Abstract
In this work, Discrete Elements Method simulations are carried out to investigate the effective stiffness of an assembly of frictional, elastic spheres under anisotropic loading. Strain probes, following both forward and backward paths, are performed at several anisotropic levels and the corresponding stress is measured. For very small strain perturbations, we retrieve the linear elastic regime where the same response is measured when incremental loading and unloading are applied. Differently, for a greater magnitude of the incremental strain a different stress is measured, depending on the direction of the perturbation. In the case of unloading probes, the behavior stays elastic until non-linearity is reached.Under forward perturbations, the aggregate shows an intermediate inelastic stiffness, in which the main contribution comes from the normal contact forces. That is, when forward incremental probes are applied the behavior of anisotropic aggregates is an incremental frictionless behavior. In this regime we show that contacts roll or slide so the incremental tangential contact forces are zero.Graphical
Highlights
Granular media are complex systems widely present in civil engineering in the form of soils or granulates, in industry including chemical synthesis, food production, thermal insulation, additive manufacturing and other application consisting of granular beds
Froiio and Roux [17], Calvetti et al [15], Kuhn et al [22] use response envelopes obtained via Discrete Element Method (DEM) multidirectional loading probes to investigate the validity of common assumptions of elasto-plastic models for granular materials subjected to anisotropic loading paths
While unloading probes seem weakly related with anisotropy, in the case of forward loading a pronounced dependency on the stress state appears, with A11 ( A31 ) decreasing with anisotropy. Details of this second regime induced by forward loading are shown in the inset.It is noteworthy to mention that, during all the applied increments, we do not see any significant change in the coordination number as we will show in details later in the section Micromechanics
Summary
Granular media are complex systems widely present in civil engineering in the form of soils or granulates, in industry including chemical synthesis, food production, thermal insulation, additive manufacturing and other application consisting of granular beds. Beside the well-known linear elastic regime in which the same stress is measured when both forward and backward incremental strains are applied, we recognize a second regime, associated with greater perturbations, that proceed the non-linear behavior, i.e. the stiffness depends on the strain amplitude We identify in this regime an inelastic stiffness in which the response becomes incrementally frictionless and the major symmetry of the macroscopic stiffness is lost 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 focus on probes parallel and orthogonal to the initial monotonic loading in order to unravel the role of contacts elasticity, sliding and rolling in the transition of the elastic, inelastic, and plastic regime where the loss of symmetry emerges
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