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.
Highlights
Identifying microstructural controls of macroscopic material behavior is key for the understanding, upscaling, and modeling of heterogenous or disordered materials
When plotted against the contact density νc,0 = φ0zc,0, all data points collapse on the same master curve that can be well described by a power law
Similar to the elastic modulus, we showed that σc scales with the initial contact density according to a power law with an exponent close to 3, independent of the bond radius [cf. sensitivity analysis in the Appendix, Fig. 13(b)]
Summary
Identifying microstructural controls of macroscopic material behavior is key for the understanding, upscaling, and modeling of heterogenous or disordered materials. The exact influence of volume fraction φ and coordination number zc is, difficult to assess, partly due to the lack of analytical approximations available for rule-based definitions of the assembling procedures for initial states Along these lines it has been previously suggested [19] that Baxter’s model of sticky hard spheres (SHS) [20] is an interesting candidate to address generic questions of disordered materials from a particle-based perspective. As mentioned in [25], the PY approximation does “remarkably well” for the coordination number as the key microstructural descriptor of granular systems It is the aim of the present paper to exploit the properties of SHS assemblies to discuss the influence of volume fraction φ and coordination number zc on the elasticity and strength of loose and cohesive granular materials. We believe that our simulations help to pinpoint the unifying aspects of mechanics, failure, and rheology of heterogeneous, foamlike, granular, and soft matter [29,30]
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