Since most of sheet metal forming process is done with a low tool velocity, it can be considered as a quasi-static process. Explicit dynamic FEM[1] has many advantages in treating severe nonlinearities such as nonlinear material, large deformation, instability and contact. In an explicit method, the time step is limited by the stability condition[2], so all solutions are essentially dynamic. Since contact algorithms used for explicit method[3] are more robust and straightforward than their implicit counterparts, explicit method are more attractive to simulate sheet metal forming [4,5]. Although there have been many researches on sheet metal forming analysis by an explicit method [4,5,[8][9][10][11][12][13][14], the dynamic effects are still not well-understood or quantified.To solve quasi-static problem in real time, a huge amount of computation time is necessary because of the small time step in an explicit method. Therefore when we use an explicit FEM for sheet metal forming analysis, it is conventional to convert the real problem to a virtual problem with a different time scale. In this context, time scaling and mass scaling techniques have been widely used in order to save computation time. If we use a large scaling factor with these methods, dynamic effects will increase and may cause incorrect results, especially for the stresses. In this situation, it is difficult to figure out how large the scaling should be to reduce computation time and still maintain the desired accuracy. The four node isoparametric shell element with one point integration with hourglass control is used by Belytschko and coworkers [6,7]. This shell element has been widely used to model sheet metal because of computational efficiency in explicit method.Several authors [5,8,9,13] have shown that the overall deformation and strain distribution can be predicted within acceptable accuracy if we use the scaling factor which yields a low ratio of total kinetic energy to total internal energy.

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SUS304 stainless steel is characterized by combined tensile and compression testing, with an emphasis on flow stress at higher strain and temperature. The plastic deformation behavior of SUS304 from room temperature to 400 °C is examined and a general approach is used to express flow stress as a closed-form function of strain, strain rate, and temperature; this is optimal when the strain is high, especially during automatic multi-stage cold forging. The fitted flow stress is subjected to elastothermoviscoplastic finite element analysis (FEA) of an automatic multi-stage cold forging process for an SUS304 ball-stud. The importance of the thermal effect during cold forging, in terms of high material strength and good strain-hardening, is revealed by comparing the forming load, die wear and die stress predictions of non-isothermal and isothermal FEAs. The experiments have shown that the predictions of isothermal FEA are not feasible because of the high predicted effective stress on the weakest part of the die.

This paper presents a new method for planar development of the 3D surfaces of a shoe upper. The 3D surface is first faceted into triangular elements and then roughly laid down on a 2D plane. Next, the nodal points of elements are repositioned by a refinement technique that minimizes the geometric errors. Even after elements have been refined by minimizing geometric errors, the resulting 2D shape still has some strain energy that needs to be reduced by a relaxation process. Hence, these elements are then used as an initial guess for further optimization during which the finite element inverse method is used to minimize the total strain energy. In fact, the two-step optimization technique not only can prevent the divergence of solutions (e.g., interferences between elements) but also yields a more reliable result. The method has been implemented as a module of the shoe design system by which a prototype shoe can be designed and manufactured more precisely and quickly.