Approximate analytical description of the nonaffine response of amorphous solids
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 μ~(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.
- Publication:
-
Physical Review B
- Pub Date:
- May 2011
- DOI:
- 10.1103/PhysRevB.83.184205
- arXiv:
- arXiv:1102.0162
- Bibcode:
- 2011PhRvB..83r4205Z
- Keywords:
-
- 62.20.de;
- 63.50.Lm;
- 81.05.Kf;
- 83.80.Fg;
- Elastic moduli;
- Glasses and amorphous solids;
- Glasses;
- Granular solids;
- Condensed Matter - Soft Condensed Matter;
- Condensed Matter - Disordered Systems and Neural Networks;
- Condensed Matter - Statistical Mechanics
- E-Print:
- Phys. Rev. B 83, 184205 (2011)