Continuum limit of amorphous elastic bodies. III. Three-dimensional systems
By Fabien Léonforte, R. Boissière, A. Tanguy, J. Wittmer, J. Barrat. 2005
197 citations recorded by the source corpus.
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 $\xi$, 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 $\xi$.
Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics, Materials Chemistry
View Paper: https://www.semanticscholar.org/paper/81e1e39091083c1ce405c5f6c9d085985358b5a1
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In Atomic and Molecular Physics, and Optics
In Materials Chemistry
Citations in the corpus
- A novel atomistic approach to determine strain-gradient elasticity constants: Tabulation and comparison for various metals, semiconductors, silica, polymers and the (Ir) relevance for nanotechnologies (2007, result): “These observations agree well with existing literature at hand (Ding et al., 2001; Espinosa et al., 2003; Lam et al., 2003; McFarland and Colton, 2005; Leonforte et al., 2005, 2006 ).”
- Modeling the mechanics of amorphous solids at different length scale and time scale (2011, background): “Here, δγ , the elementary strain step, is chosen small enough to ensure that the system remains in its initial basin when starting from any equilibrium configuration (δγ depends on the system size, probably logarithmically [147] and is on the order of 10−5 for L = 100 in LJ units in 2 and 3 dimensio”