Geodesic
Investigation of deformation of fluid-saturated media in terms of arbitrary Lagrangian-Eulerian formulation of motion. I. Kinematics and resolving equations
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 152 (2010) no. 4, pp. 106-114 Cet article a éte moissonné depuis la source Math-Net.Ru

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The present article starts a series of papers devoted to the development of a numerical algorithm for researching nonisothermal deformation of fluid-saturated porous media. The first part discusses the principal regulations of two-phase media kinematics taking into account the arbitrary Lagrangian-Eulerian formulation of motion and gives the basic set of resolving and determinative equations.
Keywords: arbitrary Lagrangian-Eulerian formulation, nonisothermic deformation, fluid-saturated porous media, viscoplasticity. 
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     title = {Investigation of deformation of fluid-saturated media in terms of arbitrary {Lagrangian-Eulerian} formulation of~motion. {I.~Kinematics} and resolving equations},
     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
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D. V. Berezhnoi; A. I. Golovanov; S. A. Malkin; L. U. Sultanov. Investigation of deformation of fluid-saturated media in terms of arbitrary Lagrangian-Eulerian formulation of motion. I. Kinematics and resolving equations. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 152 (2010) no. 4, pp. 106-114. http://geodesic.mathdoc.fr/item/UZKU_2010_152_4_a9/

[1] Donea J., Fasoli-Stella P., Giuliani S., “Lagrangian and Eulerian finite element techniques for transient fluid-structure interaction problems”, Trans. 4th Int. Conf. on Structural Mechanics in Reactor Technology, v. B, Thermal and Fluid/Structure Dynamics Analysis, eds. T. A. Jaeger, B. A. Boley, North-Holland Publ. Comp., Amsterdam, 1977, Paper B1/2, 12 pp.

[2] Belytschko T., Kennedy J. M., “Computer models for subassembly simulation”, Nucl. Engrg. Des., 49 (1978), 17–38 | DOI

[3] Donea J., “Finite element analysis of transient dynamic fluid-structure interaction”, Advanced Structural Dynamics, ed. Donea J., Appl. Sci. Publ., London, 1980, 255–290

[4] Donea J., “Arbitrary Lagrangian Eulerian finite element methods”, Computer Methods for Transient Analysis, eds. Belytschko T., Hughes T. J. R., Elsevier Sci. Publ., 1983, 473–516

[5] Hughes T. J. R., Liu W. K., Zimmermann T. K., “Lagrangian–Eulerian finite element formulation for viscous flows”, Comput. Methods Appl. Mech. Engrg., 29 (1981), 329–349 | DOI | MR | Zbl

[6] Liu W. K., “Finite element procedures for fluid-structure interactions and application to liquid storage tanks”, Nucl. Engrg. Des., 65 (1981), 221–238 | DOI

[7] Huerta A., Casadei F., “New ALE application in non-linear fast-transient solid dynamics”, Engrg. Comput., 11 (1994), 317–345 | MR | Zbl

[8] Belytschko T., Liu W. K., Moran B., Nonlinear Finite Elements for Continua and Structures, John Wiley Sons, Chichester, 2000, 650 pp. | MR

[9] Wall W. A., Fluid-Struktur-Interaktion mit stabilisierten Finiten Elementen, Ph. D. Thesis, Bericht des Instituts fur Baustatik Nr. 31, Universitat Stuttgart, 1999

[10] Braess H., Wriggers P., “Arbitrary Lagrangian Eulerian finite element analysis for free surface flow”, Comput. Methods Appl. Mech. Engrg., 190 (2000), 95–109 | DOI | Zbl

[11] Rodriguez-Ferran A., Perez-Foguet A., Huerta A., “Arbitrary Lagrangian-Eulerian (ALE) formulation for hyperelastoplacitcity”, Int. J. Numer. Methods Engrg., 53 (2002), 1831–1851 | DOI | Zbl

[12] Donea J., Huerta A., Finite Element Methods for Flow Problems, John Wiley Sons, Chichester–New York, 2003, 350 pp.

[13] Kuhl E., Hulshoff S., de Borst R., “An arbitrary Lagrangian Eulerian finite-element approach for fluid-structure interaction phenomena”, Int. J. Numer. Methods Engrg., 57 (2003), 117–142 | DOI | MR | Zbl

[14] Zaretskii Yu. K., Lektsii po sovremennoi mekhanike gruntov, Izd-vo Rost. un-ta, Rostov n/D, 1989, 607 pp.

[15] Tertsagi K., Teoreticheskaya mekhanika gruntov, Stroiizdat, M., 1961, 507 pp.

[16] Nikolaevskii V. N., Geomekhanika i flyuidodinamika, Nedra, M., 1996, 448 pp.