A dynamic explicit/rigid‐plastic finite element formulation and its application to sheet metal forming processes

Abstract

In the present work a rigid‐plastic finite element formulation using a dynamic explicit time integration scheme is proposed for numerical analysis of sheet metal forming processes. The rigid‐plastic finite element method, based on membrane elements, has long been employed as a useful numerical technique for the analysis of sheet metal forming because of its time effectiveness. The explicit scheme, in general, is based on the elastic‐plastic modelling of material requiring large computation time. The resort to rigid‐plastic modelling would improve the computational efficiency, but this involves new points of consideration such as zero energy mode instability. A damping scheme is proposed in order to achieve a stable solution procedure in dynamic sheet forming problems. In order to improve the drawbacks of the conventional membrane elements, BEAM (abbreviated from Bending Energy Augmented Membrane) elements, are employed. Rotational damping and spring about the drilling direction are introduced to prevent a zero energy mode. The lumping scheme is employed for the diagonal mass matrix and linearizing dynamic formulation. A contact scheme is developed by combining the skew boundary condition and a direct trial‐and‐error method. Computations are carried out for analysis of complicated sheet metal forming processes such as forming of an oilpan and a front fender. The numerical results of explicit analysis are compared with the implicit results, with good agreement, and it is shown that the explicit scheme requires much shorter computational times, especially when the problem becomes more complicated. It is thus shown that the proposed dynamic explicit rigid‐plastic finite element enables an effective computation for complicated sheet metal processes.