Abstract: A new method for simulating the metal forming process is given by combining the element free Galerkin meth- od with the flow theory of rigid plastic/viscoplastic mechanics. The mixed transformation method and penalty method are utilized to implement the velocity boundary conditions and incom-pressibility constraint respectively. The element free Galerkin method and its key algorithm are given based on the flow for-mulation for rigid plastic/viscoplastic materials. The numerical simulation of an axisymmetric upset forging reveals the effec-tiveness and feasibility of the present method.

Key words: Element free Galerkin method, Metal forming process, Mixed transformation method, Moving least squares approximation, Penalty method