Phase transition in monodisperse granular materials: How to model it by using a strain hardening visco-elastic-plastic constitutive relationship

Abstract

During heating (loading characterised by a progressive increase in strain rate) and cooling (loading characterised by a progressive decrease in strain rate) numerical tests, performed by using Discrete Element codes, granular materials experience phase transition phenomena, named in this paper ‘dry liquefaction’ (when from solid the material starts behaving like a fluid) and ‘dry resolidification’ (freezing, when the material from fluid starts behaving like a solid). The aim of this paper consists in reproducing phase transition phenomena by using a strain hardening visco-elastic-plastic model based on the critical state concept and kinetic theories of granular gases. The authors demonstrate that crucial is the role of isotropic softening/hardening, which describes the size of the elastic domain and the capability of the solid skeleton of storing elastic energy according to permanent force chains. The main ingredients of the model are: (i) the additivity of quasi-static and collisional stresses, (ii) the energy balance equation governing the evolution of the granular temperature, interpreted this latter as an additional internal variable for the system for the collisional contribution, (iii) the mixed isotropic and kinematic hardening characterising the quasi-static incremental constitutive relationship. The model has been both calibrated and validated on Discrete Element Method (DEM) numerical results, obtained by testing dry assemblies of monodisperse spheres under true triaxial loading conditions.