The effect of torsion on the stability of an elastic cylinder under tension

The effect of torsion on instability in the form of the formation of a neck in a stretched rod in the shape of a circular cylinder is investigated. The stability is considered using the three-dimensional equations of neutral equilibrium of an isotropic incompressible solid. The subcritical state is described by the exact solution of the problem of the non-linear theory of elasticity regarding the equilibrium of a twisted and stretched cylinder. After separating the variables, the equations of neutral equilibrium are reduced to a system of ordinary differential equations, which are solved numerically. Numerical results are obtained for a Biderman material and a material with a power dependence of the specific energy on the deformation. A region of stability is constructed in the plane of the loading parameters, which are the longitudinal elongation and the angle of torsion. This region is compared with the region of convexity of the energy per unit length of the twisted and stretched cylinder.