Modified membrane finite element formulation for sheet metal forming analysis of planar anisotropic materials

A finite element formulation is derived for sheet metal forming analysis of planar anisotropic materials. The formulation incorporates membrane elements whereas it takes the bending effect into account explicitly. The strain energy term in the formulation is decomposed into the membrane energy term for mean stretching and the bending energy term for pure bending. This procedure needs careful evaluation for the orientation of the anisotropic axes. The formulation is then combined with an effective algorithm to calculate distribution of the blank holding force in each step according to the thickness in the flange region. The calculation employs a special relation between the thickness and the blank holding force. The simulation examples demonstrate the validity and versatility of the developed computer code by showing that the thickness variation in the flange region redistributes the blank holding force during the deformation. The present algorithm can predict accurate deformed shapes and thickness strain distribution with the anisotropy of materials and the variable blank holding force.