NUMERICAL IMPLEMENTATION OF ORTHOTROPIC PLASTICITY FOR SHEET-METAL FORMING ANALYSIS

Due to rolling and crystallographic texture development, thin sheet-me tal for stamping exhibits an initial orthotropic plastic behaviour. Th e objective of the present work is to define a stress-computation algo rithm taking into account this anisotropic plastic behaviour and the u pdate of the orthotropic frame directions within a finite-element simu lation of sheet-metal forming. Following Mandel's approach, a macrosco pic behaviour model is considered which is based on the use of a rotat ional objective derivative defined from the initial micro-structure ro tation governing the orthotropic direction update. The expression of t he constitutive law in a frame rotated by this rotation permits a nume rical scheme including an elastic prediction and a plastic correction for the stress calculation. The elastic prediction ensures the increme ntal objectivity and a second-order level of accuracy. The correction stage is based on an implicit Euler-backward scheme and leads to the s olution of a non-linear equation using a local Newton method. In the p roposed simulation approach, C-0 shell finite elements are used to mod el the blank. The proposed stress-calculation algorithm takes into acc ount the mixed interpolation used in the element formulation in order to avoid shear locking. A set of numerical results is presented in cas es of the simulation of deep-drawing processes. The accuracy of the so lutions, and especially the good agreement with experimental results, shows the efficiency of the proposed approach. (C) 1997 Elsevier Scien ce S.A.