2011/02/28 by Alessio Zaccone, Enzo Scossa-Romano · 1 citation
Physics and Astronomy · #cond-mat.soft #cond-mat.dis-nn #cond-mat.stat-mech
paper · pdf · doi:10.1103/physrevb.83.184205
published as Phys. Rev. B 83, 184205 (2011)
arxiv created 2011/08/22 · arxiv updated 2011/08/23
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.