A Zero Elastic Range Hypoplasticity Model for Sand

The theory of zero purely elastic range in stress space within the framework of bounding surface plasticity is applied to sand constitutive modelling. With a vanished yield surface, plastic loading occurs for any direction of the stress ratio rate on which the loading and plastic strain rate directions now depend, rendering the model incrementally non-linear. The resulting model falls into the category of hypoplasticity in the sense of dependence of the plastic strain rate direction on the stress rate direction, that is different from another constitutive hypoplasticity theory, which does not involve classical plasticity loading-unloading criteria and additive decomposition of total strain rate into elastic and plastic parts. The simplicity of the conceptual structure of the model is particularly attractive as it consists of only one surface, the bounding/failure surface, and the stress point itself in the deviatoric stress ratio plane. The model follows the basic premises of the SANISAND family of models that unify the description for any pressure and density within critical state theory. Elimination of the classical yield surface concept circumvents the complexity associated with satisfying the consistency condition; however, the incrementally non-linear hypo-plastic nature of the new formulation requires special handling of its numerical implementation. The work shows the simulative capabilities of the model that are comparable with those of the classical model with very small yield surfaces, including simulations under cyclic and rotational shear loading.