Validation of a modified material model for use with shell elements to improve the predictive accuracy of the thickness distribution in superplastic forming of sheet metals

The automotive industry has recently begun using the superplastic forming (SPF) process to fabricate complex aluminum and magnesium alloy panels that cannot be formed at room temperature due to insufficient formability. One of the manufacturing problems encountered during SPF is excessive thinning in the form of a localized neck; which can lead to fracture. Localized necking can be predicted with the use of continuum elements in finite element analysis (FEA); however, the use of these elements in simulating SPF of large automotive panels is computationally intensive and often computationally prohibitive due to convergence issues. This paper examines the use of a modified material model (developed by engineers at Livermore Software Technology Corporation (LSTC) that can be used with conventional Belytschko–Tsay shell elements. This model considers normal stresses during SPF, which is needed to predict necking locations. The paper reports the results on investigating means for improving computational efficiency with this new formulation (i.e. element size, mass scaling, and adaptive meshing) and compares the performance of the normal stress element formulation with that of Belytschko–Tsay shell element in simulating the SPF process. The findings indicate that the newly developed formulation can be used for predicting localized thinning under SPF conditions.