Numerical study of one-dimensional compression of granular materials. I. Stress-strain behavior, microstructure, and irreversibility

Abstract

The behavior of a model granular material, made of slightly polydisperse beads with Hertz-Mindlin elastic-frictional contacts, in oedometric compression (i.e., compression along one axis, with no lateral strain) is studied by grain-level numerical simulations. We systematically investigate the influence of the (idealized) packing process on the microstructure and stresses in the initial, weakly confined equilibrium state, and prepare both isotropic and anisotropic configurations differing in solid fraction Φ and coordination number z. Φ (ranging from maximally dense to moderately loose), z (which might vary independently of Φ in dense systems), fabric and force anisotropy parameters, and the ratio K_{0} of lateral stresses σ_{2}=σ_{3} to stress σ_{1} in the compression direction are monitored in oedometric compression in which σ_{1} varies by more than three orders of magnitude. K_{0} reflects the anisotropy of the assembling process and may remain nearly constant in further loading if the material is already oedometrically compressed (as a granular gas) in the preparation stage. Otherwise, it tends to decrease steadily over the investigated stress range. It is related to force and fabric anisotropy parameters by a simple formula. Elastic moduli, separately computed with an appropriate matrix method, may express the response to very small stress increments about the transversely isotropic well-equilibrated states along the loading path, although oedometric compression proves an essentially anelastic process, mainly due to friction mobilization, with large irreversible effects apparent upon unloading. While the evolution of axial strain ε_{1} and solid fraction Φ (or of the void ratio e=-1+1/Φ) with axial stress σ_{1} is very nearly reversible, especially in dense samples, z is observed to decrease (as previously observed in isotropic compression) after a compression cycle if its initial value was high. K_{0} relates to the evolution of internal variables and may exceed 1 in unloading. The considerably greater irreversibility of oedometric compression reported in sands, compared to our model systems, should signal contact plasticity or damage.

Scaling laws for the mechanics of loose and cohesive granular materials based on Baxter's sticky hard spheres

“…This implies that the elastic modulus E, which has dimensions of strain energy per unit volume, should scale linearly with the the number of bonds per unit volume, i.e., with the contact density ν c = z c φ via E ≈ ν μ c (9) with μ = 1, which is exactly the classical result of Walton [42]. The relevance of contact density ν c was recently confirmed by [18] and [7], which showed a significant influence on the elastic moduli. In particular, [18] suggested that ν c should be used as indicator of the internal state of granular packings.…”

“…Similar to the elastic modulus, when plotted against the cohesive contact density ν c,0 = φ 0 z c,0 , all σ c data points collapse on the same curve, which is best described by a power law. By fitting the data we obtain the regression σ c,fit (ν c ) σ t = bν α c , b = 4.1 × 10 −3 , α = 3.04, (7) for the compressive strength of SHS-based cohesive assemblies. Similar to the elastic modulus, we also confirmed (in the Appendix) that the macroscopic compressive strength σ c depended linearly on the bond tensile strength σ t .…”

“…A large amount of work has been done in the past to characterize the mechanics of dense cohesionless materials (e.g., Refs. [1][2][3][4][5][6][7]), mainly in the vicinity of the jamming transition (or the critical state [8]). In contrast, in loose and cohesive granular systems (e.g., [9][10][11][12][13][14]), the mechanical behavior originates from properties of the tenuous, microstructural grain networks that sustain external loads.…”

Numerical study of one-dimensional compression of granular materials. II. Elastic moduli, stresses, and microstructure

“…The first paper [1], hereafter referred to as "Paper I", studies stress-strain relations and describes how state variables evolve in oedometric compression. Paper I clearly shows that the strain-stress relation in oedometric compression or compression cycles is not elastic, but that elastic moduli express stress-strain response in very small probes superimposed on previously well-equilibrated intermediate states, provided a very small creep phase during configuration stabilization has suppressed friction mobilization.…”

Mechanics of randomly packed filaments—The “bird nest” as meta-material

“…When plastic deformation stops, finite hysteresis remains. This persistent energy loss has been attributed to reversible micro-slippage of frictional contacts 34 . The mechanism would be quasi-static, involving static friction.…”