An equilibrium approach is suggested as an effective tool for analysis of sheet metal forming processes on the basis of force balance together with geometric relations and plasticity theory.
In computing a force balance equation, it is required to define a geometric curve approximating the shape of the sheet metal at any step of deformation from the geometric interaction between the die and the deforming sheet. Then the necessary informations for contacting and non-contacting sections of the sheet metal are known and utilized for optimization of deformation by force balance equation. In computation, the sheet material is assumed to be of normal anisotropy and rigid-plastic workhardening.
For the sake of comparision the rigid-plastic finite element method is employed which adopts continuous contact treatment and bending energy augmented membrane(BEAM in abbreviation) element. It has been shown that there are good agreements between the equilibrium approach and FEM computation for the benchmark test example and auto-body panels in which plane-strain can be assumed in sections. The proposed equilibrium approach can thus be used as a robust computational method in estimating the forming defects and forming severity rather quickly in the die design stage.
