Development of a one point quadrature shell element for nonlinear applications with contact and anisotropy

A general purpose shell element for nonlinear applications including sheet metal forming simulation is developed based on reduced integration with one point quadrature. The developed shell element has five degrees of freedom and four nodes. It covers flexible warping behavior without artificial warping correction. A physical stabilization scheme with the assumed natural strain method is employed to derive a strain field that can be decomposed into the sum of a constant and a linear term with respect to the natural coordinates. The rigid body projection is introduced to treat rigid body rotations effectively. The shell element incorporates elasto-plastic planar anisotropic material models based on the incremental deformation theory. Linear and nonlinear patch tests are performed and the results are compared with analytical or previously reported results. Simulations that include impact and deformable body contact are performed to show the robustness of the contact algorithm. Finally, to demonstrate the capability of handling anisotropic materials, the developed shell element is used for the circular cup drawing process simulation in order to predict the earing profile of Al 2008-T4 alloy sheet.