Comparison of bifurcation analysis and maximum force criteria in the prediction of necking in stretched metal sheets

In the present work, diffuse necking is investigated for stretched metal sheets using two different approaches, namely bifurcation theory and maximum force principle. The contribution includes a critical analysis and a systematic comparison of their respective ability to predict necking. In particular it is shown that, in contrast to bifurcation theory, which is of quite general applicability, some restrictions are associated with the application of maximum force conditions. It is noteworthy that the well-known Swift diffuse necking criterion is recovered through bifurcation analysis. Recall that Swift's criterion has long been attributed in the literature to the maximum force principle, while it is shown here to rather originate from the bifurcation analysis, which provides it with a sound theoretical justification.