Sheet Metal Forming Analysis with Planar Anisotropic Materials using a Modified Membrane Element considering Bending Effect

Abstract

To take the bending effect into account with a membrane element without loss of its computing efficiency, a modified membrane element was introduced which divide the strain into stretching and bending terms and calculate the curvature between the neighboring elements with linear approximation. In the past research, this element showed eminent performance in the normal anisotropic analyses of deep drawing processes. By virtue of stiffness term due to bending, the modified membrane element becomes stiffer than the ordinary membrane element and we can get larger punch force which is more compatible to the real phenomenon. Due to the characteristics of rolling process, sheet metal has anisotropy with respect to the direction in the plane. The normal anisotropic analysis cannot explain the earing phenomenon in the cylindrical deep drawing process. In this study, the modified membrane element was improved to consider planar anisotropic characteristics with the aid of Hill's quadratic criterion. To keep the objectivity in the large deformation and rotation, the convective coordinate was employed. Moreover, to apply the blank holding force onto the proper region during the analysis, the scheme for the application of the blank holding force was improved to consider the effect of material thickness variation in the region of blank holder and the more precise outline of sheet metal during the deformation was obtained.