Sheet metal forming analysis of planar anisotropic materials by a modified membrane finite element method with bending effect

Abstract

Abstract A modified membrane finite element with proper formulation is introduced to correctly enhance the flexural rigidity not only within an element but amongst elements. A finite element formulation is derived for the incremental analysis for non-steady large deformation in sheet metal forming. The formulation employs the convective coordinates to keep the objectivity in large deformation and rotation, and considers the planar anisotropy with Hill's quadratic yield criterion. The formulation is then combined with an effective contact algorithm to deal with the contact between the material and the dies. The simulation examples demonstrate the validity and versatility of the computer code, showing the earing phenomenon in cylindrical cup deep drawing processes and the variation in deformation with different orientations of the initial blank in rectangular cup drawing. The present simulation allows the thickness variation in the flange region to redistribute the blank-holding force during deformation, which can predict a more precise contour line in the flange region and a more precise deformed shape with strain distribution than the prediction made by conventional simulation.