Finite elastic torsional instability of incompressible thermo-hyperelastic cylinder

Torsional instability of an incompressible thermo-hyperelastic cylindrical rod, subjected to axial stretching and large torsions, is examined within the framework of finite elasticity. When the cylinder is stretched and twisted by a sufficiently large degree, a knot may form suddenly at one point. This inherent elastic instability is analyzed with the minimum potential energy principle and the critical values of torsion are obtained. The distribution of stresses as well as the tensile force and the torque are studied. Effect of temperature change is specifically discussed. The project supported by the National Natural Science Foundation of China (10402018, 10272069) and Shanghai Key Project Program (Y0103) The English text was polished by Keren Wang.