Summary
Generalized Ilyushin's deviatoric stress and strain spaces are introduced, which make it possible to apply directly the postulate of isotropy to initially isotropic materials with plastic properties influenced by the third deviatoric stress invariant and to a certain class of initially anisotropic materials. The generalizations proposed are connected with a new concept of description of plastic hardening, the main idea of which is also briefly presented.
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References
Ilyushin, A. A.: On the foundations of the general mathematical theory of plasticity. In: Voprosy Teorii Plastichnosti, pp. 3–29. Moskva: Izd. AN SSSR 1961. (In Russian).
Ilyushin, A. A.: Plasticity. Foundations of the general mathematical theory, p. 26. Moskva: Izd. AN SSSR 1963. (In Russian).
Lensky, V. S.: Experimental verification of the law of isotropy and of the principle of delay in the case of combined loading. Izv. AN SSSR OTN11, 15–24 (1958). (In Russian).
Lensky, V. S.: Analysis of plastic behavior of metals under complex loading. Plasticity. Proc., 2nd Symp. on Naval Struct. Mech., pp. 259–278. Brown University, 1960.
Życzkowski, M.: Combined loadings in the theory of plasticity, p. 185. Warszawa: Polish Scientific Publishers 1981.
Ohashi, Y., Tokuda, M., Yamashita, H.: Effect of third invariant of stress deviator on plastic deformation of mild steel. J. Mech. Phys. Solids23, 295–323 (1975).
Ohashi, Y., Kawashima, K., Mori, N.: On proportional combined loading tests of an aluminum alloy and its analytical formulation. Trans. ASME J. Eng. Mat. Techn.98, 282–288 (1976).
Ohashi, Y., Kawashima, K.: Plastic deformation of aluminum alloy under abruptly-changing loading or strain paths. J. Mech. Phys. Solids25, 409–421 (1977).
Novozhilov, V. V.: On a certain direction in the theory of plasticity (in Russian). Izv. AN SSSR Mekhanika i Mashinostroyenye3, 176–181 (1961).
Novozhilov, V. V.: Once more on the postulate of isotropy (in Russian). Izv. AN SSSR Mekhanika i Mashinostroyenye1, 205–208 (1962).
Baltov, A., Sawczuk, A.: A rule of anisotropic hardening. Acta Mechanica1, 81–92 (1965).
Shiratori, E., Ikegami, K., Yoshida, F.: The subsequent yield surfaces after proportional preloading of the Tresca-type material. Bull. Jap. Soc. Mech. Eng.19, 1122–1128 (1976).
von Mises, R.: Mechanik der plastischen Formänderungen von Kristallen. Z. Angew. Math. Mech.8, 161–185 (1928).
Sobotka, Z.: Anisotropy, deviation and the angle of deviation. Stavebnicky Časopis15, 359–364 (1967).
Sobotka, Z.: Theorie des plastischen Fließens von anisotropen Körpern. Z. Angew. Math. Mech.49, 25–32 (1969).
Tolokonnikov, L. A., Matchenko, N. M.: On representations of limiting conditions for initially anisotropic bodies. Problemy Prochnosti3, 54–56 (1974). (In Russian).
Hill, R.: Theory of yielding and plastic flow of anisotropic metals. Proc. Royal SocietyA 193, 281–297 (1948).
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Życzkowski, M., Kurtyka, T. Generalized Ilyushin's spaces for a more adequate description of plastic hardening. Acta Mechanica 52, 1–13 (1984). https://doi.org/10.1007/BF01175961
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DOI: https://doi.org/10.1007/BF01175961