Triaxial Test Instability of a Nonassociated Flow-Rule Model

The Mohr-Coulomb yield condition with a nonassociated flow rule is often used to model the behavior of dry or drained sand. A previous paper demonstrated, using a single shear band with a rotating orientation, that a genuine but limited instability would occur in such a model at each state of triaxial stress in the inelastic range. This paper develops the equations, explores the quantitative behavior of the model, and examines possible alternative patterns of deformation. The extent of the unstable jumps in plastic strains (0.01) and displacements, and the largely hidden transient stress jumps (15%), are calculated for such a model of sand with properties similar to those given by Lade in his papers reporting triaxial test stability in the wedge region. When the incremental elastic response is too small to stabilize the plastic, any similar model with a nonassociated flow rule likewise is unstable. The mathematical requirements for stability and the modeling of stable granular media are commented upon briefly.