zbMATH — the first resource for mathematics

Theory of plasticity and creep taking account of microstrains. (English. Russian original) Zbl 0626.73023
J. Appl. Math. Mech. 50, 690-696 (1986); translation from Prikl. Mat. Mekh. 50, 890-897 (1986).
A relationship between the theories of plasticity and creep of the type shown e.g. (*) by the first two authors, ibid. 32, 908-922 (1968; Zbl 0182.590) and theories based on the concept of slip is set up. A most logical structure is proposed for the constitutive equations of the theory which is convenient for engineering calculations. It has been shown that the theory of slip results from the theories (*). However, it remains unclear whether a deeper connection exists between these theories. Moreover, the connection between creep theories constructed using the approach (*) and creep theories based on the slip concept was not generally examined. A survey of the development of polycrystalline strain theory yields a complete representation of the state of matters in plasticity and creep theories.
74C99 Plastic materials, materials of stress-rate and internal-variable type
74A60 Micromechanical theories
74M25 Micromechanics of solids
Full Text: DOI
[1] Kadashevich, Yu.I.; Novozhilov, V.V., On taking microstresses into account in plasticity theory, Inzh., mekhan. tverd. tela, 3, (1968) · Zbl 0182.59004
[2] Kadashevich, Yu.I.; Novozhilov, V.V., On the influence of initial microstresses on the macroscopic strain of polycrystals, Pmm, 32, 5, (1968) · Zbl 0182.59004
[3] Kadashevich, Yu.I.; Novozhilov, V.V., On the limiting versions of a plasticity theory taking account of initial microstresses, Izv. akad. nauk SSSR, mekhan. tverd. tela, 3, (1980) · Zbl 0487.73040
[4] Batdorf, S.B.; Budiansky, B., A mathematical theory of plasticity based on the concept of slip, Naca tn 1871, (1949)
[5] Novozhilov, V.V., Means of developing a theory of polycrystal strain, non-linear models and problems of the mechanics of a deformable solid, (1984), Nauka Moscow
[6] Kadashevich, Yu.I.; Novozhilov, V.V., Theory of creep of microinhomogeneous media, () · Zbl 0389.73035
[7] Kadashevich, Yu.I; Novozhilov, V.V., Theories of plasticity and creep of metals taking account of microstresses, () · Zbl 0087.18602
[8] Leonov, M.Ya., Fundamental postulates of plasticity theory, Dokl. akad. nauk SSSR, 199, 1, (1971) · Zbl 0236.73054
[9] Rusinko, K.N., Theory of plasticity and unsteady creep, (1981), Vishcha Shkola L’vov
[10] Malmeister, A.K., Principles of strain localization theories, Mekhan. polimerov, 4, (1965)
[11] Knets, I.V., Fundamental modern directions in the mathematical theory of plasticity, (1971), Zinatne Riga · Zbl 0229.73032
[12] Mokhel’, A.N.; Salganik, R.L.; Khristianovich, S.A., On the plastic strain of hardening metals and alloys: constitutive equations and computations with them, () · Zbl 0722.73031
[13] Shvaiko, N.Yu., On a theory of plasticity based on the concept of slip, Prik. mekhan., 12, 11, (1976) · Zbl 0434.73036
[14] Leonov, M.Ya.; Shvaiko, N.Yu., Complex plane strain, Dokl. akad. nauk SSSR, 159, 5, (1964)
[15] Rusinko, K.N.; Besaraba, D.M., Creep under thermal cyclic action, Phys. khim mekhan. materialov, 4, (1984)
[16] Likhachev, V.A.; Malinin, V.G., Physicomechanical model of the elastic plastic properties of materials taking account of the structural strain levels and the kinetic properties of real crystals, Izv. VUZ, fizika, 9, (1984)
[17] Pan, J.; Fice, J.R., Rate sensitivity of plastic flow and implications for yield-surface vertices, Intern. J. solids struct., 19, 11, (1983)
[18] Kadashevich, Yu.I.; Kleev, V.S., On the question of a generalized mazing principle, Problemy prochnosti, 5, (1985)
[19] Kadashevich, Yu.I.; Kleev, V.S., Equations of state of unstable materials. questions of ship construction, ()
[20] Novozhilov, V.V.; Zadashevich, Yu.I.; Chernyakov, Yu.A., Theory of plasticity taking account of microstrains, Dokl. akad nauk SSSR, 284, 4, (1985) · Zbl 0637.73035
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.