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Abstract: Optimization integrated with either one step solver (low fidelity model) or incremental nonlinear finite element solver (high fidelity model) has respectively gained increasing popularity in the design of sheet metal forming process to improve product quality and shorten lead time. However, the one step solver directly incorporated with optimization may result in inadequate design precision, while the incremental method often leads to a prohibitively low computing efficiency. In order to take the full advantages of both the one step solver and incremental solver, we present a variable fidelity algorithm which integrates the one step solver with incremental solver for optimizing sheet metal forming process in this study. In the variable fidelity method established, we need to determine the difference between the two solvers at some predefined experimental points firstly, and then constructing a corrected function using surrogate models for compensating the responses of the one step solver at other points. Different surrogate models, such as response surface methodology (RSM), Kriging (KRG), radial basis function (RBF) and support vector regression (SVR), are considered and compared for best modeling accuracy in this paper. The compensated low fidelity model can be used as a high fidelity model in the optimization process. In this study, we adopt the artificial bee colony (ABC) algorithm to obtain the global optimum. To demonstrate the capability of the variable fidelity method combined with the ABC algorithm, the optimal design of draw-bead restraining forces for an automobile inner panel is exemplified herein. The results show that the optimization with variable fidelity method presented significantly improves the computational efficiency and formability of the workpiece. [Copyright &y& Elsevier]

Abstract: Degenerated shell element and membrane element have been widely applied in thin sheet metal forming analysis. However, for medium thick plate metal forming, especially in the case of typical double-sided contact problems such as local bulge forming or pure bending with a small radius, these two element models cannot accurately simulate normal extrusion deformation of the sheet metal. In this paper, a new finite element (FE) solver based on the solid-shell element dynamic explicit algorithm and implicit algorithm is developed for the simulation of medium thick plate metal forming and springback. The solid-shell element model considers bending effects with a thickness-direction multiple-point integration approach. The viscous damping hourglass control algorithm eliminates the spurious deformation modes activated by in-plane reduced integration (RI). The double sided contact analysis considering thickness variation describes the extrusion deformation in the thickness direction accurately. An improved plane-stress constitutive model in co-rotational configuration together with Hill''s quadratic anisotropic yield criterion is employed to update the stress field. The solid-shell element obtains both solid-like and shell-like behaviours to simulate large membrane deformation, shear deformation and rotation. To test the performance of the solid-shell element, some numerical examples are taken and compared with experiments. The comparison results demonstrate that the solid-shell element model is competitive enough in the simulation of medium thick plate metal forming and springback. [Copyright &y& Elsevier]

Abstract: The paper discusses the application of a finite strain model to predict springback in sheet forming. The concept combines both isotropic and kinematic hardening and utilizes a new algorithm based on the exponential map. A special focus is put on the simulation of the draw-bend test of DP600 dual phase steel sheets and the comparison of the numerical results with experimental data. Further, we investigate the sensitivity of the results with respect to geometry parameters as the tool radius and the sheet thickness as well as the ratio between isotropic and kinematic hardening. In addition, the model is applied to the S-rail benchmark problem and the thermoforming of thermoplastic blends, where large elastic strains occur. The simulation results match the experiments very well. [Copyright &y& Elsevier]

Currently, more and more tailor-welded blanks (TWBs) are used in the automobile industry. It is very important to locate the weld line and predict its movement during the forming process. The initial weld line can be predicted by one-step finite-element analysis according to the desired weld line in the final workpiece. Meanwhile, weld line movement during the deformation process can be evaluated in advance. In this paper, the procedures of finite-element analysis of one-step FEM with TWBs are established. The contact between tool and blank and the effect of restraining forces under the blankholder due to drawbead and blankholder pressure are considered as well. Forming limit diagram (FLD) is used to show not only the tendency of reduction in thickness and fracture but also of increase in thickness and wrinkle. Hydraulic controlled pads used to clamp the weld line during the deep drawing process are simplified as static external force to eliminate the movement of the weld line. In order to speed up and ensure the convergence of Newton-Raphson iterations, energy-based 3D mesh mapping algorithm is introduced to obtain the initial solution. The above-mentioned methods have been implemented in the authors’ in-house one-step FEM code InverStamp. A rectangular cup drawing case demonstrates that this approach can be easily implemented to evaluate weld line movement and develop initial blank in sheet metal stamping with tailor-welded blanks. [ABSTRACT FROM AUTHOR]

In this paper, an implicit simulation code which can simulate a general three-dimensional sheet-metal forming is presented. An 8-node degenerated shell element is employed to approximate the continuous updated Lagrangian formulation of the global mechanical problem. Emphasis is put on expressing the contact conditions and taking into account the geometrical non-linearity. The characteristics of the authors’ contact algorithm is that the contact conditions just act as the boundary conditions of the FEM equations and need not be introduced into the stiffness matrix. Finally, two numerical examples demonstrating the effectiveness of the present approach are given. [Copyright &y& Elsevier]