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Register a new userScaling Law for Cracking in Shrinkable Granular Packings
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Hydrated granular packings often crack into discrete clusters of grains when dried. Despite its ubiquity, accurate prediction of cracking remains elusive. Here, we elucidate the previously overlooked role of individual grain shrinkage---a feature common to many materials---in determining crack patterning using both experiments and simulations. By extending the classical Griffith crack theory, we obtain a scaling law that quantifies how cluster size depends on the interplay between grain shrinkage, stiffness, and size---applicable to a diverse array of shrinkable, granular packings.
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Many clays, soils, biological tissues, foods, and coatings are shrinkable, granular materials: they are composed of packed, hydrated grains that shrink when dried. In many cases, these packings crack during drying, critically hindering applications. However, while cracking has been widely studied for bulk gels and packings of non-shrinkable grains, little is known about how packings of shrinkable grains crack. Here, we elucidate how grain shrinkage alters cracking during drying. Using experiments with model shrinkable hydrogel beads, we show that differential shrinkage can dramatically alter crack evolution during drying---in some cases, even causing cracks to spontaneously self-close. In other cases, packings shrink without cracking or crack irreversibly. We developed both granular and continuum models to quantify the interplay between grain shrinkage, poromechanics, packing size, drying rate, capillarity, and substrate friction on cracking. Guided by the theory, we also found that cracking can be completely altered by varying the spatial profile of drying. Our work elucidates the rich physics underlying cracking in shrinkable, granular packings, and yields new strategies for controlling crack evolution.
It is demonstrated, by numerical simulations of a 2D assembly of polydisperse disks, that there exists a range (plateau) of coarse graining scales for which the stress tensor field in a granular solid is nearly resolution independent, thereby enabling an `objective definition of this field. Expectedly, it is not the mere size of the the system but the (related) magnitudes of the gradients that determine the widths of the plateaus. Ensemble averaging (even over `small ensembles) extends the widths of the plateaus to sub-particle scales. The fluctuations within the ensemble are studied as well. Both the response to homogeneous forcing and to an external compressive localized load (and gravity) are studied. Implications to small solid systems and constitutive relations are briefly discussed.
Based on discrete element method simulations, we propose a new form of the constitution equation for granular flows independent of packing fraction. Rescaling the stress ratio $mu$ by a power of dimensionless temperature $Theta$ makes the data from a wide set of flow geometries collapse to a master curve depending only on the inertial number $I$. The basic power-law structure appears robust to varying particle properties (e.g. surface friction) in both 2D and 3D systems. We show how this rheology fits and extends frameworks such as kinetic theory and the Nonlocal Granular Fluidity model.
Due to high viscosity, glassy systems evolve slowly to the ordered state. Results of molecular dynamics simulation reveal that the structural ordering in glasses becomes observable over experimental (finite) time-scale for the range of phase diagram with high values of pressure. We show that the structural ordering in glasses at such conditions is initiated through the nucleation mechanism, and the mechanism spreads to the states at extremely deep levels of supercooling. We find that the scaled values of the nucleation time, $tau_1$ (average waiting time of the first nucleus with the critical size), in glassy systems as a function of the reduced temperature, $widetilde{T}$, are collapsed onto a single line reproducible by the power-law dependence. This scaling is supported by the simulation results for the model glassy systems for a wide range of temperatures as well as by the experimental data for the stoichiometric glasses at the temperatures near the glass transition.
For packings of hard but not perfectly rigid particles, the length scales that govern the packing geometry and the contact forces are well separated. This separation of length scales is explored in the force network ensemble, where one studies the space of allowed force configurations for a given, frozen contact geometry. Here we review results of this approach, which yields nontrivial predictions for the effect of packing dimension and anisotropy on the contact force distribution $P(f)$, the response to overall shear and point forcing, all of which can be studied in great numerical detail. Moreover, there are emerging analytical approaches that very effectively capture, for example, the form of force distributions.
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