Three dimensional steady‐state locus for dry monodisperse granular materials: DEM numerical results and theoretical modelling

Abstract

In this paper, steady-state conditions for ideal monodisperse dry granular materials are both theoretically and numerically analysed. A series of discrete element (DEM) numerical simulations have been performed on a periodic cell by imposing stress paths characterized by different Lode angles, pressures, and deviatoric strain rates. The dependence of the material response on both inertial number and loading path has been discussed in terms of void ratio, fabric, and granular temperature. DEM numerical results have been finally compared with the prediction of an already conceived model based on both kinetic and critical state theories, here suitably modified to account for three-dimensional conditions.In the literature, the constitutive models proposed within the soil mechanics community 8-10 consider only the quasi-static regime and do not take collisions among grains into account. The state variables generally employed in these models are the void ratio and the fabric tensor, the latter describing, the inherent/induced anisotropy. These models are commonly validated by means of simple and complex laboratory experimental tests (very often either triaxial or true triaxial), [11][12][13] and, more recently, even by performing discrete element (DEM) numerical analyses. [14][15][16][17][18] By contrast, to study the collisional regime, simple shear DEM numerical simulations are commonly employed, 19-21 and the rheological models are based on either the kinetic theory of granular gases 4,5,[22][23][24][25] or the − I∕ − I approach. [26][27][28] This paper focuses on the response of granular materials under steady true triaxial conditions. The material is assumed to be completely dry, the grains not to be crushable and particles to be spherical and identical with a fixed diameter d and a fixed density p . The ultimate goal of this paper is to formulate a physically based theoretical model suitably tailored to capture the response of dry granular materials from quasi-static to dynamic steady-state conditions. As in Johnson and Jackson, 29 Savage, 30 Louge, 31 Lee and Huang, 32 Vescovi et al, 33 Redaelli et al, 34 and Berzi and Jenkins, 35 the model proposed by the authors assumes a parallel scheme according to which stresses are calculated as the sum of a quasi-static and a collisional contribution. The former is assumed to be associated with long elapsing frictional contacts among grains involved in force chains and is evaluated by employing the so-called critical state theory. The latter contribution is associated with inelastic collisions among grains and is calculated according to the kinetic theories for granular gases accounting for frictional and deformable particles and correlated motion between grains. As a consequence, according to this approach, the energy can be stored by the medium as either elastic or kinetic, increasing the latter one with the material agitation, and can be dissipated by means of either sliding among grains when permanent contacts develop or grain inelastic collisions. The transition from...

Shear Is Not Always Simple: Rate-Dependent Effects of Flow Type on Granular Rheology

“…In this work, we use discrete element method (DEM) simulations to explore the rheology of frictional granular materials across different irrotational flow geometries. By deforming systems to very large strains and quantifying the rate-and friction-dependence of stress envelopes, this extends results from earlier studies on the dependence of granular rheology on loading geometry [7,[11][12][13][14]. The relative importance of the loading geometry is measured in terms of a strength ratio Ψ, the ratio of the shear stress in triaxial extension (TXE) to compression (TXC).…”

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

“…𝑒 𝑐 is the jamming void ratio, that is the void ratio at which force chains start developing within the granular medium under steady conditions. According to Zhao and Guo, 44 Zhou et al 45 and Redaelli and di Prisco, 27 𝑒 𝑐 is independent of the loading path. In contrast, Barreto and O'Sullivan 46 and Huang et al 41 have numerically shown that 𝑒 𝑐 depends on Lode angle…”

“…The quasi-static contribution is modelled by employing a time independent elastic-plastic anisotropic strain hardening formulation, based on the critical state theory, interpreted this latter as a limit steady state for 𝑇 going to zero. 27 According to elastic-plasticity, stiffness tensor 𝑫 𝑞𝑠 of Equation ( 2) is assumed to coincide with the elastic stiffness tensor 𝑫 𝒆𝑙 (Subsection 3.2.1) under unloading, whereas under loading:…”

“…4,[24][25][26] To this category of models belongs the so called μ-I rheology, 4 according to which, under simple shear conditions, a unique relationship between stress level μ, void ratio e and inertial number I exists: high values of I correspond to agitated conditions, whereas small I values to quasi-static regimes. The unicity of such relationship, in case of deformable spheres, has been recently critically discussed by Redaelli and di Prisco 27,28 and Marveggio et al 29 The challenging goal of this paper consists in introducing a constitutive approach capable of reproducing phase transition phenomena ('dry liquefaction', when from solid the material starts behaving like a fluid, and 'freezing' or 'dry resolidification', when the material from fluid starts behaving like a solid) experienced by granular assemblies when either confining pressure is nullified/increased or strain rate is increased/decreased. The proposed model considers transient conditions and is based on the comprehension of the dissipative and storing mechanisms governing the phenomena and on the hypothesis of distinguishing collisional dissipation contributions from the ones related to long elapsing force chains.…”

“…The proposed model considers transient conditions and is based on the comprehension of the dissipative and storing mechanisms governing the phenomena and on the hypothesis of distinguishing collisional dissipation contributions from the ones related to long elapsing force chains. For steady conditions, the model follows the approach proposed in Berzi et al, 30 Vescovi et al 31 and Redaelli and di Prisco, 27 where a parallel scheme is adopted to account for separately both quasi static (i.e., force chains related) and collisional terms. The former contribution is evaluated by employing the so-called critical state theory, 32 whereas the latter one according to the kinetic theories of granular gases.…”