%0 Journal Article
%T Breakdown of continuum elasticity in amorphous solids
%A Edan Lerner
%A Eric DeGiuli
%A Gustavo D¨ıring
%A Matthieu Wyart
%J Physics
%D 2013
%I arXiv
%X We show numerically that the response of simple amorphous solids (elastic networks and particle packings) to a local force dipole is characterized by a lengthscale $\ell_c$ that diverges as unjamming is approached as $\ell_c \sim (z - 2d)^{-1/2}$, where $z \ge 2d$ is the mean coordination, and $d$ is the spatial dimension, at odds with previous numerical claims. We also show how the magnitude of the lengthscale $\ell_c$ is amplified by the presence of internal stresses in the disordered solid. Our data suggests a divergence of $\ell_c\sim (p_c-p)^{-1/4}$ with proximity to a critical internal stress $p_c$ at which soft elastic modes become unstable.
%U http://arxiv.org/abs/1312.2146v1