Closed-form solution for bulging through elliptical dies

An analytical model is proposed for the elliptical bulging of sheet metals. The model uses the deformation theory and the classical Hill yield criterion. Some assumptions are made on the geometry of the part, in order to derive a closed-form solution. It can be applied to both strain-hardening and superplastic materials for the analysis of the bulging tests through circular and elliptical dies. The results shown are in good agreement with the experiments and the finite element predictions. It is a fast analytical tool to estimate the forming pressure and the formability of the material using this specific mechanical test.