Abstract: The bifurcation analysis was derived in three-dimensional stress states by using a critical state constitutive model by Yao et al. (2004), which based on the nonassociated flow rule. Theoretical analysis shows that, bifurcation is dependent closely on the stress path. Bifurcation occurs in the hardening regime under the Lode angle changing between minus twenty-five degree and fifteen degree, and the stress ratio, principal strain at bifurcation and inclination angle of shear bands first increase and then decrease with increasing of the Lode angle. But there is no bifurcation occurring in other stress path under constant mean stress. Finally, the return mapping algorithm is adopted in order to implement the model into a nonlinear finite element analysis software ABAQUS through the user material subroutine (UMAT) interface. Numerical simulation results show that the bifurcation also exists in the numerical analysis. The comparison between the numerical results and theoretical solutions indicates that both are in good agreement.

Key words: critical state model, nonassociated flow rule, bifurcation analysis, three-dimension, sand