Adiabatic heating of material in elastoplastic torsion with finite deformations

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.