Degenerated shell element analysis of circular rail drawing of sheet metal

Abstract

The prediction of formability in sheet metal forming by numerical simulation allows the manufacturer to reduce the costs of designing tools and to shorten the time‐to‐market cycle. This research aims to create an elastoplastic incremental finite element computer code to simulate a circular rail drawing process of sheet metals. A methodology of formulating an elastoplastic three‐dimensional finite element model, based on the Prandtl–Reuss flow rule and von Mises yield criterion respectively and associated with an updated Lagrangian formulation, is developed to simulate the sheet metal forming process. The shape function derived from a four‐node quadrilateral degenerated shell element is associated into the stiffness matrix to constitute the finite element model. An extended rmin algorithm is proposed to formulate the boundary condition, such as nodal penetration and separation, strain and rotation increment, and altered elastoplastic state of material. The proposed solution for simulation includes algorithms implemented in the finite element code which make it possible to obtain accurate prediction results. Numerical simulation can produce information on the whole deformation history, such as the distribution of thickness, the distribution of stress, the distribution of strain, and the shape after the drawing process. The simulation result was then compared with experimental data to verify the feasibility and reliability in simulation process using this finite element analysis program. It shows good agreement between the simulated results and experimental outcomes. Therefore, the elastoplastic large deformation finite element program can reasonably simulate the circular rail drawing process.