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

• Published in: Engineering computations Vol. 12; no. 8; pp. 707 - 722
• Main Authors: Jung, D.W., Yoo, D.J., Yang, D.Y.
• Format: Journal Article
• Language: English
• Published: MCB UP Ltd 01-08-1995
• Subjects: Finite elements; Rigid-plastic; Sheet metal forming; Dynamics
• ISSN: 0264-4401; 1758-7077
• DOI: 10.1108/02644409510104695

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.