Do athermal amorphous solids exist?
Abstract
We study the elastic theory of amorphous solids made of particles with finite range interactions in the thermodynamic limit. For the elastic theory to exist, one requires all the elastic coefficients, linear and nonlinear, to attain a finite thermodynamic limit. We show that for such systems the existence of nonaffine mechanical responses results in anomalous fluctuations of all the nonlinear coefficients of the elastic theory. While the shear modulus exists, the first nonlinear coefficient B_{2} has anomalous fluctuations and the second nonlinear coefficient B_{3} and all the higher order coefficients (which are nonzero by symmetry) diverge in the thermodynamic limit. These results call into question the existence of elasticity (or solidity) of amorphous solids at finite strains, even at zero temperature. We discuss the physical meaning of these results and propose that in these systems elasticity can never be decoupled from plasticity: the nonlinear response must be very substantially plastic.
 Publication:

Physical Review E
 Pub Date:
 June 2011
 DOI:
 10.1103/PhysRevE.83.061101
 arXiv:
 arXiv:1101.0101
 Bibcode:
 2011PhRvE..83f1101H
 Keywords:

 62.20.de;
 61.43.j;
 63.50.x;
 Elastic moduli;
 Disordered solids;
 Vibrational states in disordered systems;
 Condensed Matter  Statistical Mechanics;
 Condensed Matter  Soft Condensed Matter
 EPrint:
 11 pages, 11 figures