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

Abstract

The complex incremental behavior of granular materials is explored with multi-directional loading probes. An advanced discrete element model (DEM) was used to examine the reversible and irreversible strains for small loading probes, which follow an initial monotonic axisymmetric triaxial loading. The model used non-convex non-spherical particles and an exact implementation of the Hertz-like Cattaneo-Mindlin model for the contact interactions. Orthotropic true-triaxial probes were used in the study (i.e., no direct shear strain or principal stress rotation), with small strains increments of 2 × 10 −6 . The reversible response was linear but exhibited a high degree of stiffness anisotropy. The irreversible behavior, however, departed in several respects from classical elasto-plasticity. A small amount of irreversible strain and contact slipping occurred for all directions of the stress increment (loading, unloading, transverse loading, etc.), demonstrating that an elastic domain, if it exists at all, is smaller than the strain increment used in the simulations. Irreversible strain occurred in directions tangent to the primary yield surface, and the direction of the irreversible strain varied with the direction of the stress increment. For stress increments within the deviatoric pi-plane, the irreversible response had rounded-corners, evidence of multiple plastic mechanisms. The response at these rounded corners varied in a continuous manner as a function of stress direction. The results are placed in the context of advanced elasto-plasticity models: multi-mechanism plasticity and tangential plasticity. Although these models are an improvement on conventional elasto-plasticity, they do not fully fit the simulation results.

DEM simulation of anisotropic granular materials: elastic and inelastic behavior

“…Key parameters are the magnitude and direction of the probes applied to stressed, anisotropic states, compared with the strain under which the aggregate is initially loaded. In such framework, Froiio and Roux [17], Calvetti et al [15], Kuhn et al [22] use response envelopes obtained via DEM multidirectional loading probes to investigate the validity of common assumptions of elasto-plastic models for granular materials subjected to anisotropic loading paths. We, instead, operate with limited loading conditions because we have a different goal.…”

Quasi-static incremental behavior of granular materials: Elastic–plastic coupling and micro-scale dissipation

“…For example, the shape of the response envelopes of elastic increments in Fig. 8 indicates the difficulty of applying a linear Hooke stiffness to the elastic strain increments, although in a related work we show that a linear stiffness relation precisely fits the reversible increments [34].…”

“…At a strain of 0.5%, the reversible Young's modulus in the axial direction was more than twice the transverse modulus, giving rise to the reversible dilation, for constant-p loading, seen in Fig. 10b (see [34] for further analysis of the reversible moduli). The irreversible (and plastic) volume rate transitioned from contractive, at the start of loading, to dilative, at strains greater than 0.2% and was responsible for the initial contractive behavior.…”

“…On the other hand, in a separate analysis of the reversible strains, we found that the reversible strain increments, indeed, conform closely to a linear form C ijkl dσ kl . (see [34]).…”

“…That is, plastic strains are not of the form g ij f kl dσ kl for some yield direction f kl and flow direction g ij . This aspect of the incremental behavior was noted in the simulations of Kishino [31] and Wan and Pinheiro [49], is quantified by the authors in [34], and is addressed by certain constitutive models with incremental non-linearity [15,17,14].…”