Dynamic necking of an elastic-plastic cylinder under uniaxial stretching (Q761088)

The axisymmetric necking process of an elastic-plastic cylinder under uniaxial stretching is analyzed by treating the problem as an initial- value-eigenvalue problem. One end of the cylinder is subjected to a prescribed constant axial velocity relative to the other end and both ends are shear free. The eigenmodes of deviated motion departing from a uniform stretch beyond that of quasi-static bifurcation by \textit{J. W. Hutchinson} and \textit{J. P. Miles} [J. Mech. Phys. Solids 22, 61-71 (1974; Zbl 0271.73042)] are determined. Of all uniformly excited eigenmodes of motion, only certain modes will grow. The rate of necking depends on the geometry, material properties and stretching velocity of the cylinder.