Implications of the definition of the Φ function in elastic-viscoplastic models

A discrepancy has been identified in existing overstress theory based elastic-viscoplastic models regarding the definition of the Φ function, which determines the magnitude of the viscoplastic strain increment. Based on existing experimental data, some authors define the function Φ assuming that any given loading surface is a locus of constant volumetric viscoplastic strain rate. Others, instead, assume that a loading surface is a locus of constant Φ. This paper examines the implications of using either of the above approaches. It is shown that the two approaches yield very similar predictions for stress states far from failure (for stress levels up to approximately 0·6), however, critical-state conditions are reproduced only when the current loading surface is assumed to be a locus of constant Φ.