Mean-field stability map of hard-sphere glasses

Abstract

The response of amorphous solids to an applied shear deformation is an important problem, both in fundamental and applied research. To tackle this problem, we focus on a system of hard spheres in infinite dimensions as a solvable model for colloidal systems and granular matter. The system is prepared above the dynamical glass transition density, and we discuss the phase diagram of the resulting glass under compression, decompression, and shear strain, expanding on previous results [P.Urbani and F.Zamponi, Phys.Rev.Lett. 118, 038001 (2017)]. We show that the solid region is bounded by a "shear jamming" line, at which the solid reaches close packing, and a "shear yielding" line, at which the solid undergoes a spinodal instability towards a liquid, flowing phase. Furthermore, we characterize the evolution of these lines upon varying the glass preparation density. This work aims to provide a general overview on yielding and jamming phenomena in hard sphere systems by a systematic exploration of the phase diagram.

A jamming plane of sphere packings

“…In Fig. 11(b), we plot ϕ c (ϕ eq ) for a few different ϕ eq on the HS phase diagram, which is qualitatively consistent with the mean-field result [49]. To avoid confusion we note that Fig.…”

A direct link between active matter and sheared granular systems

“…The limit of infinite dimension provides an exact benchmark to investigate properties of structural glasses ( 14 , 39 ) and has been successfully used, for instance, to study quasistatic shear or compression ( 8 – 14 ). In this framework, we can show that AQS and AQRD are strictly equivalent upon a simple rescaling of the accumulated strain, with a dependence on the correlation length .…”

“…Moreover, the local shear modulus µ, defined as the slope of the stress-strain curve along elastic branches, is significantly different from the macroscopic coarsegrained shear modulus µ global , defined as the ratio of the average stress at yield to the average strain at yield. This observation is directly related to marginal stability (42) and can be qualitatively predicted from infinite-dimensional analytic theory (8)(9)(10)(11)(12)(13)(14).…”

“…Meanwhile, the dynamics of athermal sheared disordered materials, where energy is injected at the largest scale, globally from the boundaries, have been the subject of intense study for decades. A recent breakthrough allows an exact analytic solution for the behavior of slowly sheared systems in infinite dimensions, where interactions are exactly mean field ( 8 – 14 ). These results qualitatively explain many features in sheared two- and three-dimensional glassy solids.…”

“…In this work, we focus on AQRD because simulations and experiments which control strain rate (or displacements) are known to be very useful for characterizing material properties, and so there are a large amount of data in the literature for comparison. We focus on the preyielding regime, corresponding with the “start-up” phase of a simulation or experiment where the response depends strongly on the initial preparation of the material and the infinite-dimensional mean-field equations are solvable ( 8 – 14 , 31 ). In contrast, stress-controlled creep experiments are fundamentally limited because the system can cross only energy barriers which are surmountable by the fixed applied stress, and under slow driving they exhibit complicated discontinuous stick–slip dynamics ( 32 , 33 ).…”