Influence of the choice of a~rheological law on computer simulation results of slab subduction

S. N. Korobeynikov ; V. V. Reverdatto ; O. P. Polyansky ; V. G. Sverdlova ; A. V. Babichev

Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 14 (2011) no. 1, pp. 71-90.

Résumé

The influence of the choice of the type of the yield surface for elastoplastic materials and material constants for the plate and the mantle on the scenario of mathematical modeling of the plates collision is investigated. Computer simulation is performed by the FEM numerical solution of nonlinear equations for deformable solid mechanics using MSC.Marc 2005 code. The simulation results essentially depend on the choice of material constants for the plate and the mantle, as well as on the type of the yield surface for the elastoplastic material of a subducting plate. The presented numerical simulations have demonstrated that the primary driving mechanism of subduction can be a geometrical inhomogeneity of the subduction plate near to a zone of plates collision, by providing a simultaneous consideration of the consolidation of a plate material as this plate descends into the mantle.

Bibliographie

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

[2] 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

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

[4] Korobeinikov S. N., Polyanskii O. P., Sverdlova V. G., Babichev A. V., Reverdatto V. V., “Kompyuternoe modelirovanie poddviga i subduktsii v usloviyakh perekhoda gabbro-eklogit v mantii”, Dokl. RAN, 420:5 (2008), 654–658 | Zbl

[5] Korobeinikov S. N., Reverdatto V. V., Polyanskii O. P., Sverdlova V. G., Babichev A. V., “Kompyuternoe modelirovanie poddviga i subduktsii pri stolknovenii plit”, Sib. zhurn. vychisl. matematiki, 12:1 (2009), 71–90

[6] Polyanskii O. P., Korobeinikov S. N., Sverdlova V. G., Babichev A. V., Reverdatto V. V., “Vliyanie reologii kory na kharakter subduktsii plit po rezultatam matematicheskogo modelirovaniya”, Dokl. RAN, 430:4 (2010), 518–522

[7] Capitano F. A., Morra G., Goes S., “Dynamic models of downgoing plate-buoyancy driven subduction: Subduction motions and energy dissipation”, Earth and Planetary Science Letters, 262 (2007), 284–297 | DOI

[8] Capitano F. A., Goes S., Morra G., Giardini D., “Retracted: Signatures of downgoing plate-buoyancy driven subduction in motions and seismic coupling at major subduction zones”, Earth and Planetary Science Letters, 262 (2007), 298–306 | DOI

[9] Zlotnik S., Díez P., Fernández M., Vergés J., “Numerical modelling of tectonic plates subduction using X-FEM”, Comput. Methods Appl. Mech. Engrg., 196 (2007), 4283–4293 | DOI | Zbl

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

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

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

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

[14] Zienkiewicz O. C., Taylor R. L., The Finite Element Method, 5th ed., Butterworth-Heinemann, Oxford, 2000

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

[16] Curnier A., Computational Methods in Solid Mechanics, Kluwer Academic Publ., Dordretch, 1994 | MR | Zbl

[17] Bonnet J., Wood R. D., Nonlinear Continuum Mechanics for Finite Element Analysis, Cambridge Univ. Press, Cambridge, 1997 | MR

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

[19] Jarrard R. D., “Relations Among Subduction Parameters”, Rev. Geophys., 24:2 (1986), 217–284 | DOI

[20] Abers G. A., “Plate structure and the origin of double seismic zones in Subduction Top to Bottom”, Geophysical Monograph 96, eds. G. E. Bebout, D. Scholl, S. Kirby, AGU, Washington, 1996, 223–228

[21] Rondenay S., Abers G. A., van Keken P. E., “Seismic imaging of subduction zone metamorphism”, Geology, 36:4 (2008), 275–278 | DOI

[22] Seliverstov N. I., Geodinamika zony sochleneniya Kurilo-Kamchatskoi i Aleutskoi ostrovnykh dug, Izd-vo KamGU, Petropavlovsk-Kamchatskii, 2009

[23] Gordeev E. I., Pavlov V. M., “Subduktsiya tikhookeanskoi plity pod Kamchatku: “seismicheskaya” skorost poddviga”, Fizika Zemli, 2009, no. 4, 56–66

[24] Dragert H., Hyndman R. D., Rogers G. C., Wang K., “Current deformation and the width of the seismogenic zone of the northern Cascadia subduction thrust”, J. Geophys. Res., 99:B1 (1994), 653–668 | DOI

[25] Nadai A., Theory of Flow and Fracture of Solids, v. 1, 2nd ed., McGraw Hill, New York–Toronto–London, 1950; Nadai A., Plastichnost i razrushenie tverdykh tel, v. 1, IL, M., 1954

[26] Boresi A. P., Schmidt R. J., Sidebottom O. M., Advanced Mechanics of Materials, 5th ed., Wiley, New York, 1993

[27] Duxbury P., Li X., “Development of elasto-plastic material models in a natural coordinate system”, Comput. Methods Appl. Mech. Engrg., 135 (1996), 283–306 | DOI | Zbl

[28] Kojić M., Bathe K. J., Inelastic Analysis of Solids and Structures, Springer, Berlin et al., 2005 | MR

[29] Makarov P. V., Smolin I. Yu., Stefanov Yu. P. i dr., Nelineinaya mekhanika geomaterialov i geosred, Izd-vo “GEO”, Novosibirsk, 2007

[30] Hiermaier S. J., Structures Under Crash and Impact: Continuum Mechanics, Discretization and Experimental Characterization, Springer, New York et al., 2008

[31] Irgens F., Continuum Mechanics, Springer, Berlin et al., 2008

[32] Hill R., “A general theory of uniqueness and stability in elastic-plastic solids”, J. Mech. Phys. Solids., 6:3 (1958), 236–249 | DOI | Zbl

[33] 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

[34] Brown C. D., Phillips R. J., “Crust-mantle decoupling by flexure of continental litosphere”, J. Geophys. Res., 105:B6 (2000), 13221–13237 | DOI

[35] Regenauer-Lieb K., Yuen D. A., “Quartz rheology and short-time-scale crustal instabilities”, Pure Appl. Geophys., 163 (2006), 1915–1932 | DOI

[36] Burov E., Yamato P., “Continental plate collision, P-T-t-z conditions and unstable vs. stable dynamics: Insights from termo-mechanical modeling”, Lithos, 103 (2008), 178–204 | DOI