Abstract: Because of the shortcoming of plastic deformation theory of the traditional inverse finite element method of sheet metal forming：No consideration of the effect of deformation history, a novel multi-step inverse finite element method based on the principle of virtue work is proposed. Elasto-plastic material model is adopted to improve calculation accuracy. DKT12 shell element is introduced to consider the effect of deformation history such as bending-unbending around die entrance. In order to improve the stress calculation, a novel constitutive equation based on plastic flow theory is proposed, which can well reflect the actual forming condition such as elastic/plastic deformation or loading/unloading condition. The notion of the equivalent stress is adopted for stress and strain updating, which in turn can avoid numerous iterations to ensure the numerical stability and maintain the calculation efficiency at the same time. Above mentioned improvements are implemented in our in-house inverse analysis software InverStamp/Multi-step module. The presented algorithms are applied to S-rail deep drawing example. The numerical results compared with explicit dynamic solver LS-DYNA confirm its validity in prediction of the thickness distribution of formed part.

Key words: Constitutive equations, Inverse finite element method, Multi-step forming, Sheet metal forming