Abstract: Method for predicting post-buckling deformation of a sheet of metal during a draw forming process, for use with a computer including memory, by introducing a set of springs to stabilize the sheet metal close to the onset of buckling, thereby enhancing convergence of numerical solutions. The method is for use with sheet metal forming tools including a draw die, a punch and binder having surfaces designed to form the sheet metal into a part, the sheet metal being represented as a mesh including a plurality of nodes. The method includes applying a displacement increment to the sheet metal nodes and identifying a singularity in a tangent stiffness matrix associated with the sheet metal close to the onset of buckling. The method also includes introducing a plurality of springs at the sheet metal nodes so as to eliminate the singularity and enhance convergence of the numerical solution of the displacement increment.

Abstract: Method and system for evaluating sheet metal forming tooling design, for use with a draw die including a punch and binder designed to form the sheet metal into a part, utilizing improved implicit time integration methods that reduce numerical instability, thereby enhancing convergence of numerical solutions. The sheet metal and tool surface of the punch are each represented as a mesh having a plurality of nodes. Contact nodes between the sheet metal mesh nodes and the tool surface mesh can be identified. A first embodiment includes minimizing discontinuities generated by unloading by determining a stress increment of a sampling point in the sheet metal mesh according to an incremental deformation theory of plasticity. A second embodiment includes modelling a draw-bead as a plurality of nonlinear elastic springs to minimize discontinuities in the spring force during unloading.