Classes of flow rules for finite viscoplasticity

Classes of flow rules for finite viscoplasticity are defined by assuming that certain measures for plastic strain rate and plastic spin depend on the state variables but not on the plastic deformation. It is shown that three of these classes are mutually exclusive for finite elastic strains. For small elastic shear strains, two of the three classes are approximately equivalent. A number of exact and approximate kinematic relations between the various measures for plastic strain rate and plastic spin are derived. Some inconsistent flow rules encountered in the literature are also discussed. Throughout the paper, arbitrarily anisotropic materials are considered, and some of the simplifications resulting from the assumption of isotropy are noted.