Prediction of sheet necking with shell finite element models

In sheet forming simulations, the prediction of localised necking is an important goal. A pragmatic approach is to compare calculated principal strains with a forming limit curve (FLC). However, the FLC’s are known to depend on the strain path and most experimental FLC’s are determined for straight deformation paths. Localisation can also be determined numerically with a Marciniak–Kuczynski analysis (M–K). It is recognised that a FEM analysis with shell elements resembles the M–K analysis very much. For uniform deformations a band with slightly reduced thickness is necessary to trigger localisation. In practical forming conditions, however, the non-uniformity of the process automatically triggers localisation and an arbitrary initial imperfection is not needed. FEM models have the additional benefit that boundary conditions, non-proportional deformation and e.g. friction with the tools are completely included.