  - ru
ID  - MM_2008_20_4_a9
ER  - 
%0 Journal Article
%A V. A. Gasilov
%A M. V. Golovin
%T On the numerical investigations of stress-strain behavior of materials based on isotropic elasticity model for multimodulus media
%J Matematičeskoe modelirovanie
%D 2008
%P 117-127
%V 20
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MM_2008_20_4_a9/
%G ru
%F MM_2008_20_4_a9
V. A. Gasilov; M. V. Golovin. On the numerical investigations of stress-strain behavior of materials based on isotropic elasticity model for multimodulus media. Matematičeskoe modelirovanie, Tome 20 (2008) no. 4, pp. 117-127. http://geodesic.mathdoc.fr/item/MM_2008_20_4_a9/

[1] Ambartsumyan S. A., Raznomodulnaya teoriya uprugosti, Nauka, M., 1982 | MR

[2] Jones R. M., “Stress-strain relations for materials with different moduli in tension and compression”, AIAA J., 15:1 (1977), 16–23 | DOI

[3] Lebedev A. A., Kovalchuk B. I., Giginyak F. F., Lamashevskii V. P., Mekhanicheskie svoistva konstruktsionnykh materialov pri slozhnom napryazhennom sostoyanii. Spravochnik, Nauk. dumka, Kiev, 1983

[4] Leonov M. Ya., Panyaev V. A., Rusinko K. N., “Zavisimost mezhdu deformatsiyami i napryazheniyami dlya polukhrupkikh tel”, Inzh. zh. MTT, 1967, no. 6, 26–32

[5] Rzhevskii V. V., Novik G. Ya., Osnovy fiziki gornykh porod, 4-e izd., Nedra, M., 1984

[6] Schock R. N., “The response of rocks to large stresses”, Impact and explosion cratering, Pergamon Press, N.Y., 1977, 657–688; Shok R., “Povedenie gornykh porod pod deistviem bolshikh napryazhenii”, Udar, vzryv i razrushenie, Mekhanika. Novoe v zarubezhnoi nauke, 26, Mir, M., 1981, 116–130

[7] Nikolaevskii V. N., “Granitsa Mokhorovichicha kak predelnaya glubina khrupko-dilatansionnogo sostoyaniya gornykh porod”, DAN SSSR, 249:4 (1979), 817–821

[8] Lomakin E. V., “Opredelyayuschie sootnosheniya deformatsionnoi teorii dlya dilatiruyuschikh sred”, Izv. AN SSSR. MTT, 1991, no. 6, 66–75

[9] Mori V., “Mekhanizmy razrusheniya v stenkakh skvazhin, podzemnykh sooruzhenii i vyrabotok”, Mekhanika gornykh porod primenitelno k problemam razvedki i dobychi nefti, Mir, M., 1994, 361–411

[10] Santarelli F. Zh., Braun I. T., “Povedenie stvola glubokoi skvazhiny, proburennoi v porode, kharakterizuyuscheisya modulem uprugosti, zavisyaschim ot gornogo davleniya”, Mekhanika gornykh porod primenitelno k problemam razvedki i dobychi nefti, Mir, M., 1994, 88–96

[11] Geno A., “Napryazheniya i razrusheniya v stenkakh neftyanykh skvazhin”, Mekhanika gornykh porod primenitelno k problemam razvedki i dobychi nefti, Mir, M., 1994, 73–87

[12] Geno A., “Problema neustoichivosti stvola skvazhiny na bolshikh glubinakh”, Mekhanika gornykh porod primenitelno k problemam razvedki i dobychi nefti, Mir, M., 1994, 97–107

[13] Lyakhovskii V. A., Myasnikov V. P., “O povedenii uprugoi sredy s mikronarusheniyami”, Izv. AN SSSR. Fizika zemli, 1984, no. 10, 71–75 | MR

[14] Myasnikov V. P., Oleinikov A. I., “Osnovnye obschie sootnosheniya modeli izotropno-uprugoi raznosoprotivlyayuscheisya sredy”, DAN SSSR, 322:1 (1992), 57–60 | Zbl

[15] Gasilov V. A., Golovin M. V., Myasnikov V. P., Pergament A. Kh., Reznik A.A., Matematicheskoe modelirovanie napryazhenno-deformirovannogo sostoyaniya gornykh porod na osnove raznomodulnoi modeli sploshnoi sredy, Preprint No 112, IPM im. M. V. Keldysha RAN, 1997

[16] Gasilov V. A., Golovin M. V., Myasnikov V. P., Pergament A. Kh., “Primenenie raznomodulnoi modeli sploshnoi sredy k analizu povedeniya gornykh porod pod deistviem bolshikh napryazhenii”, Izv. RAN. MTT, 2000, no. 2, 86–92

[17] Zienkiewicz O. C., Taylor R. L., The finite element method, 5-th ed., 2000

[18] Ortega Dzh., Reinbolt V., Iteratsionnye metody resheniya nelineinykh sistem uravnenii so mnogimi neizvestnymi, Mir, M., 1976

[19] Maslyankin V. I., Mukhina M. I., Reznik A. A., “K resheniyu sistemy lineinykh uravnenii s razrezhennoi matritsei iteratsionnymi metodami”, Matem. modelirovanie, 4:5 (1992), 100–108 | MR