On the route to shear jamming, are fragile states real?

Abstract: Starting from an unjammed initial state, applying shear to a granular material of a fixed packing fraction below $\phi_J$, i.e. the isotropic jamming density of frictionless spheres can produce shear jamming states, as have been discovered recently. In addition, it has also been discovered that the system will first experience a bulk fragile state before evolving into a shear jammed state. Due to the existence of friction between the system and the third dimension in the previous studies, it is unclear whether such fragile state would still exist on the route to shear jamming if the friction with the third dimension were completely eliminated and the background noise level were greatly reduced. Using a novel apparatus, we have completely eliminated the friction between particles and the third dimension by floating the particles on the surface of a shallow water layer thus revealing more details of the route of shear-jamming. We are able to measure weak boundary pressure of three orders of magnitude below the resolution of the photo-elastic method through the combination force-gauges of high sensitivity and a cantilever-like simple-beam apparatus. In a system with weak cohesion, we have indeed observed the bulk fragile states before the shear jamming; in addition, we have also discovered the boundary fragile states and regimes of negligible shear modus compared to bulk modulus. Most importantly, we now have a much better understanding of the bulk fragile state: its existence requires an auxiliary in some form, e.g. the weak cohesion in this experiment. By constructing a way to freely tune down the cohesion to more than six orders of magnitude smaller, to our surprise, we have discovered the complete vanishing of the bulk fragile states, which thus allows us to determine the plausible origin of the bulk fragile state.