Modeling a smooth elastic–inelastic transition with a strongly objective numerical integrator needing no iteration

Abstract

Large deformation evolution equations for elastic distortional deformation and isotropic hardening/softening have been developed that model a smooth elastic---inelastic transition for both rate-independent and rate-dependent response with no need for loading---unloading conditions. A novel special case is a rate-independent overstress model. Specific simplified constitutive equations are proposed that capture the main effects of elastic-plastic and elastic-viscoplastic materials with only a few material parameters. Moreover, a robust and strongly objective numerical integrator for these simplified evolution equations has been developed which needs no iteration. Examples show the influence of the various parameters on the predicted material response. The smoothness of the elastic---inelastic transition in the proposed model, with the associated overstress, tends to spread the inelastic region. This side effect prevents severe deformation from being localized in an element region that continues to reduce in size with mesh refinement. However, preliminary calculations indicate the need for additional modeling of a material characteristic length that independently controls the size of a localized severely deformed region.