Computer simulation of underthrust and subduction at collision of plates

S. N. Korobeinikov ; V. V. Reverdatto ; O. P. Polyanskii ; V. G. Sverdlova ; A. V. Babichev

Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 12 (2009) no. 1, pp. 71-90

Résumé

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.