Geodesic
Study of discontinuities in solutions of the Prandtl-Reuss elastoplasticity equations
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 56 (2016) no. 4, pp. 650-663 
A. G. Kulikovskii; A. P. Chugainova. Study of discontinuities in solutions of the Prandtl-Reuss elastoplasticity equations. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 56 (2016) no. 4, pp. 650-663. http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_4_a9/
@article{ZVMMF_2016_56_4_a9,
     author = {A. G. Kulikovskii and A. P. Chugainova},
     title = {Study of discontinuities in solutions of the {Prandtl-Reuss} elastoplasticity equations},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {650--663},
     year = {2016},
     volume = {56},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_4_a9/}
}
TY  - JOUR
AU  - A. G. Kulikovskii
AU  - A. P. Chugainova
TI  - Study of discontinuities in solutions of the Prandtl-Reuss elastoplasticity equations
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2016
SP  - 650
EP  - 663
VL  - 56
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_4_a9/
LA  - ru
ID  - ZVMMF_2016_56_4_a9
ER  - 
%0 Journal Article
%A A. G. Kulikovskii
%A A. P. Chugainova
%T Study of discontinuities in solutions of the Prandtl-Reuss elastoplasticity equations
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2016
%P 650-663
%V 56
%N 4
%U http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_4_a9/
%G ru
%F ZVMMF_2016_56_4_a9

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

Relations across shock waves propagating through Prandtl–Reuss elastoplastic materials with hardening are investigated in detail. It is assumed that the normal and tangent velocities to the front change across shock waves. In addition to conservation laws, shock waves must satisfy additional relations implied by their structure. The structure of shock waves is studied assuming that the principal dissipative mechanism is determined by stress relaxation, whose rate is bounded. The relations across shock waves are subject to a qualitative analysis, which is illustrated by numerical results obtained for quantities across shocks.

[1] Kulikovskii A. G., Chugainova A. P., “Udarnye volny v uprugoplasticheskikh credakh so strukturoi, opredelyaemoi protsessom relaksatsii napryazhenii”, Tr. MIAN, 289, 2015, 178–194 | MR

[2] Balashov D. V., “O prostykh volnakh uravnenii Prandtlya–Reissa”, Prikl. matem. i mekhan., 56:1 (1992), 124–133 | MR | Zbl

[3] Kulikovskii A. G., Chugainova A. P., “Ob oprokidyvanii voln Rimana v uprugoplasticheskikh sredakh s uprochneniem”, Prikl. matem. i mekhan., 77:4 (2013), 486–500

[4] Sadovskii V. M., Razryvnye resheniya v zadachakh dinamiki uprugoplasticheskikh sred, Nauka, M., 1997 | MR

[5] Sadovskii V. M., “Uprugoplasticheskie volny silnogo razryva v lineino uprochnyayuschikhsya sredakh”, Izv. RAN. Ser. Mekhanika tverdogo tela, 1997, no. 6, 104–111 | MR

[6] Sadovskii V. M., “K teorii udarnykh voln v szhimaemykh plasticheskikh sredakh”, Izv. RAN. Ser. Mekhanika tverdogo tela, 2001, no. 5, 87–95

[7] Bykovtsev G. I., Kretova L. D., “O rasprostranenii udarnykh voln v uprugoplasticheskikh sredakh”, Prikl. matem. i mekhan., 36:1 (1972), 106–116 | Zbl

[8] Druyanov B. A., “Obobschennye resheniya v teorii plastichnosti”, Prikl. matem. i mekhan., 50:3 (1986), 483–489 | MR | Zbl

[9] Godunov S. K., Romenskii E. I., Elementy mekhaniki sploshnykh sred i zakony sokhraneniya, Ucheb. posobie dlya fiz. i matem. spets. vuzov, Nauch. kn., Novosibirsk, 1998

[10] Kukudzhanov V. I., “Nelineinye volny v uprugoplasticheskikh sredakh”, Volnovaya dinamika mashin, ed. K. V. Frolov, Nauka, M., 1991, 126–140

[11] Kulikovskii A. G., “O poverkhnostyakh razryva, razdelyayuschikh idealnye sredy s razlichnymi svoistvami. Volny rekombinatsii”, Prikl. matem. i mekhan., 32:6 (1968), 1125–1131 | Zbl