Ml. Boubakar et al., NUMERICAL IMPLEMENTATION OF ORTHOTROPIC PLASTICITY FOR SHEET-METAL FORMING ANALYSIS, Journal of materials processing technology, 65(1-3), 1997, pp. 143-152
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.