On the validity of the flow rule postulate for geomaterials

Abstract

SUMMARY This paper is concerned with a fundamental assumption in the theory of plasticity: the direction of plastic strain increments is independent of the loading (stress) increment direction. This assumption, also known as plastic flow rule postulate, works quite well for metal‐like materials. However, geomaterials such as sand present deformational mechanisms that are distinctive from those of metals when they are loaded. As such, we hereby examine the validity of this postulate for granular media accounting for their discrete nature. This is accomplished by analysing the mechanical behaviour of a cubic assembly of polydispersed spherical articles using a particle flow code. An extension to Gudehus' response envelope to three‐dimensional conditions is used to study the incremental character and influence of loading direction on the behaviour of these materials. It is found that plastic flow in granular media is governed by both current state variables and incremental loading direction and magnitude, especially under non‐axisymmetric stress conditions. The flow rule postulate of plasticity remains valid only in axisymmetric and biaxial conditions. We also verified that the plastic response might be significantly influenced by the stress path (or history) taken prior to loading. These findings raise the question of whether or not classic elastoplastic models based on the above postulate will have serious shortcomings, especially in true‐triaxial conditions. Copyright © 2013 John Wiley & Sons, Ltd.

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

“…Similar ambiguity is found with the assumption of a single direction of the plastic strain increment at a particular stage of loading (principle 5). In particular, Kishino [14] and Wan and Pinheiro [23] shed doubt on the fifth principle with simulations that probed a material in multiple stress directions and discovered small changes in the directions of the resulting plastic strain increments. 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.…”

“…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.…”

“…The shape, sizes, and arrangement of the particles were calibrated to closely simulate the behavior of the fine-grain poorly-graded medium-dense Nevada Sand (see the Appendix and [36]). The assembly was large enough to capture the average material behavior but sufficiently small to prevent meso-scale localization, such as shear bands [37,23]. A distinctive feature of sands is the dependence of the elastic moduli upon the confining (mean) stress.…”

“…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.…”

Directional plastic flow and fabric dependencies in granular materials

“…However, there is a significant effect on the direction of the plastic strain increment when the sample is loaded with a tangent path following the failure surface. In that case, the plastic strain increment is deviated towards the direction of the loading path [8]. For each state of stress on the failure surface, the sample obtained with a radial path and with a tangent path has the same fabric tensor up to the 4 th decimal place of…”