Theoretical analysis and numerical simulation of three-dimensional bifurcation by constitutive model for over-consolidated clays

Bifurcation depends much on the elastoplastic matrix of constitutive model. An analytical solution of bifurcation is derived in three-dimensional stress states by taking the elastoplastic constitutive model proposed by Yao et al. for over consolidated clay based on the revised Hvorslev envelope. The bifurcation solution to the model along different stress paths under constant mean stress is obtained. The theoretical analysis shows that the onset of bifurcation occurs in the hardening regime at the Lode's angle in the range of -26.5°～7.5°, and that the change in the inclination angle of shear band after bifurcation is steady. There is no bifurcation occurring at the Lode's angle in the ranges of -30°～-26.5° and 7.5°～30°. On the other hand, 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. The numerical simulation of true triaxial tests on isotropically homogenous cubic specimens along different stress paths under constant mean stress is carried out. A comparison indicates that the numerical results agree with the theoretical solutions.