A general constitutive model for dense, fine-particle suspensions validated in many geometries
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Abstract:
Fine-particle suspensions (such as cornstarch mixed with water) exhibit dramatic changes in viscosity when sheared, producing fascinating behaviors that captivate children and rheologists alike. Examination of these mixtures in simple flow geometries suggests intergranular repulsion and its influence on the frictional nature of granular contacts is central to this effect-for mixtures at rest or shearing slowly, repulsion prevents frictional contacts from forming between particles, whereas when sheared more forcefully, granular stresses overcome the repulsion allowing particles to interact frictionally and form microscopic structures that resist flow. Previous constitutive studies of these mixtures have focused on particular cases, typically limited to 2D, steady, simple shearing flows. In this work, we introduce a predictive and general, 3D continuum model for this material, using mixture theory to couple the fluid and particle phases. Playing a central role in the model, we introduce a microstructural state variable, whose evolution is deduced from small-scale physical arguments and checked with existing data. Our space- and time-dependent model is implemented numerically in a variety of unsteady, nonuniform flow configurations where it is shown to accurately capture a variety of key behaviors: 1) the continuous shear-thickening (CST) and discontinuous shear-thickening (DST) behavior observed in steady flows, 2) the time-dependent propagation of "shear jamming fronts," 3) the time-dependent propagation of "impact-activated jamming fronts," and 4) the non-Newtonian, "running on oobleck" effect, wherein fast locomotors stay afloat while slow ones sink.Keywords:
Shearing (physics)
Dilatant
Dilatant
Void ratio
Statically indeterminate
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Dilatant
Void ratio
Void (composites)
Triaxial shear test
Material Point Method
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The discrete-element method (DEM) has gained popularity for developing a qualitative understanding of soil behaviour under a critical state soil mechanics (CSSM) framework. Most studies with a three-dimensional assembly of particles have used spheres as representative granular material to reduce computational demands. However, most granular materials – for example, sands – are not rounded, but possess features of angularity. Therefore, ellipsoid and cluster particles with different degrees of eccentricity were used in this study to evaluate the effect of the particle shape on the drained and undrained triaxial loading behaviour after isotropic and K 0 consolidation. The particle numerical properties and grain size distributions were kept the same for all specimens, irrespective of particle shape. The critical state data points for spheres and ellipsoids plotted on almost the same critical state line (CSL) in e–log(p′) space, whereas the CSLs of clusters plotted above them. Additionally, M lines shifted downward with increasing sphericity. It was also found that the stress ratio at the triggering of static liquefaction (η IS = q/p′) in η IS –ψ space was affected by particle shape and consolidation path. The dilatancy (d = dε v p /dε q p ) was also affected by particle shape. It was found that dilatancy parameters for the SANISAND constitutive model are affected by particle shape, which may contribute to an improved understanding of particle shape in constitutive modelling.
Dilatant
Void ratio
Consolidation
Sphericity
Particle (ecology)
Stress path
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Citations (52)