Stability by Lyapunov of solutions in endochronic plasticity theory without fluidity surface in flat tension conditions

V. P. Radchenko ; G. A. Pavlova ; S. V. Gorbunov

Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 2 (2008), pp. 143-151.

Résumé

The variant of endochronic theory of high-temperature plasticity without fluidity surface for a collapsing material is studied. Stability by Lyapunov of solutions in flat tension conditions is investigated. The limiting surface of steady deformation is constructed. It is shown that transition through this surface correlates with divergence of numerical iterative calculation procedure. Calculation examples are quoted.

Détail

Keywords: high-temperature plasticity, damage of material, the endochronic theory, Lyapunov stability of solutions, a limiting surface, divergence of iterative procedure.

Bibliographie

[1] Kadashevich Yu. I., Novozhilov V. V., “Teoriya plastichnosti i polzuchesti, uchityvayuschaya nasledstvennye svoistva i vliyanie skorosti plasticheskogo deformirovaniya na lokalnyi predel tekuchesti materiala”, Dokl. AN SSSR, 238:1 (1978), 36–38 | Zbl

[2] Klebanov Ya. M., Kokorev I. A., “Metodika opredeleniya parametrov neuprugogo reonomnogo deformirovaniya”, Zavodskaya laboratoriya, 1985, no. 4, 80–83

[3] Sadakov O. S., “Analiz napryazhenno-deformirovannogo sostoyaniya elementov konstruktsii na osnove strukturnoi modeli sredy”, Materialy Vsesoyuznogo simpoziuma po malotsiklovoi ustalosti pri povyshennykh temperaturakh, Vyp. 3, Chelyabinsk, 1974, 95–127

[4] Kadashevich Yu. I., Peisakhov A. M., Pomytkin S. P., “Rasshirennyi variant teorii polzuchesti, uchityvayuschii mikrorazrusheniya”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 2008, no. 1(16), 33–35 | DOI

[5] Kadashevich Yu. I., “Teoriya plastichnosti i polzuchesti, uchityvayuschaya mikrorazrusheniya”, Dokl. AN SSSR, 266:6 (1982), 79–87

[6] Novozhilov V. V., Kadashevich Yu. I., Mikronapryazheniya v konstruktsionnykh materialakh, Mashinostroenie, L., 1990, 224 pp.

[7] V. V. Struzhanov, Vyach. V. Bashurov, “Modifikatsionnaya model Mazinga”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 1(14) (2007), 29–39 | DOI

[8] Radchenko V. P., Eremin Yu. A., Reologicheskoe deformirovanie i razrushenie materialov i elementov konstruktsii, Mashinostroenie-1, M., 2004, 265 pp., ISBN 5–94275–111–0

[9] Struzhanov V. V., “Svoistva razuprochnyayuschikhsya materialov i opredelyayuschie sootnosheniya pri odnoosnom napryazhennom sostoyanii”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 2007, no. 2(15), 69–78 | DOI

[10] Struzhanov V. V., Mironov V. I., Deformatsionnoe razuprochnenie materiala v elementakh konstruktsii, UrO RAN, Ekaterinburg, 1995, 191 pp.

[11] Radchenko V. P., “Matematicheskaya model neuprugogo deformirovaniya i razrusheniya metallov pri polzuchesti energeticheskogo tipa”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 1996, no. 4, 43–63 | DOI

[12] Radchenko V. P., Pavlova G. A., Gorbunov S. V., “Ob ustoichivosti reshenii odnogo varianta endokhronnoi teorii odnoosnoi plastichnosti”, Matem. modelirovanie i kraev. zadachi. Ch. 1. Matematicheskie modeli mekhaniki, prochnosti i nadëzhnosti elementov konstruktsii, Tr. Pyatoi Vseros. nauchn. konf. s mezhdunar. uchastiem, SamGTU, Samara, 2008, 255–261

[13] Samarin Yu. P., Uravneniya sostoyaniya materialov so slozhnymi reologicheskimi svoistvami, Kuibyshevskii gosuniversitet, Kuibyshev, 1979, 84 pp.

[14] Sosnin O. V., Sosnin O. O., “O termoplastichnosti”, Probl. prochnosti, 1988, no. 12, 3–9

[15] Merkin D. R., Bauer S. M., Smirnov A. L., Smolnikov B. A., Teoriya ustoichivosti v primerakh i zadachakh, NITs “Regulyarnaya i khaoticheskaya dinamika”, In-t kompyuternykh issledovanii, M.–Izhevsk, 2007, 208 pp.

[16] Zhizherin S. V., Struzhanov V. V., Mironov V. I., “Iteratsionnye metody raschëta napryazhenii pri chistom izgibe balki iz povrezhdaemogo materiala”, Vychislitelnye tekhnologii, 6:5 (2001), 24–33 | Zbl