Bulk metal forming process simulation based on rigid-plastic/viscoplastic element free Galerkin method

Abstract

A rigid-plastic/viscoplastic element free Galerkin method is established based on the flow formulation for rigid-plastic/viscoplastic materials to simulate bulk metal forming processes. According to incomplete generalized variational principle, stiffness equations and solution formulas are derived. The transformation method is adopted to impose the essential boundary condition in the local coordinate system. The arctangent frictional model is used to implement the frictional boundary conditions, and the transform matrix from the global coordinate system to local coordinate system is given. The analysis software is developed. The method for dealing with the rigid region is introduced. Pressure projection method is used to solve volumetric locking and pressure oscillation problems. The contact and detachment criterion for the workpiece and die is given to judge the contact state. Numerical examples of bulk metal forming process are analyzed based on rigid-plastic/viscoplastic element free Galerkin method. The material flow, field variable distributions, etc. are analyzed. The numerical analysis results obtained by the method proposed in the paper are in good agreement with those obtained by the finite element method and experiment. The correctness of the presented method is demonstrated.