Two simple triangular shell elements for springback simulation after deep drawing of thin sheets

This paper deals with the formulation of two simple shell elements for the springback simulation after the sheet forming process. The first element is the DKT12 shell element resulting from the superposition of the CST membrane element and the DKT6 plate element with three displacement dof at each corner node and one rotation dof around each side. The second element is called DKTRF element (Discrete Kirchhoff Triangular Rotation Free Element) with only 3 translational dof at the corner nodes of each element and its three neighbors. For that element the rotation: around each mid side is expressed in terms of the translational dof of the corner nodes of the elements sharing that side, in a slightly different manner compared to Brunet at al., Onate et al. Some improvements make the formulation more general and accurate. Special attention is paid to treat the boundary conditions using fictitious elements. A static implicit algorithm is adopted for the springback simulation based on a simple and efficient Updated Lagrangian Formulation at each Iteration (ULFI). Some academic examples and benchmark tests show the accuracy and the efficiency of these two shell elements for the springback simulation.