Comment on the use of the associated flow rule for transversely isotropic elasto-viscoplastic materials

The constitutive modeling of rate-dependent plasticity of anisotropic materials is critically examined. Specifically, the paper concentrates on the use of the associated flow rule, also known as the normality rule, which is typically applied to formulate a constitutive rule for the plastic strain rate tensor from a static yield criterion (Bishop and Hill, 1951, Hill, 1948 and Hill, 1971). For anisotropic yielding, the associated flow rule is based on the yield criterion of Hill (1948). Using the resulting plastic strain-rate tensor in a dynamic model for elasto-viscoplasticity and studying the onset of yielding, one finds that the resulting stresses at yielding are inconsistent with the values of the yield stresses initially contained in the yield criterion of Hill. A procedure is developed to quantify the inconsistency in a compact form and to correct the associated flow rule to achieve consistency. By analyzing experimental yield data for transversely isotropic polypropylene, the magnitude of the required correction term is quantified. In contrast to the associated flow rule, consistency-related corrections are practically obsolete for a recently developed constitutive rule for the plastic strain rate tensor that is of statistical origin and not based on a yield criterion.