Geodesic
Estimation of geometric nonlinearity effect on mathematical simulation of tectonic processes
Numerical methods and programming, Tome 7 (2006) no. 3, pp. 278-293.

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Nonlinear equations of deformable solid mechanics are applied for the mathematical simulation of tectonic processes. All three possible types of nonlinearities are used in the formulation of equations: material, geometric, and contact ones. We consider the tectonic processes for which the simulation is necessary to use the material and contact nonlinearities. The importance of accounting for the geometric nonlinearity of equations of deformable solid mechanics is studied when solving typical problems of tectonic processes simulation. The problem is solved on the thrust fault of a deformable plate on an absolutely rigid solid. The solution is carried out numerically by using the MSC.Marc 2005 code. The finite element method is used for spatial discretization of the equations of deformable solid mechanics. The step-by-step procedure with an iterative solution refinement is used for time integration of equations. The plate lower part is modeled by an elasto-plastic material, whereas the plate upper part is modeled by a brittle material. The performed computations have shown the importance of accounting for the geometric nonlinearity. The plate rupture scenario is developed in the geometrically linear approximation. This scenario differs significantly from the plate rupture scenario obtained when solving the same problem with taking into account the geometric nonlinearity of deformation.
Keywords: tectonic processes, numerical simulation, finite element method, geometric nonlinearity. 
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     author = {S. N. Korobeinikov and V. V. Reverdatto and O. P. Polyanskii and V. G. Sverdlova and A. V. Babichev},
     title = {Estimation of geometric nonlinearity effect on mathematical simulation of tectonic processes},
     journal = {Numerical methods and programming},
     pages = {278--293},
     publisher = {mathdoc},
     volume = {7},
     number = {3},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMP_2006_7_3_a10/}
}
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S. N. Korobeinikov; V. V. Reverdatto; O. P. Polyanskii; V. G. Sverdlova; A. V. Babichev. Estimation of geometric nonlinearity effect on mathematical simulation of tectonic processes. Numerical methods and programming, Tome 7 (2006) no. 3, pp. 278-293. http://geodesic.mathdoc.fr/item/VMP_2006_7_3_a10/