Eulerian elasto-viscoplastic formulation for modeling steady-state deformations with strain-induced anisotropy

An Eulerian finite element formulation for modeling elasto-viscoplastic, steady-state metal forming processes of practical significance has been developed. Emphasis is placed on precisely modeling the kinematics as well as the constitutive behavior of the material as it undergoes large strains while maintaining an Eulerian reference frame. This formulation is capable of predicting the residual stresses and the texture in metals resulting from steady-state forming processes. The primary advantages of this formulation are the accuracy of the equations describing the material behavior and its use of an Eulerian reference frame.; It is particularly important in any deformation analysis to select an appropriate choice of variables to describe the state of the material and its evolution. The deformation of metals involving large inelastic strains is the focus of this work. For metals, the inelastic strains dominate the deformation process; the elastic strains are generally small, but nonetheless significant and necessary for obtaining residual stresses. The use of appropriate kinematics in conjunction with a realistic microstructurally motivated constitutive model provides for an accurate description of the material behavior in the formulation presented herein. Both isotropic and anisotropic material behavior have been incorporated using material models based on microstructural phenomenology. Isotropic behavior is modeled using scalar internal variable models, and anisotropic behavior is modeled using a polycrystalline based formulation.; Several examples involving rolling and extrusion are presented which demonstrate that the algorithm can predict residual stresses and material texture consistent with what has been observed in experiments and is predicted in theory.