Limit State and Bifurcation Point in Hypoelastic Materials for Some Objective Stress Rates

The limit state in hypoelastic materials, analogous to the failure or yield in classical theory of plasticity, along with the bifurcation point, corresponding to a localized instability, have been studied. Analytical equations for the limit state subject to various choices of the objective stress rates have been developed for a rather general form of the hypoelastic constitutive equation. In a rational procedure, it was shown that a general form of the limit state, which can be reduced to any conventional form of the failure criteria in the theory of plasticity, can be achieved. We mean by rationality, the nondependence of the equations on any physical assumption or a particular form of the constitutive equation. Results were examined against available experimental data.