| Modeling of manufacturing processes such as stamping, extruding, forging, and hot metal forming requires appropriate time-temperature dependent constitutive models and the proper kinematic formulation for analyzing the nonlinearities of the large strains inherent in the processes. The finite element method, which is used extensively in the analysis of these large strain manufacturing processes, has been shown to produce physically unrealistic results when the kinematic formulation is an updated Lagrange approach and the constitutive relation is based on the Jaumann stress rate. Furthermore, the use of a stress rate formulation has been shown to require thermoelastic constraints on the material parameters in the constitutive law. A new approach based on a functional form of the constitutive law where stress is written explicitly as a function of strain, strain rate, and temperature with stress rates including rate of change of material properties is presented. This functional form of the constitutive law is demonstrated analytically for an elastic-plastic material obeying the von Mises yield criterion and Prandtl-Reuss flow law. Implementation of this formulation into a finite element analysis, with the description of the kinematics of large displacement using the deformation gradient tensor and the logarithmic strain, is demonstrated with rubber elasticity for a variety of load cases. The stamping of an aluminum billet, where the Bodner-Partom viscoplastic unified constitutive model is used to describe inelastic strains, is also analyzed. This example demonstrates the formulation for a large strain manufacturing process and compares the results with test data. A review of various kinematic approaches, stress and strain measures, and constitutive models is also included. |
