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IssuesArchive of Issues2011-4pp.544-553

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V.M. Greshnov, "Physical-Mathematical Theory of Irreversible Strains in Metals," Mech. Solids. 46 (4), 544-553 (2011)
Year 2011 Volume 46 Number 4 Pages 544-553
DOI 10.3103/S0025654411040054
Title Physical-Mathematical Theory of Irreversible Strains in Metals
Author(s) V.M. Greshnov (Ufa State Aviation Technical University, K.Marksa 12, Ufa, Bashkortostan, 450000 Russia, greshnov_vm@list.ru)
Abstract We give a systematic presentation of the physical-mathematical theory of irreversible strains in metallic materials. The fundamental postulates of the classical mathematical theory of plasticity are stated as corollaries of the fundamental statements of the physical-mathematical theory of plasticity.
Keywords strain mechanics, strain physics, loading history, synthetic approach, constitutive relations
References
1.  V. N. Kukudzhanov, "Coupled Models of Elastoplasticity and Damage and Their Integration," Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 6, 103-135 (2006) [Mech. Solids (Engl. Transl.) 41 (6), 83-109 (2006)].
2.  Yu. V. Grinyaev and V. E. Panin, "The Field Theory of Defects on the Mesolevel," Dokl. Ross. Akad. Nauk 353 (1), 37-39 (1997) [Dokl. Phys. (Engl. Transl.) 42 (3), 108-110 (1997)]
3.  V. M. Greshnov, "A Model of a Viscoplastic Body Taking into Account the Loading History," "A Model of Viscoplastic Body with the Loading History Taken into Account," Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 2, 117-125 (2005) [Mech. Solids (Engl. Transl.) 40 (2), 97-103 (2005)].
4.  A. Yu. Ishlinskii and D. D. Ivlev, Mathematical Theory of Plasticity (Fizmatlit, Moscow, 2001) [in Russian].
5.  Yu. N. Rabotnov, Creep of Construction Elements (Nauka, Moscow, 1996) [in Russian].
6.  V. M. Segal, "Development of Metal Treatment by Intensive Shear Strain," Metally, No. 1, 5-14 (2004).
7.  Farid H. Abed, "Physically Based Multiscale-Viscoplastic Model for Metals and Alloys: Theory and Computation," http://etd.lsu.edu/docs/available/etd-07062005-094112/.
8.  J. Lin and T. A. Dean, "Modelling of Microstructure Evolution in Hot Forming Using Unified Constitutive Equations," J. Mat. Proc. Tech. 167 (2-3), 354-362 (2005).
9.  B. Berisha, P. Hora, and A. Wahlen, "A Dislocation Based Material Model for Warm Forming Simulation," Int. J. Mater. Form. 1 (3), 135-141 (2008).
10.  V. M. Greshnov, "On Perspectives of the Use of Physical Theory of Plastic Strain in Computational Method of Plasticity Theory," in Collection of Abstracts of Intern. Sci.-Techn. Conference "Plasticity Problems in Technology" (OrelGTU, Orel, 1995), p. 13 [in Russian].
11.  V. M. Greshnov, I. V. Potyaeva, and V. E. Sidorov, "Physico-Mathematical Theory of Metal Plasticity and Creeping," Vest. UGATU 9 (6), 143-152 (2007).
12.  V. M. Greshnov, F. F. Safin, and M. V. Greshnov, "Physico-Phenomenological Model of Metal Resistance to Plastic Deformation for the Calculation of the Processes of Metal Plastic Working. Part 1. Statement of the Problem and Derivation of the General Equation," Probl. Prochn., No. 6, 107-115 (2002) [Strength of Materials (Engl. Transl.) 4 (6), 606-611 (2002)].
13.  V. M. Greshnov, F. F. Safin, and M. V. Greshnov, "Physico-Phenomenological Model of Metal Resistance to Plastic Deformation for the Calculation of the Processes of Metal Plastic Working. Part 2. Particular Cases of the Model and Its Experimental Validation," Probl. Prochn., No. 1, 87-97 (2003) [Strength of Materials (Engl. Transl.) 4 (1), 60-67 (2003)].
14.  V. M. Greshnov, "One Plasticity Model for Problems of Plastic Metal Working," Zh. Prikl. Mekh. Tekhn. Fiz. 49 (6), 159-169 (2008) [J. Appl. Mech. Tech. Phys. (Engl. Transl.) 49 (6), 1021-1029 (2008)].
15.  M. A. Stremel, Strength of Alloys. Part 2. Deformation (MISIS, Moscow, 1997) [in Russian].
16.  R. Becker, "Über die Plastizität amorpher und kristalliner fester Körper," Phys. Zeitschr. 26, 919-925 (1925).
17.  P. I. Polukhin, G. Ya. Gun, and A. M. Galkin, Resistance of Metals and Alloys to Plastic Deformation: Handbook (Metallurgiya, Moscow, 1983) [in Russian].
Received 26 June 2009
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