Breakdown of continuum elasticity in amorphous solids

Abstract

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.

8 pages, 6 figures