Necking of an anisotropic plastic material

The two conditions for stable necking, treated as a bifurcation of stress path, are derived. The anisotropic material considered is one for which the plastic work increment = $\overline{\sigma }d\overline{e}$, where both the generalized yield stress $\overline{\sigma }$ and generalized plastic strain increment $d\overline{e}$ are invariant functions. The method is applied to the necking of a thin cylinder under internal pressure.