Numerical investigation of large deformations of hyperelastic solids. III. Statements of problem and solution algorithms
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Kazanskii Gosudarstvennyi Universitet. Uchenye Zapiski. Seriya Fiziko-Matematichaskie Nauki, Tome 151 (2009) no. 3, pp. 108-120
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The current article is the third part of a research work cycle “Numerical investigation of large deformations of hyperelastic solids”. The article describes the design algorithms for 3D-solids of hyperelastic materials on the basis of consecutive stress method. Different variants of problem statement are regarded. An algorithm is presented for investigating the deformation of hyperelastic low-compressible materials.
Keywords: large deformations, hyperelasticity, strain energy potential, statement of problem, algorithm.
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     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
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A. I. Golovanov; Yu. G. Konoplev; L. U. Sultanov. Numerical investigation of large deformations of hyperelastic solids. III. Statements of problem and solution algorithms. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Kazanskii Gosudarstvennyi Universitet. Uchenye Zapiski. Seriya Fiziko-Matematichaskie Nauki, Tome 151 (2009) no. 3, pp. 108-120. http://geodesic.mathdoc.fr/item/UZKU_2009_151_3_a8/

[1] Golovanov A. I., Konoplev Yu. G., Sultanov L. U., “Chislennoe issledovanie konechnykh deformatsii giperuprugikh tel. I. Kinematika i variatsionnye uravneniya”, Uchen. zap. Kazan. un-ta. Ser. Fiz.-matem. nauki, 150, no. 1, 2008, 29–37 | Zbl

[2] Golovanov A. I., Konoplev Yu. G., Sultanov L. U., “Chislennoe issledovanie konechnykh deformatsii giperuprugikh tel. II. Fizicheskie sootnosheniya”, Uchen. zap. Kazan. un-ta. Ser. Fiz.-matem. nauki, 150, no. 3, 2008, 122–132

[3] Vasidzu K., Variatsionnye metody v teorii uprugosti i plastichnosti, Mir, M., 1987, 542 pp.

[4] Grin A., Adkins D., Bolshie uprugie deformatsii i nelineinaya mekhanika sploshnoi sredy, Mir, M., 1965, 455 pp. | MR | Zbl

[5] Korobeinikov S. N., Nelineinoe deformirovanie tverdykh tel, Novosibirsk, 2000, 262 pp.

[6] Lure A. I., Nelineinaya teoriya uprugosti, Nauka, M., 1980, 512 pp. | MR

[7] Oden D., Konechnye elementy v nelineinoi mekhanike sploshnykh sred, Mir, M., 1976, 464 pp.

[8] Konyukhov A. V, Konoplev Yu. G., “Model termogiperuprugosti i ee primenenie k issledovaniyu poteri ustoichivosti razduvaemykh plastin. Chast II”, Izv. vuzov. Aviats. tekhnika, 2006, no. 4, 7–13

[9] Maniatty A. M., Liu Y., Klaas O., Shephard M., “Higher order stabilized finite element method for hyperelastic finite deformation”, Comput. Meth. Appl. Mech. Eng., 191 (2002), 1491–1503 | DOI | Zbl

[10] Vujosevic L., Lubarda V. A., “Finite strain thermoelasticity based on multiplicative decomposition of deformation gradient”, Theor. Appl. Mech., 28–29 (2002), 379–399 | DOI | MR | Zbl

[11] Miehe C., “Entropic thermoelasticity at finite strain. Aspects of the formulation and numerical implementation”, Comput. Meth. Appl. Mech. Eng., 120 (1995), 243–269 | DOI | MR | Zbl

[12] Liu C. H., Wong J. Y., Mang H. A., “Large strain finite element analysis of sand: model, algorithm and application to numerical simulation of tire-sand interaction”, Comput. Struct., 74 (2000), 253–265 | DOI