Emergence of linear elasticity from the atomistic description of matter

TL;DR

This paper explores how continuum elasticity emerges from atomistic models at zero temperature, highlighting the roles of disorder and vibrational modes in the transition.

Contribution

It provides a unifying numerical framework linking atomistic details to continuum elastic behavior through disorder and vibrational length scales.

Findings

Continuum elastic limit depends on disorder and vibrational length scale.

Long-range shear stress and strain correlations develop with disorder.

Fluctuations of local elastic constants are influenced by vibrational modes.

Abstract

We investigate the emergence of the continuum elastic limit from the atomistic description of matter at zero temperature considering how locally defined elastic quantities depend on the coarse graining length scale. Results obtained numerically investigating different model systems are rationalized in a unifying picture according to which the continuum elastic limit emerges through a process determined by two system properties, the degree of disorder, and a length scale associated to the transverse low-frequency vibrational modes. The degree of disorder controls the emergence of long-range local shear stress and shear strain correlations, while the transverse length scale influences the amplitude of the fluctuations of the local elastic constants.