Research on rigid/visco-plastic element-free Galerkin method and key simulation techniques for three-dimensional bulk metal forming processes

Abstract

The element-free Galerkin method is introduced into the analysis of three-dimensional bulk metal forming processes according to flow formulation for rigid/visco-plastic material. The transformation method is used to impose the essential boundary condition directly. The stiffness matrix equation is derived according to incomplete generalized variational principle. And the corresponding key simulation techniques are developed. The case that matrix A(x) appears irreversible is discussed, and the approaches for treating with this problem are given. Volumetric strain rate method is proposed for releasing the volume locking problem. The method for describing shapes of dies is presented. In order to impose arbitrarily shaped boundary conditions in three-dimensional problems, the local coordinate system is established and the transformation matrix between the local coordinate system and the global coordinate system is calculated. Methods for exerting velocity and frictional contact conditions are introduced. Dynamic adjustment techniques for the boundary of the workpiece including the contact/detachment judgment criterion and the method for modifying the contact nodes’ positions are given. Finally, the effectiveness of the method and key techniques is demonstrated by simulating a two-stage three-dimensional forging process.