Instability and bifurcation of a nonassociated extended mises model in the hardening regime

Abstract

Instability of configuration and instability of path under quasistatic loading in the hardening regime are examined for a nonassociated elastic-plastic extended Mises model or similar model with a smooth potential surface. In plane strain, the configuration of such a model of a homogeneous body under homogeneous stress and strain becomes unstable almost immediately upon entering the plastic range, just as for the Mohr-Coulomb model studied previously. The unstable jump exhibited is in the form of a shear band with boundaries that rotate as the band undergoes an abrupt limited excursion. On the contrary, the homogeneous triaxial test stress state configuration is stable, not unstable as for Mohr-Coulomb. No shear band can form at fixed load; the requirement of zero out-of-plane strain rate is fully stabilizing. Also, as for the Mohr-Coulomb, no kinetically consistent axisymmetric pattern can be associated with any unstable “wedge path” in stress space. However, as the load in a triaxial test increases and the plastic hardening modulus decreases, an instability of path is found well within the hardening range. An unstable shear band can initiate and develop much before a classical shear band bifurcation.