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

Proceeding of: IUTAM Symposium on Dynamic Instabilities in Solids, May 17-20, 2016, Madrid, SpainA 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 epsilone determines the value of stress and the hardening parameter kappa determines the onset of inelasticity. These quantities {epsilone, kappa} are obtained by integrating time evolution equations. The main and perhaps surprising result of this paper is that, based on the critical growth rate omegacr 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.JARM is indebted to the Ministerio de Economía y Competitividad de España (Projects EUIN2015-62556 and DPI2014-57989-P) for the financial support which permitted to conduct part of this work. The research leading to these results has received funding from the European Union’s Horizon2020 Programme (Excellent Science, Marie-Sklodowska-Curie Actions) under REA grant agreement 675602 (Project OUTCOME). This research was also partially supported by MB Rubin’s Gerard Swope Chair in Mechanics