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Power law type Poynting effect and non-homogeneous radial deformation in the boundary-value problem of torsion of a nonlinear elastic cylinder

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Abstract

The boundary value problem of torsion of a solid cylinder is analyzed for a class of hyperelastic materials that exhibit the power law type dependence of the strain energy density on the magnitude of the deformation gradient. The Saint Venant hypotheses are generalized by including the non-homogeneous longitudinal and radial deformations. A nonlinear variational problem with respect to the function of the radial/surface deformation, the function of the longitudinal deformation, the normalized torque and the normalized axial force is formulated. The asymptotic analytical solutions are obtained for the hard device torsion and for large angles of twist. They illustrate the power law type dependencies of the axial force and the reaction torque on the angle of twist with the exponents p and p−1, respectively. For Treloar (neo-Hookean) materials with p = 2, the classical results can be obtained. The finite element analysis of the hard device torsion is performed by MATLAB. The results indicate that for a homogeneous class of materials and large angles of twist non-homogeneous radial/surface deformation can be observed.

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Authors and Affiliations

  1. National Mineral Resources University (University of Mines), Bldg. 2, Line 21, V.O., Saint Petersburg, 199106, Russian Federation

    Igor A. Brigadnov

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  1. Igor A. Brigadnov
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Correspondence to Igor A. Brigadnov.

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Brigadnov, I.A. Power law type Poynting effect and non-homogeneous radial deformation in the boundary-value problem of torsion of a nonlinear elastic cylinder. Acta Mech 226, 1309–1317 (2015). https://doi.org/10.1007/s00707-014-1243-9

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  • DOI: https://doi.org/10.1007/s00707-014-1243-9

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