Mechanics of Solids (about journal) Mechanics of Solids
A Journal of Russian Academy of Sciences
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IssuesArchive of Issues2020-2pp.273-276

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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,
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 2018Revised 30 August 2019Accepted 08 October 2019
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