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Continuum limit of amorphous elastic bodies: A finite-size study of low frequency harmonic vibrations

A. Tanguy·J. P. Wittmer·F. Leonforte·J. -L. Barrat
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Abstract

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 ξis confirmed by the analysis of the (non-gaussian) noisy part of the low frequency vibrational eigenmodes. Moreover, we relate it to the {\em 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.

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A. Tanguy, J. P. Wittmer, F. Leonforte, J. -L. Barrat. 2002-04-11. Continuum limit of amorphous elastic bodies: A finite-size study of low frequency harmonic vibrations. https://doi.org/10.1103/physrevb.66.174205

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