Approximate analytical description of the nonaffine response of amorphous solids
Soft Condensed Matter
2011-08-23 v2 Disordered Systems and Neural Networks
Statistical Mechanics
Abstract
An approximation scheme for model disordered solids is proposed that leads to the fully analytical evaluation of the elastic constants under explicit account of the inhomogeneity (nonaffinity) of the atomic displacements. The theory is in quantitative agreement with simulations for central-force systems and predicts the vanishing of the shear modulus at the isostatic point with the linear law {\mu} ~ (z - 2d), where z is the coordination number. The vanishing of rigidity at the isostatic point is shown to be a consequence of the canceling out of positive affine and negative nonaffine terms.
Keywords
Cite
@article{arxiv.1102.0162,
title = {Approximate analytical description of the nonaffine response of amorphous solids},
author = {Alessio Zaccone and Enzo Scossa-Romano},
journal= {arXiv preprint arXiv:1102.0162},
year = {2011}
}