Towards a universal theory for fluid AND solid mechanics.
Jamming/un-jamming, the transition between solid- and fluid-like behavior in granular matter, is an ubiquitous phenomenon in need of a sound understanding. In addition to the usual un-jamming by vanishing pressure due to a decrease of density, there is also yield (plastic, irreversible shear rearrangements) if, for a given pressure, the shear stress becomes too large. Similar to the van der Waals transition between vapor and water, we believe that another mechanism causing yield is the loss of the energy’s convexity (causing isotropic modes with irreversible rearrangements of the micro-structure, both locally and globally).
We focus on the jamming/unjamming mechanisms in the context of the constitutive theoretical framework granular solid hydrodynamics (GSH), generalized for very soft materials. We also complemented/completed GSH+ by using various insights and observations from particle simulations and calibrating some of their theoretical parameters — from both continuum and particle points of view. This GSH+ energy-potential-based elastic-plastic theory, properly calibrated by either experimental or numerical data, can describe granular solids as well as fluids and the various transitions between these states. Not only describing granular gas, fluid, and solid states simultaneously (as basic GSH does) it can follow the system transitions and evolution through all states from jammed into un-jammed, possibly dynamic/collisional states — and back to elastically stable situations.
In the figure, the states from gas to fluid to solid are sketched, with the respective kinetic-to-potential energy ratio K transiting from very large to very small along the states. The fundamental theoretical challenge is a stochastic, quasi-static component that adds to the kinetic fluctuation energy density, which makes the interpretation and theoretical modeling interesting.
We can model how the un-jamming dynamics starts off, unfolds, develops, and ends, both analytically and numerically, and bring together this material-point continuum model with particle simulations quantitatively. Finishing this calibration with DEM is one of the ongoing projects, while the merging of the stochastic local instabilities into the universal continuum model GSH++ is a challenge for the future.
Persons involved
