 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
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| In English (Mech. Solids): | | 4810 |
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| G.M. Sevastyanov, "Torsion with Circular Shear of a Mooney-Rivlin Solid," Mech. Solids. 55 (2), 273-276 (2020) |
| Year |
2020 |
Volume |
55 |
Number |
2 |
Pages |
273-276 |
| DOI |
10.3103/S0025654420020156 |
| Title |
Torsion with Circular Shear of a Mooney-Rivlin Solid |
| Author(s) |
G.M. Sevastyanov (Institute of Machinery and Metallurgy, Far East Branch, Russian Academy of Sciences, Komsomolsk-on-Amur, 681005 Russia, akela.86@mail.ru) |
| Abstract |
The axisymmetric torsion of a layer of incompressible Mooney-Rivlin material placed between two rigid coaxial cylindrical surfaces is considered. It is assumed that the ends of the cylinder are fixed to avoid axial displacement and the cross-sections orthogonal to the axis of symmetry do not distort during deformation. In this case, the material points move along arcs of circles with an angular velocity which in the general case may depend on both the axial and the radial coordinates. Closed-form solution of the equilibrium equation is obtained. The well-known Rivlin solution is a particular case of this solution. Like in the classical solution, the stress tensor is a function of only the radial coordinate and the twist angle of the material points is a linear function of the axial coordinate. It is shown that torsion that is symmetric about a plane orthogonal to the axis of rotation can be realized only within the framework of the Rivlin solution. The obtained exact solution can be realized in the presence of friction on cylindrical surfaces. The initial-boundary-value problem described by this solution is considered. |
| Keywords |
torsion, shear, Mooney-Rivlin solid, nonlinear elasticity, exact solution, hollow cylinder |
| Received |
30 May 2018 | Revised |
30 August 2019 | Accepted |
08 October 2019 |
| Link to Fulltext |
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