In this paper, the thermodynamics of granular material is developed to get constitutive relations for unified modelling of undrained viscoplastic flow behavior with complex combined effects of state, rate, time, and path. The proposed formulations of energy storages and dissipations lead to the state-dependent hyperelasticity with an elastic instable region and the viscoplasticity with considerations of the granular kinetic flow. Subjected to strict thermodynamic restraints, a generalized law of viscoplastic shear flow is proposed for granular material as the combination of state-based and rate-based viscoplastic flows, which predictively captures the diversity of undrained granular flow pattern with elastic-plastic coupled non-coaxialities among stresses, (total/ viscoplastic/elastic) strains, and their increments. The viscoplastic flow is also linked with the granular temperature that accounts for the granular kinetic fluctuation varying from dilative dense flow to large unlimited flow under shear-induced static liquefaction. This enables predictions of the creep and the stress relaxation as well as the over- and -under shooting of stress under stepwise changes in strain rate. The model is well validated by predicting the flow potential, phase transformation, critical state, and rate/time effects under undrained conventional triaxial shearing and simple shearing for Toyoura sand, which are strongly related to the void ratio, the confining pressure, the shear stress, and the shear mode.

A thermodynamics-based constitutive model predicting the critical state behavior of sands is developed in this paper. The model includes hyperelastic and plastic constitutive relations derived from thermodynamics. Using the concept of elastic potential, hyperelastic relations are derived to describe the stress- and -density dependency of the elastic stiffness of sands, which naturally lead to the elastic limit with stress-induced anisotropy in effective stress space. The plastic constitutive relations coupled with the nonlinear hyperelasticity are then derived based on the energy dissipations and the second law of thermodynamics. The model is capable of predicting the critical state behavior of sands without concepts of yield surface and plastic potential surface. The model is validated by predicting the undrained shear behavior of Toyoura sand. The modeling results show that different patterns of undrained shear response, such as the pure dilation type, the contraction-dilation type with hardening, the contraction-dilation type with softening, and the pure contraction type, can be well captured by the model, depending on the confining pressure and the void ratio. The distinctions of contraction/dilation and critical state behavior between triaxial compression and extension are also predicted. It is shown that the critical state behavior of sand is the combined results of the pressure/density/path-dependent hyperelasticity and plasticity coupled with each other.