Geodesic
Computer simulation of underthrust and subduction at collision of plates
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 12 (2009) no. 1, pp. 71-90 
S. N. Korobeinikov; V. V. Reverdatto; O. P. Polyanskii; V. G. Sverdlova; A. V. Babichev. Computer simulation of underthrust and subduction at collision of plates. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 12 (2009) no. 1, pp. 71-90. http://geodesic.mathdoc.fr/item/SJVM_2009_12_1_a5/
@article{SJVM_2009_12_1_a5,
     author = {S. N. Korobeinikov and V. V. Reverdatto and O. P. Polyanskii and V. G. Sverdlova and A. V. Babichev},
     title = {Computer simulation of underthrust and subduction at collision of plates},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {71--90},
     year = {2009},
     volume = {12},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2009_12_1_a5/}
}
TY  - JOUR
AU  - S. N. Korobeinikov
AU  - V. V. Reverdatto
AU  - O. P. Polyanskii
AU  - V. G. Sverdlova
AU  - A. V. Babichev
TI  - Computer simulation of underthrust and subduction at collision of plates
JO  - Sibirskij žurnal vyčislitelʹnoj matematiki
PY  - 2009
SP  - 71
EP  - 90
VL  - 12
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/SJVM_2009_12_1_a5/
LA  - ru
ID  - SJVM_2009_12_1_a5
ER  - 
%0 Journal Article
%A S. N. Korobeinikov
%A V. V. Reverdatto
%A O. P. Polyanskii
%A V. G. Sverdlova
%A A. V. Babichev
%T Computer simulation of underthrust and subduction at collision of plates
%J Sibirskij žurnal vyčislitelʹnoj matematiki
%D 2009
%P 71-90
%V 12
%N 1
%U http://geodesic.mathdoc.fr/item/SJVM_2009_12_1_a5/
%G ru
%F SJVM_2009_12_1_a5

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

Mathematical simulation of a collision of lithospheric slabs at which one slab is sank into the mantle under another one is carried out. Problems of the crust and the mantle deformation are numerically solved, so that the finite element method is used for spatial discretization of the equations of deformable solid mechanics, and for evolution of the collision process, the step-by-step integration of the quasistatic deformation equations is applied. Problems of the slabs movement are solved at geometric nonlinear statement in view of large deformations of bodies and contact interactions of slabs and the mantle. The solution is numerically carried out by using the MSC.Marc 2005.code, in which the formulations of equations with required types of nonlinearites are implemented. That part of the Earth's crust which has no tendency to sinking in the mantle is simulated by the prescribed movement of a rigid body. Another part of the Earth's crust, which by virtue of properties of the initial geometry should sink, is simulated by a deformable body with an elastic-plastic strain hardening material. The mantle is simulated by an ideal elastic-plastic material with a small value of yield stress. Parts of the Earth's crust with different geometric parameters are considered. From the computer simulation of plates ollision it follows that in standard conditions, the underthrust of one slab under another one is realized, and at some initial thickening of a plate in a contact zone the subduction (deep sinking) of this plate is possible. It is shown that in the latter case it is necessary to take into account the known experimental fact of material condensation of a sunk piece of the plate.

[1] Korobeinikov S.N., Polyanskii O.P., Likhanov I.I., Sverdlova V.G., Reverdatto V.V., “Matematicheskoe modelirovanie nadviga kak prichiny formirovaniya andaluzit-kianitovoi metamorficheskoi zonalnosti v Eniseiskom kryazhe”, Dokl. RAN, 408:4 (2006), 512–516

[2] Korobeinikov S.N., Reverdatto V.V., Polyanskii O.P. i dr., “Otsenka effekta geometricheskoi nelineinosti pri matematicheskom modelirovanii tektonicheskikh protsessov”, Vychislitelnye metody i programmirovanie, 7:2 (2006), 130–145

[3] Spear F.S., Hickmott D.D., and Selverstone J., “Metamorphic consequences of thrust emplacement, Bellows Falls, New Hampshire”, G.S.A. Bulletin, 102 (1990), 1344–1360 | 2.3.CO;2 class='badge bg-secondary rounded-pill ref-badge extid-badge'>DOI

[4] Likhanov I.I., Reverdatto V.V., Kozlov P.S., Popov N.V., “Kollizionnyi metamorfizm dokembriiskikh kompleksov v zaangarskoi chasti Eniseiskogo kryazha”, Petrologiya, 16:2 (2008), 149–174

[5] Xiao L., Wang Ch., and Pirajno F., “Is the underthrust Indian lithosphere split beneath the Tibetan plateau?”, Int. Geol. Rev., 49:1 (2007), 90–98 | DOI

[6] Seago R.D., Chapman T.J., “The confrontation of structural styles and the evolution of a fore-land basin in central SW”, J. of the Geological Society, 145:5 (1988), 789–800 | DOI

[7] Rabotnov Yu.N., Mekhanika deformiruemogo tverdogo tela, Nauka, M., 1988 | Zbl

[8] Korobeinikov S.N., Nelineinoe deformirovanie tverdykh tel, Izd-vo SO RAN, Novosibirsk, 2000

[9] Bathe K.-J., Finite Element Procedures, Prentice Hall, New Jersey, Upper Saddle River, 1996

[10] Zeinkiewicz O.C., Taylor R.L., The Finite Element Method, Butterworth-Heinemann, Oxford, 2000

[11] MARC Users Guide. Vol. A: Theory and Users Information, MSC.Software Corporation, Santa Ana (CA), 2005

[12] Golovanov A.I., Berezhnoi D.V., Metod konechnykh elementov v mekhanike deformiruemykh tverdykh tel, DAS, Kazan, 2001

[13] Kleiber M., Incremental Finite Element Modelling in Non-linear Solid Mechanics, Ellis Horwood, Chichester, 1989 | MR | Zbl

[14] Osias J.R., Swedlow J.L., “Finite elastic-plastic deformation-1. Theory and numerical examples”, Int. J. Solids Structures, 10:3 (1974), 321–339 | DOI | Zbl

[15] McMeeking R.M., Rice J.R., “Finite element formulations for problems of large elastic-plastic deformation”, Int. J. Solids Structures, 11 (1975), 601–616 | DOI | Zbl

[16] Hughes T.J.R., The Finite Element Method: Linear Static and Dynamic Finite Element Analysis, Prentice-Hall, Englewood Cliffs, 1987 | MR | Zbl

[17] Shemenda A.I., Subduction: Insights from Physical Modeling, Kluwer Academic Publishers, Dordrecht et al., 1994

[18] Strang G., Fix G.J., An Analysis of the Finite Element Method, Prentice Hall, Englewood Cliffs, N.J., 1973 ; Streng G., Fiks Dzh., Teoriya metoda konechnykh elementov, Mir, M., 1977 | MR | Zbl | MR

[19] PATRAN Users Guide, MSC.Software Corporation, Santa Ana (CA), 2005

[20] Green D.H., Ringwood A.E. at al., Petrology of the Upper Mantle, Australian National University Publication, 444, 1966; Grin D.Kh., Ringvud A.E. i dr., Petrologiya verkhnei mantii, Mir, M., 1968