Predictions of bifurcation and instabilities during dynamic extension

Dynamic bifurcation and flow instabilities of cylindrical bars, made of an incompressible strain hardening plastic material, are investigated. A Lagrangian linear perturbation analysis is performed to obtain a fourth order partial differential equation which governs the evolution of the perturbation. The analysis shows that inertia slows down the growth of long wavelengths while bidimensional effects conjugated to strain hardening extinct short wavelengths. The present approach is applied successfully to the analysis of bifurcation and instabilities in (i) a rectangular block during plane strain extension, (ii) a circular bar during uniaxial extension. New results are obtained in the case of rate independent materials and a synthetical point of view is obtained for rate dependent behaviors.