Rigid-plastic finite element analysis of sheet metal forming processes using explicit time integration scheme

Abstract

A rigid-plastic finite element formulation using the dynamic explicit time integration scheme has been proposed for numerical analysis of sheet metal forming processes. In the present work, BEAM elements and damping energy augmented BEAM elements have been introduced in the explicit analysis. In order to stabilize the dynamic analysis, artificial spring and damping applied to the drilling direction have been employed to prevent a zero energy mode. In the explicit analysis, in order to save computation time, the increased punch velocity is employed as compared with the actual punch velocity at the cost of solution accuracy. A reasonable punch velocity within the appropriate range should be chosen so that computation time and solution reliability can be compromised and the inertia effect should be properly controlled. In the mass scaling scheme the mass density is taken to be the increased value multiplying the actual density by some factor without influencing the solution reliability for economic analysis. In order to make comparative investigation into the explicit rigid-plastic method and the explicit elastic-plastic method under the same condition, an elastic-plastic finite element formulation using the dynamic explicit time integration scheme has been derived. Although the dynamic explicit elastic-plastic finite element method has proven to be an effective method to solve complicated sheet metal forming problems, but it still requires large computation time. In order to show the validity and effectiveness of the proposed dynamic explicit rigid-plastic finite element method, several industrially useful complex auto-body panels, such as an oil pan, a front fender, a fuel tank and a rear hinge have been simulated and the numerical results of the explicit analysis are compared with the experimental results and the implicit results, showing good agreements between them. It is then shown that the explicit scheme requires much shorter computation time especially wh...