A general rigid-plastic/rigid-viscoplastic FEM for metal-forming processes based on the potential reduction interior point method

Abstract

In general, the finite element method (FEM) constructed on the Markov variational principle for rigid-plastic/rigid-viscoplastic (RP/RVP) problems is solved by an iterative method, which leads to many difficulties in ensuring convergence and dealing with incompressibility, contact and friction forces in practical implementation. It is shown in this paper that the objective function becomes a convex and twice continuously differentiable function after a simple but very useful transformation, and a globally and superlinearly convergent nonlinear programming algorithm can then be used to solve the resulting optimization problem. The algorithm is very efficient and is particularly suitable for solving large-scale optimization problems. Compared with the traditional iterative solution in the RP/RVP FEM, the new method has no convergence problems, and can deal with contact, incompressibility and friction force effectively. In addition, unlike the linear programming solution of the RP/RVP FEM, it does not need linearization of the yield surface, which will bring in many additional variables. The scale of the solution can thus be reduced, so it is very suitable for general RP/RVP problems. Finally, to improve the efficiency of the aforementioned method for solving very large-scale problems, a domain decomposition-based algorithm is introduced. This is important for real applications.