Abstract
Jamming/un-jamming, the transition between solid- and fluid-like behavior in granular matter, is an ubiquitous phenomenon in need of a sound understanding. As argued here, in addition to the usual un-jamming by vanishing pressure due to a decrease of density, there is also yield (plastic rearrangements and un-jamming that occur) if, e.g., for given pressure, the shear stress becomes too large. Similar to the van der Waals transition between vapor and water, or the critical current in superconductors, we believe that one mechanism causing yield is by the loss of the energy’s convexity (causing irreversible re-arrangements of the micro-structure, either locally or globally). We focus on this mechanism in the context of granular solid hydrodynamics (GSH), generalized for very soft materials, i.e., large elastic deformations, employing it in an over-simplified (bottom-up) fashion by setting as many parameters as possible to constant. Also, we complemented/completed GSH by using various insights/observations from particle simulations and calibrating some of the theoretical parameters—both continuum and particle points of view are reviewed in the context of the research developments during the last few years. Any other energy-based elastic-plastic theory that is properly calibrated (top-down), by experimental or numerical data, would describe granular solids. But only if it would cover granular gas, fluid, and solid states simultaneously (as GSH does) could it follow the system transitions and evolution through all states into un-jammed, possibly dynamic/collisional states—and back to elastically stable ones. We show how the un-jamming dynamics starts off, unfolds, develops, and ends. We follow the system through various deformation modes: transitions, yielding, un-jamming and jamming, both analytically and numerically and bring together the material point continuum model with particle simulations, quantitatively.Graphic abstract
Highlights
The macroscopic Navier-Stokes equations allow one to describe Newtonian fluids with constant transport coefficients
Some open questions are: How can we understand phenomena that originate from the particle- or meso-scale, which is intermediate between atoms and the macroscopic, hydrodynamic scale? And how can we formulate a theoretical framework that takes the place of the Navier-Stokes equations?
We present a review of granular solid hydrodynamics (GSH) and new constitutive relations based on particle simulations, as well as a minimalist version, in Sect. 3, allowing for analytic solutions in Sect. 4, and numeric calculations to catch some transitions in Sect
Summary
The macroscopic Navier-Stokes equations allow one to describe Newtonian fluids with constant transport coefficients (e.g., viscosity). In many non-Newtonian systems, complex fluids [1], colloidal suspensions, review [2,3,4], and especially granular matter [5] in its flowing state [6], the transport coefficients depend on various state-variables such as the density and the granular temperature [7]. The research on granular matter in the last decades—to a good fraction inspired by works of Bob Behringer and co-workers—will be briefly reviewed
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