Design and analysis of large deformation continuous elastoplastic manufacturing processes via a steady displacement-based formulation

A reference frame formulation for large deformation steady state processes is proposed. The displacement and material state variables appear as the primary response fields in this mixed formulation. Unlike displacement based Lagrangian formulations, our formulation does not require a transient analysis to simulate a quasi-steady process and yields results that are free of numerical oscillations and which require considerably less computational effort. And unlike velocity based Eulerian methods, our formulation does not require free surface corrections or streamline integration algorithms. An iterative design environment for quasi-steady forming processes is developed from the computationally efficient reference frame formulation. The direct differentiation method is used to efficiently evaluate the response sensitivities. Select forming response measures and their sensitivities are combined with nonlinear programming methods to optimize the process. To illustrate these methods, the die shape in a drawing process is designed to minimize the distortion of the work-piece.