An analysis of sheet necking under combined stretching and bending

The stretchability of sheet metal may be considerably influenced by the prior or simultaneous application of curvature. We explore this effect using finite element simulations as well as analytical modelling. The latter allows us to derive a generalised Considere criterion which predicts the onset of necking under combined stretching and bending quite accurately, as evidenced by a comparison with the finite element simulation results. The criterion predicts that, whereas prior bending reduces the sheets stretchability, a simultaneous bending component may enhance it.