Influence of unobservable overstress in a rate-independent inelastic loading curve on dynamic necking of a bar

A nonlinear rate-independent overstress model with a smooth elastic-inelastic transition is used to analyze instabilities during dynamic necking of a bar. In the simplified model the elastic strain εe determines the value of stress and the hardening parameter κ determines the onset of inelasticity. These quantities {εe, κ} are obtained by integrating time evolution equations. The main and perhaps surprising result of this paper is that, based on the critical growth rate ωcr of a perturbation, two rate-independent materials with a smooth elastic-plastic transition due to overstress and nearly the same loading curve (elastic strain or stress versus total strain) can have different susceptibilities to tensile instabilities. Specifically, increase in overstress causes decreased material instability near the onset of the smooth elastic-inelastic transition and increased instability when the elastic strain approaches its saturated value. To the authors' knowledge, this new insight has not been reported in the literature.