A coupled finite element-element-free Galerkin method for simulating viscous pressure forming

Abstract

Viscous pressure forming (VPF) is a kind of sheet flexible-die forming process which uses a semisolid, flowable and viscous material as the pressure-transmitting medium. Unlike the conventional rigid die punching or hydroforming process, there are strong nonlinear features between the sheet metal and viscous medium in VPF. In this paper, a numerical analysis method for coupling sheet metal deformation and bulk deformation of viscous medium is presented. A static explicit approach based on the Updated Lagrangian (U.L.) formulation is adopted. The elastoplastic deformation of sheet metal is analyzed with finite element method (FEM), and the visco-elastoplastic bulk deformation of viscous medium is analyzed with the element-free Galerkin method (EFGM), which can eliminate mesh distortion unavoidable during the deformation of viscous medium in FEM. The contact and friction between the sheet metal and viscous medium are treated by the penalty function method. An FEM–EFGM program for coupled deformation between sheet metal and viscous medium is developed, called CDSB–FEM–EFGM for short. Several numerical examples of coupled deformation between viscous mediums with different viscosities and sheet metal are presented to demonstrate the effectiveness of the proposed method. Compared the numerical simulation results with experimental measurements, the validity of the CDSB–FEM–EFGM program is obtained.