An incremental elastic-viscoplastic theory indicating a reduced modulus for non-proportional buckling

Abstract

The small deformation elastic-viscoplastic constitutive equations of Bodner-Partom are modified to model strong non-proportional loading paths such as experienced in corner turning tests and certain cases of inelastic buckling. An essential generalization is made to the flow rule, causing the magnitude and direction of plastic strain rate to become an explicit function of deviatoric total strain rate as well as of stress and hardening variables. With this and other modifications, the equations indicate some of the important characteristics of the response to abrupt changes in the loading direction. These are: (a) a reduced effective shear modulus; (b) a transient drop in the effective stress; and (c) a transient non-coaxiality of the plastic strain rate relative to the deviatoric stress. Predictions of the modified theory compare reasonably well with experimental values for inelastic torsional buckling of axially compressed cruciform columns and for corner turning tests.