Strain Localization Prediction of Anisotropic Sand under Plane Strain Conditions Based on a Non-Coaxial Constitutive Model

Predicting the formation of shear bands is important for understanding the damage mechanisms of sands. Whereas the accuracy of strain localization predictions strongly relies on the selection of the constitutive model. In this paper, the generalized non-coaxial plastic flow theory proposed by Hashiguchi is firstly used to release the coaxiality limitation of the three-dimensional state-dependent dilatancy model of sand, and to establish the non-coaxial constitutive model of sand. In order to further accurately describe the characterization of the strength of the sand as a function of the angle of deposition (direction of principal stresses), the original anisotropic state variables were corrected using an interpolating function. After that, a series of plane strain simulations were carried out for Toyoura sands under different depositional angles and confining pressures. The results show that the established constitutive model can accurately capture the stress-strain relationship before bifurcation, reflect the variation pattern of the peak stress ratio of the sand with the deposition angle, and substantially improve the prediction of the bifurcation axial strain and the shear band inclination. On the other hand, it is proved by mathematical derivation that the non-coaxial stress rate tangent to the yield surface in the deviatoric plane is essentially composed of four orthogonal stress rate components.