Directional plastic flow and fabric dependencies in granular materials

Abstract

Abstract. The constitutive modelling of granular materials both at the microstructural level and the continuum level is well established. Much recent effort has been devoted to the theoretical mechanics and computer simulations of granular media through discrete element modelling (DEM). The current study uses DEM to obtain theoretical insights and extract constitutive information such as the nature of the yield and plastic flow behaviour of granular materials. In particular, we look at the influence of granular fabric on the plastic deformation response under a number of conditions. As such, a representative element volume (REV) of a granular material idealized as a numerical DEM sample is subjected to different loading paths to reach the same stress states, but with different fabrics, on the plastic failure surface. At this stage, directional stress probes of equal magnitudes are applied, so that the strain response envelopes thus obtained represent characteristics of the increment of plastic strain, i.e. the nature of the flow rule. The discussion then focuses on the relationship between fabric, stress state, loading path, direction of the plastic strain increment, and whether this direction can be considered unique or not.

Multi-directional behavior of granular materials and its relation to incremental elasto-plasticity

“…without corners and having unit normal direction f ) [11,15,20,21,17,19]. Other programs, however, found evidence of a possibly cornered yield surface [14,18,22]. Similar ambiguity is found with the assumption of a single direction of the plastic strain increment at a particular stage of loading (principle 5).…”

“…The sixth principle, which disallows plastic strain for stress increments that lie along the yield surface (i.e., tangential increments), was refuted by Kishino [14] and Plassiard et al [20], who detected small 3 Table 3: Results of previous 3D simulations and their conformance with the six principles of conventional elasto-plasticity: Y = conforms with the principle, N = contradicts the principle. Kishino Calvetti Tamagnini Harthong Wan & Elasto-plasticity principle [14] et al [17] et al [18] & Wan [22] Pinheiro [23] (1) dε = dε (e) + dε (p) , dε (e) is reversible Y (2) dε (e) linear: (p) domains are semi-spaces, normal f N Y * N (5) Plastic increments dε (p) in single flow direction g N N N N (6) |dε (p) | = f · dσ N Y * "Y" applies to virgin loading conditions. A finite elastic domain was not found with pre-loaded conditions.…”

“…Yet principle 3 was affirmed in several other studies. In regard to principle 4, some studies have found that the elastic and plastic regions in incremental stress-space are distinct and are separated by a flat hyperplane (i.e., a yield surface 2 Lewin & Burland [9] shale powder triaxial --10 kPa Tatsuoka & Ishihara [10] sand triaxial -E-P 0.001-0.006 Bardet [11] disks linear DEM E-P ≈ 1×10 −3 Anandarajah et al [12] sand -triaxial E-P ≈ 1×10 −4 Royis & Doanh [13] sand -triaxial E-P ≈ 1×10 −4 Kishino [14] spheres linear GEM E-P 1 kPa Alonso-Marroquín [15,16] polygons linear DEM E-P 10 kPa ≈ 1×10 −5 Calvetti et al [17,18] spheres linear 3 DEM R-I ≈ 2×10 −4 Sibille et al [19] spheres linear DEM R-I -Plassiard et al [20] spheres linear 4 DEM R-I ≈ 2×10 −5 Froiio and Roux [21] disks linear DEM 5 -≈ 4×10 −6 Harthong & Wan [22] spheres linear DEM E-P 0.1kPa Wan & Pinheiro [23] spheres -DEM R-I & E-P 0.1 kPa Kuhn & Daouadji [24] sphere-clusters linear & Hertz DEM R-I & E-P 2×10 −6 Current work sphere-clusters Hertz DEM R-I 2×10 −6 1 GEM = Granular Element Method; triaxial = laboratory experiments 2 R-I = reversible-irreversible; E-P = elastic-plastic (see Section 2.2) 3 with rotational restraint of particles 4 with rolling friction of contacts 5 hybrid method: assembly loaded with DEM; probes applied with method similar to GEM [14,25] Table 2: Results of previous 2D simulations and their conformance with the six principles of conventional elasto-plasticity: Y = conforms with the principle, N = contradicts the principle.…”

Micro‐inertia origin of instabilities in granular materials

“…As introduced by Gudehus 32 and widely used in the literature, directional analysis is a convenient framework to track the existence of stress increments leading to the vanishing of the second-order work. 4,14,29,33,34 In this study, we restrict our stability analysis to stress increments lying in the plane of axisymmetry such that d xx = d yy (Rendulic's plane). In this plane ( √ 2d xx , d zz ), a stress increment d is fully described by its polar coordinates ||d || and such that In practice, finite stress increments of ||d || = 5 kPa are imposed in the form of a stress loading rate of 142 kPa.s −1 (corresponding to 10 000 numerical time increments) followed by a stabilization phase letting the system evolves toward a new equilibrium position as F unb < 10 −5 .…”

“…As introduced by Gudehus and widely used in the literature, directional analysis is a convenient framework to track the existence of stress increments leading to the vanishing of the second‐order work . In this study, we restrict our stability analysis to stress increments lying in the plane of axisymmetry such that d σ x x =d σ y y (Rendulic's plane).…”