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

• The associated flow rule is inconsistent for rate-dependent anisotropic plasticity.
• A correction scheme to restore point-wise consistency is presented.
• A novel fluctuation-based flow rule is shown to be a viable alternative.
• Both flow rules are compared on the basis of experimental data for polypropylene.

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 (Hütter and Tervoort, 2008a, Hütter and Tervoort, 2008b, Hütter and Tervoort, 2008c and Hütter and Tervoort, 2013).