The approach of the elastic continuum limit in small amorphous bodies formed by weakly polydisperse Lennard-Jones beads is investigated in a systematic finite-size study. We show that classical continuum elasticity breaks down when the wavelength of the sollicitation is smaller than a characteristic length of approximately 30 molecular sizes. Due to this surprisingly large effect ensembles containing up to N = 40, 000 particles have been required in two dimensions to yield a convincing match with the classical continuum predictions for the eigenfrequency spectrum of disk-shaped aggregates and periodic bulk systems. The existence of an effective length scale ξ is confirmed by the analysis of the (non-gaussian) noisy part of the low frequency vibrational eigenmodes. Moreover, we relate it to the non-affine part of the displacement fields under imposed elongation and shear. Similar correlations (vortices) are indeed observed on distances up to ξ ≈ 30 particle sizes.

We analyze in detail the atomistic response of a model amorphous material submitted to plastic shear in the athermal, quasi-static limit. After a linear stress-strain behavior, the system undergoes a noisy plastic flow. We show that the plastic flow is spatially heterogeneous. Two kinds of plastic events occur in the system: quadrupolar localized rearrangements, and shear bands. The analysis of the individual motion of a particle shows also two regimes: a hyper-diffusive regime followed by a diffusive regime, even at zero temperature.