Sheet metal forming analysis of planar anisotropic materials with a proper numerical scheme for the blank holding force

Abstract

A modified membrane finite element with a proper formulation for planar anisotropic materials is introduced to correctly enhance the flexural rigidity not only within an element but among elements. 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 deal with the contact between the material and the dies. Distribution of the blank holding force is calculated 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 computer code by showing the earing phenomenon in circular cup drawing and the variation of the blank holding force in rectangular cup drawing. The results shows that the thickness variation in the flange region redistributes the blank holding force during the deformation. The present algorithm can predict more precise contour lines in the flange region and a more precise shape and strain distribution.