Mechanics of Solids (about journal) Mechanics of Solids
A Journal of Russian Academy of Sciences
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936

Russian Russian English English About Journal | Issues | Guidelines | Editorial Board | Contact Us

IPMech RASWeb hosting is provided
by the Ishlinsky Institute for
Problems in Mechanics
of the Russian
Academy of Sciences
IssuesArchive of Issues2018-4pp.381-384

Archive of Issues

Total articles in the database: 9179
In Russian (. . ): 6485
In English (Mech. Solids): 2694

<< Previous article | Volume 53, Issue 4 / 2018 | Next article >>
D.V. Georgievskii, "An Order of Smallness of the Poynting Effect from the Standpoint of the Tensor Nonlinear Functions Apparatus," Mech. Solids. 53 (4), 381-384 (2018)
Year 2018 Volume 53 Number 4 Pages 381-384
DOI 10.3103/S0025654418040039
Title An Order of Smallness of the Poynting Effect from the Standpoint of the Tensor Nonlinear Functions Apparatus
Author(s) D.V. Georgievskii (Lomonosov Moscow State University, Leninskie Gory 1, Moscow, 119992 Russia; Institute for Problems in Mechanics RAS, pr. Vernadskogo 101, str. 1, Moscow, 119526 Russia,
Abstract A class of constitutive relations is considered that connect symmetric stress and small strain tensors in three-dimensional space using an isotropic potential tensor nonlinear function of a rather general form. Various definitions of tensor nonlinearity are given and their equivalence is shown. From the standpoint of the mathematical apparatus of the theory of tensor nonlinear functions, the interpretation of the Poynting effect known in experimental mechanics and similar phenomena has been carried out. It is proved that these effects are not necessarily the result of the tensor nonlinearity of the defining relations, but may be due to the dependence on one of the material functions on the quadratic invariant, which is absent, for example, in the physically linear case. From here conclusions are drawn about the order of smallness of these effects. The possibility of modeling the Poynting effect by tensor-linear defining relations is discussed.
Keywords tensor nonlinearity, scalar nonlinearity, stress, deformation, defining relation, material function, invariant, Poynting effect
1.  R.S. Rivlin, "Elasticity Theory in the Second Order," J. Rat. Mech. Anal. 2 (9), 53-81 (1953).
2.  R.S. Rivlin and J.L. Ericksen, "Stress Deformation Relations for Isotropic Materials," J. Rat. Mech. Anal. 4 (2), 323-425 (1955).
3.  V.K. Devendiran, R.K. Sandeep, K. Kannan, and K.R. Rajagopal, "A Thermo-Dynamically Consistent Constitutive Equation for Describing the Response Exhibited by Several Alloys and the Study of a Meaningful Physical Problem," Int. J. Sol. Struct. 108 (1), 1-10 (2017).
4.  V. Kulvait, J. Málek, and K.R. Rajagopal, "Modeling Gum Metal and Other Newly Developed Titanium Alloys Within a New Class of Constitutive Relations for Elastic Bodies," Arch. Mech. 69 (3), 223-241 (2017).
5.  D.V. Georgievskii, Selected Problems of Continuum Mechanics (LENAND, Moscow 2018) [in Russian].
6.  D.V. Georgievskii, "Potentiality of Isotropic Nonlinear Tensor Functions Connecting Two Deviators," Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 5, 148-152 (2016) [Mech. Sol. 51 (5), 619-622 (2016)].
7.  B.E. Pobedrya, Lectures on Tensor Analysis (MGU, Moscow, 1986) [in Russian].
8.  D.V. Georgievskii, "Angle Between Deviators of Stress and Strain Rates in a Tensor-Nonlinear Isotropic Medium," Vest. Mos. Univ. Ser. 1. Mat. Mekh. No. 6, 63-66 (2013) [Moscow Univ. Math. Bull. 72 (2), 63-66 (2013)].
9.  A.E. Green, "A Note on the Second-Order Effects of Incompressible Cylinders," Proc. Camb. Philos. Soc. 50 (3), 488-490 (1954).
10.  A.I. Lurie, Nonlinear Theory of Elasticity (Nauka, Moscow, 1980) [in Russian].
11.  M. Chen and Z. Chen, "Secondary Order of an Elastic Circular Shaft During Torsion," Appl. Math. Mech. 12 (9), 769-776 (1991).
12.  R.C. Batra, F. dell'Isola, and G.C. Ruta, "Generalized Poynting Effects in Prismatic Bars," J. Elast. 50 (2), 181-196 (1998).
13.  V.F. Astapov, A.A. Markin, and M.Yu. Sokolova, "Torsion of a Solid Cylinder of an Isotropic Elastic Material," Izv. Tula State Univ. Ser. Mat. Mech. Comp. Sci. 5 (2), 43-48 (1999).
14.  A. Akinola, "An Energy Function for the Reverse Isotropic Elastic Material and the Pointing Effect," Korean J. Comp. Appl. Math. 6 (3), 639-649 (1999).
15.  T.V. Gavrilyachenko and M.I. Karyakin, "Specific Features of the Nonlinearly Elastic Behavior of Cylindrical Compressible Bodies in Torsion," Zh. Prikl. Mekh. Tekhn. Fiz. 41 (2), 188-193 (2000) [J. App. Mech. Tech. Phys. 41 (2), 377-381 (2000)].
16.  R.V. Goldstein, V.A. Gorodtsov, and D.S. Lisovenko, "Torsion of Cylindrical Anisotropic Nano/Microtubes from 7-Constant Tetragonal Crystals. Poynting Effect," Fiz. Mesomech. 18 (6), 5-11 (2015).
Received 27 March 2018
Link to Fulltext
<< Previous article | Volume 53, Issue 4 / 2018 | Next article >>
Orphus SystemIf you find a misprint on a webpage, please help us correct it promptly - just highlight and press Ctrl+Enter

101 Vernadsky Avenue, Bldg 1, Room 246, 119526 Moscow, Russia (+7 495) 434-3538
Founders: Russian Academy of Sciences, Branch of Power Industry, Machine Building, Mechanics and Control Processes of RAS, Ishlinsky Institute for Problems in Mechanics RAS
© Mechanics of Solids
Rambler's Top100