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

F. Léonforte (1) , R. Boissière (1) , Arnaud Tanguy (1) , J.P. Wittmer (2) , J.-L. Barrat (1)

1 LPMCN - Laboratoire de Physique de la Matière Condensée et Nanostructures
2 ICS - Institut Charles Sadron

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 $\xi$.

Domaines: Mécanique statistique [cond-mat.stat-mech]; Science des matériaux [cond-mat.mtrl-sci]; Systèmes désordonnés et réseaux de neurones [cond-mat.dis-nn]

F. Léonforte, R. Boissière, Arnaud Tanguy, J.P. Wittmer, J.-L. Barrat. Continuum limit of amorphous elastic bodies (III): Three dimensional systems. 2005. ⟨hal-00004977⟩