ABSTRACT
In this chapter, all three of the governing equations developed in Chapters 3−5 are collected to develop the following two formulations for elasto-plastic problems: updated Lagrangian formulation and Eulerian formulation. In the updated Lagrangian formulation, the final deformed configuration is analyzed in several increments using the governing equations in the incremental form. The domain, the deformation and the stresses are updated at the end of each increment. This formulation can also be used for steady-state problems like rolling, drawing, extrusion, etc. However, for such problems, it is possible to identify a fixed region in the space (called the control volume) where the deformation gets concentrated. Thus, the flow-type Eulerian formulation is convenient for such problems where only the control volume containing the deformation is analyzed. In this formulation, the velocity is treated as a primary unknown, and therefore, the strain rate tensor (or the rate of deformation tensor) is employed as the measure of deformation, and the constitutive equation is expressed in rate form.
