Cross-sectional warping in sheet metal forming simulations

For most sheet metal forming simulations, shell elements that consider a reduced stress state, in particular, assuming a zero transverse normal stress 𝜎33 and neglecting the shear stress components 𝜎13 and 𝜎23 in the yield function, are used. Moreover, certain kinematic assumptions, like cross-sectional material fibers being assumed to remain straight during deformation, are typically applied. However, for some applications, like bending with small radii and thick sheets, this approach is not a workable solution to obtain accurate and reliable results, since the prerequisites that justify the aforementioned kinematic assumptions are not met anymore. In this contribution, a 3d-shell element is presented that allows for cross-sectional warping. For the evaluation, numerical results of a metal stripe drawn through a draw bead are compared against experimental data. The results demonstrate that the 3d-shell element is able to represent warping of cross-sectional material fibers during deformation. In addition, further numerical tests conducted with this element are shown.