Continuum limit of amorphous elastic bodies (III): Three dimensional systems

F. Léonforte; R. Boissière; A. Tanguy; J. P. Wittmer; J. -L. Barrat

doi:10.1103/physrevb.72.224206

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Continuum limit of amorphous elastic bodies (III): Three dimensional systems

F. Léonforte·R. Boissière·A. Tanguy·J. P. Wittmer·J. -L. Barrat

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Abstract

Extending recent numerical studies on two dimensional amorphous bodies, we characterize the approach of elastic continuum limit in three dimensional (weakly polydisperse) Lennard-Jones systems. While performing a systematic finite-size analysis (for two different quench protocols) we investigate the non-affine displacement field under external strain, the linear response to an external delta force and the low-frequency harmonic eigenmodes and their density distribution. Qualitatively similar behavior is found as in two dimensions. We demonstrate that the classical elasticity description breaks down below an intermediate length scale $ξ$, which in our system is approximately 23 molecular sizes. This length characterizes the correlations of the non-affine displacement field, the self-averaging of external noise with distance from the source and gives the lower wave length bound for the applicability of the classical eigenfrequency calculations. We trace back the "Boson-peak" of the density of eigenfrequencies (obtained from the velocity auto-correlation function) to the inhomogeneities on wave lengths smaller than $ξ$.

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F. Léonforte, R. Boissière, A. Tanguy, J. P. Wittmer, J. -L. Barrat. 2005-05-25. Continuum limit of amorphous elastic bodies (III): Three dimensional systems. https://doi.org/10.1103/physrevb.72.224206

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