Approximation of Strain Rate Parameters for Use with Eulerian Viscoplastic Constitutive Models Based on True Cauchy Stresses and True Strains Obtained at Nominal Strain Rates

In several previous studies, strain rate sensitivity parameters are given for universal stress strain curves for true Cauchy stress and true (logarithmic) strain data; however, the required true strain rate was approximated using nominal (engineering) strain rate. The problem with this is that for finite viscoplastic deformations, both Eulerien and Lagrangian variables are being combined within the proposed viscoplasic constitutive models which makes the models inconsistent with the exact equations of motion, and required deformation power requirements. To be consistent, it is required that the true Cauchy stress be the work energy conjugate to the true strain measure whose rate is the rate of deformation tensor along with the current density per current unit volume. Therefore, in this study, the objective is to illustrate the difference associated with using the strain rate sensitivity constants from true stress versus true strain data obtained at several nominal axial strain rates with the true axial rates of deformation.