Emergence of linear isotropic elasticity in amorphous and polycrystalline materials

We investigate the emergence of isotropic linear elasticity in amorphous and polycrystalline solids via extensive numerical simulations. show that elastic properties are correlated over a finite length scale ${\ensuremath{\xi}}_{E}$, so central limit theorem dictates continuum on increasing specimen size. The stiffness matrix systems size $L>{\ensuremath{\xi}}_{E}$ is obtained, adding to predicted by random one spectral norm ${(L/{\ensuremath{\xi}}_{E})}^{\ensuremath{-}3/2}$ three spatial dimensions. further demonstrate corresponds structural correlations, which polycrystals reflect typical grain boundaries scales characterizing correlations stress field. finally affects decay anisotropic long-range locally defined shear modulus stress.