Abstract:
In this paper, we study the torsion of an incompressible circular cylinder with fixed ends made of polymer material relative to the axis of symmetry taking into account adiabatic heating. The conservative deformation mechanism is determined by the elastic Mooney–Rivlin potential, and the dissipative deformation mechanism by the Tresca–Saint-Venant plastic potential. The problem is solved using multiplicative division of the total Almansi strain measure into elastic and plastic components. It is assumed that the local change in material temperature is due only to plastic dissipation. The thermal deformation of the material and hardening are neglected. The exact solution of the problem is obtained for an arbitrary dependence of the mechanical characteristics of the material on temperature. In particular, the axial force, the torque, and the temperature distribution in the sample as a function of increasing loading parameter are determined. The obtained solution is compared with the available experimental data.
Keywords:
torsion of cylindrical rods, finite deformations, elastoplastic problem, related thermoplasticity, temperature softening, adiabatic conditions, Mooney-Rivlin incompressible material, Tresca condition, Poynting effect.
Citation:
G. M. Sevastyanov, A. A. Burenin, “Adiabatic heating of material in elastoplastic torsion with finite deformations”, Prikl. Mekh. Tekh. Fiz., 60:6 (2019), 149–161; J. Appl. Mech. Tech. Phys., 60:6 (2019), 1104–1114
\Bibitem{SevBur19}
\by G.~M.~Sevastyanov, A.~A.~Burenin
\paper Adiabatic heating of material in elastoplastic torsion with finite deformations
\jour Prikl. Mekh. Tekh. Fiz.
\yr 2019
\vol 60
\issue 6
\pages 149--161
\mathnet{http://mi.mathnet.ru/pmtf382}
\crossref{https://doi.org/10.15372/PMTF20190616}
\elib{https://elibrary.ru/item.asp?id=41444473}
\transl
\jour J. Appl. Mech. Tech. Phys.
\yr 2019
\vol 60
\issue 6
\pages 1104--1114
\crossref{https://doi.org/10.1134/S0021894419060166}
Linking options:
https://www.mathnet.ru/eng/pmtf382
https://www.mathnet.ru/eng/pmtf/v60/i6/p149
This publication is cited in the following 8 articles:
G. N. Kuvyrkin, D. R. Rakhimov, “Computational algorithm for analyzing the governing relations of the endochronic theory of thermoplasticity for isotropic materials”, J. Appl. Mech. Tech. Phys., 65:3 (2024), 496–501
G. M. Sevastyanov, A. S. Begun, A. A. Burenin, “Finite-Strain Elastic-Plastic Circular Shear in Materials with Isotropic Hardening”, Prikladnaâ matematika i mehanika, 88:2 (2024), 313
A. A. Burenin, A. V. Tkacheva, “Gadolin problem of assembling a prestressed two-layer pipe”, J. Appl. Mech. Tech. Phys., 64:5 (2024), 929–942
Gelacio Juárez-Luna, A. Gustavo Ayala, Ángel Uriel Martínez-Miranda, “Closed form solutions for the strain localization problem in a softening circular bar in pure torsion with the continuum damage and the embedded discontinuity models”, Mechanics of Materials, 169 (2022), 104303
G. M. Sevast'yanov, “PLASTIC TORSION AT HIGH PRESSURE WITH NON-UNIFORM STRESS STATE”, Mech. Solids, 56:3 (2021), 368
Georgiy M. Sevastyanov, “Adiabatic heating effect in elastic-plastic contraction / expansion of spherical cavity in isotropic incompressible material”, European Journal of Mechanics - A/Solids, 87 (2021), 104223
Georgiy M. Sevastyanov, “Analytical solution for high-pressure torsion in the framework of geometrically nonlinear non-associative plasticity”, International Journal of Solids and Structures, 206 (2020), 383
B. D. Annin, E. V. Karpov, A. Yu. Larichkin, “Influence of Anisotropy on the Deformation of a Polymer Composite with Shape Memory”, Mech. Solids, 55:6 (2020), 761
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