Shear-transformation-zone theory of linear glassy dynamics

Abstract

We present a linearized shear-transformation-zone (STZ) theory of glassy dynamics in which the internal STZ transition rates are characterized by a broad distribution of activation barriers. For slowly aging or fully aged systems, the main features of the barrier-height distribution are determined by the effective temperature and other near-equilibrium properties of the configurational degrees of freedom. Our theory accounts for the wide range of relaxation rates observed in both structural glasses and soft glassy materials such as colloidal suspensions. We find that the frequency dependent loss modulus is not just a superposition of Maxwell modes. Rather, it exhibits an α peak that rises near the viscous relaxation rate and, for nearly jammed, glassy systems, extends to much higher frequencies in accord with experimental observations. We also use this theory to compute strain recovery following a period of large, persistent deformation and then abrupt unloading. We find that strain recovery is determined in part by the initial barrier-height distribution, but that true structural aging also occurs during this process and determines the system's response to subsequent perturbations. In particular, we find by comparison with experimental data that the initial deformation produces a highly disordered state with a large population of low activation barriers, and that this state relaxes quickly toward one in which the distribution is dominated by the high barriers predicted by the near-equilibrium analysis. The nonequilibrium dynamics of the barrier-height distribution is the most important of the issues raised and left unresolved in this paper.

Electrostatic precursors to granular slip events

“…The role of defects in the inception of slip events has previously been documented in studies of grains and colloids (31,32), in models of earthquake dynamics (33), and in research into disorder transitions in a broad range of glassy materials (34). The hypothesis engendered by the present work is that the initiation of these defects precedes large slip events, and that the formation of defects in powder beds produces distinctive voltage spikes.…”

Two-state model to describe the rheological behavior of vibrated granular matter

“…In particular, granular media behave either as solids or liquids, depending on the mechanical solicitations to which they are subjected. Still, recently developed mesoscopic models, such as SGR, STZ, or MCT [1][2][3][4], that capture some of the flow and deformation features of amorphous materials are not able to account for all experimentally observed rheological behaviors of flowing granular matter [5][6][7][8]. This is certainly linked to the discrete, macroscopic nature of granular materials.…”

Shear-transformation-zone theory of yielding in athermal amorphous materials

“…The STZ equations of motion that determine these behaviors are subject to constraints imposed by the first and second laws of thermodynamics. This theory has been discussed extensively in the literature [10,17] along with its applications to shear banding [18], fracture toughness [19], oscillatory viscoelasticity [20], and the like. In what follows, I briefly summarize the main features of the STZ 1539-3755/2015/92(1)/012318 (7) 012318-1 ©2015 American Physical Society theory without repeating detailed derivations.…”