Application of rigid(visco)–plastic element free Galerkin method to simulation of plane strain forming

A rigid–plastic/viscoplastic element free Galerkin (EFG) method is introduced based on the flow formulation for rigid–plastic/viscoplastic materials to analyse the metal forming processes. The penalty function method is employed to introduce the volume constancy condition, and the stiffness matrix equation is derived according to incomplete generalised variational principle. The transformation method is adopted to impose the essential boundary condition in the local coordinate system. In order to implement the frictional boundary conditions, the transform matrix from the global coordinate system to the local coordinate system is given, and the arctangent frictional model is used. The meshless analysis techniques for metal forming processes with arbitrary shaped die are developed. The plane strain forming process is analysed numerically by using the rigid(visco)–plastic EFG method. The simulation results of the EFG method are in good agreement with those obtained by using the rigid(visco)–plastic FEM, and the effectiveness of the model and key techniques is verified.