Asymptotic stability analysis for sheet metal forming - Part I: Theory

In his paper is presented a general methodology for predicting puckering in stabilities in sheet metal forming applications. A novel approach is introd uced which does not use shell theory approximations. The starting point is Hill's stability functional for a three-dimensional rate independent stress ed solid which is modified for contact. By using a multiple scale asymptoti c technique with respect to the small dimensionless thickness parameter eps ilon, one can derive the two-dimensional version of the stability functiona l which is accurate up to O(epsilon (4)), thus taking into account bending effects. Loss of positive definiteness of this functional indicates possibi lity of a puckering instability in a sheet metal forming problem with a kno wn stress and deformation state. An advantage of the proposed method is tha t the puckering investigation is' independent of the algorithm used for cal culating the deformed state of the sheet. [S0021-8936(00)00804-7].