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

Abstract

We have conducted discrete element simulations (pfc3d) of very loose, cohesive, granular assemblies with initial configurations which are drawn from Baxter's sticky hard sphere (SHS) ensemble. The SHS model is employed as a promising auxiliary means to independently control the coordination number z_{c} of cohesive contacts and particle volume fraction ϕ of the initial states. We focus on discerning the role of z_{c} and ϕ for the elastic modulus, failure strength, and the plastic consolidation line under quasistatic, uniaxial compression. We find scaling behavior of the modulus and the strength, which both scale with the cohesive contact density ν_{c}=z_{c}ϕ of the initial state according to a power law. In contrast, the behavior of the plastic consolidation curve is shown to be independent of the initial conditions. Our results show the primary control of the initial contact density on the mechanics of cohesive granular materials for small deformations, which can be conveniently, but not exclusively explored within the SHS-based assembling procedure.

Modeling Snow Failure Behavior and Concurrent Acoustic Emissions Signatures With a Fiber Bundle Model

“…Many current models used for studying snow failure, however, do not consider any healing mechanism or consider only sintering (e.g., Gaume et al, 2017;Reiweger et al, 2009;Steinkogler et al, 2015). Moreover, we showed that if we add viscous deformation and with it load relaxation, the FBM is capable of reproducing the observed loading rate dependence of the snow failure (e.g., larger strain at equal stress, no divergence, and higher τ for low loading rates).…”

Ice Spheres as Model Snow: Tumbling, Sintering, and Mechanical Tests

“…The ice bead samples, in contrast, are rather clustered. Partially this can be explained by looking at the contact density ν c , as resolved in the magnification (Figure 7B), for which an increasing relation with E is expected (Gaume et al, 2017) and seen in the results of the poured samples. For tapped samples, the relation is rather vague, due the uncertainty intervals of all parameters and their small ranges.…”

“…The relation of compressive strength and sintering time (Figure 9) shows the reproducibility of the experiments, despite the large scatter, which however is typical for snow. The requirements for the representative elementary volume (REV) are met for the ice beads with 32 r p and n p ∈ (1, 000, 1, 200) at the lower limit, which was found in 30 r p (Wiacek and Molenda, 2016) or n p ≥ 1, 000 particles (Gaume et al, 2017). In contrast, the requirements are clearly fulfilled for the RG snow samples.…”

“…To demonstrate the reproducibility of the ice bead structures, we determined the number of particles n p , the number of bonds n b and the ice volume fraction φ as structural parameters from the CT images, Table 2. From these values we calculated the contact density ν c = φZ c , as used by Gaume et al (2017), with the coordination number Z c = 2n b /n p . For all samples these values, normalized by the mean of the respective sample class, are shown in Figure 5A, for the poured (left) and tapped beads (middle).…”

“…The remaining difficulty is then to map the experimental microstructures onto a sphere assembly that captures properties of real snow. The existing approaches include e.g., generic (ballistic) deposition models (Mulak and Gaume, 2019) or configurations drawn from Baxter's sticky hard spheres (Gaume et al, 2017). While these approaches capture some aspects of the microstructure, they do not overcome the complex shape of the snow crystals that affects the particle interactions, and thus the mechanical response is strongly simplified.…”