Thermodynamics-based modelling of undrained viscoplastic flow deformation in granular material

Abstract

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.