Three-dimensional numerical simulation of the deep-drawing process using solid finite elements

The main goal of this work is to present a three-dimensional mechanical model for the numerical simulation of the deep-drawing process. The model takes into account the large elastoplastic strains and rotations that occur in the deep-drawing process. Hill’s orthotropic yield criteria with isotropic and kinematics hardening describes the anisotropic plastic properties of the sheet. Coulomb’s classical law models the frictional contact problem treated with an augmented Lagrangian approach. This method yields a mixed system where the final unknowns of the problem are static (frictional contact forces) and kinematic (displacements) variables. To solve this problem use is made of a fully implicit algorithm of Newton–Raphson type. Three-dimensional isoparametric finite elements with a selective reduced integration are used for the spatial discretization of the deformed body. The geometry of the forming tools is modelled by Bézier surfaces. The numerical results of the deep-drawing of a square cup are presented to focus their good agreement with the results of experiment.