Effects of polydispersity on the plastic behaviors of dense two-dimensional granular systems under shear.

We study particle-scale motion in sheared highly polydisperse amorphous materials, in which the largest particles are as much as ten times the size of the smallest. We find strikingly different behavior from the more commonly studied amorphous systems with low polydispersity. In particular, an analysis of the nonaffine motion of particles reveals qualitative differences between large and small particles: The smaller particles have dramatically more nonaffine motion, which is induced by the presence of the large particles. We characterize how the nonaffine motion changes from the low- to high-polydispersity regimes. We further demonstrate a quantitative way to distinguish between "large" and "small" particles in systems with broad distributions of particle sizes. A macroscopic consequence of the nonaffine motion is a decrease in the energy dissipation rate for highly polydisperse samples, which is due both to a geometric consequence of the changing jamming conditions for higher polydispersity and to the changing character of nonaffine motion.

Isomorphs in sheared binary Lennard-Jones glass: Transient response.

We have studied shear deformation of binary Lennard-Jones glasses to investigate the extent to which the transient part of the stress strain curves is invariant when the thermodynamic state point is varied along an isomorph. Shear deformations were carried out on glass samples of varying stability, determined by cooling rate, and at varying strain rates, at state points deep in the glass. Density changes up to and exceeding a factor of two were made. We investigated several different methods for generating isomorphs but none of the previously developed methods could generate sufficiently precise isomorphs given the large density changes and nonequilibrium situation. Instead, the temperatures for these higher densities were chosen to give state points isomorphic to the starting state point by requiring the steady-state flow stress for isomorphic state points to be invariant in reduced units. In contrast to the steady-state flow stress, we find that the peak stress on the stress strain curve is not invariant. The peak stress decreases by a few percent for each ten percent increase in density, although the differences decrease with increasing density. Analysis of strain profiles and nonaffine motion during the transient phase suggests that the root of the changes in peak stress is a varying tendency to form shear bands, with the largest tendency occurring at the lowest densities. We suggest that this reflects the effective steepness of the potential; a higher effective steepness gives a greater tendency to form shear bands.

Isomorph invariance of dynamics of sheared glassy systems.

We study hidden scale invariance in the glassy phase of the Kob-Andersen binary Lennard-Jones system. After cooling below the glass transition, we generate a so-called isomorph from the fluctuations of potential energy and virial in the NVT ensemble: a set of density, temperature pairs for which structure and dynamics are identical when expressed in appropriate reduced units. To access dynamical features, we shear the system using the SLLOD algorithm coupled with Lees-Edwards boundary conditions and study the statistics of stress fluctuations and the particle displacements transverse to the shearing direction. We find good collapse of the statistical data, showing that isomorph theory works well in this regime. The analysis of stress fluctuations, in particular the distribution of stress changes over a given strain interval, allows us to identify a clear signature of avalanche behavior in the form of an exponential tail on the negative side. This feature is also isomorph invariant. The implications of isomorphs for theories of plasticity are discussed briefly.