Force Chains, Microelasticity, and Macroelasticity

It has been claimed that quasistatic granular materials, as well as nanoscale materials, exhibit departures from elasticity even at small loadings. It is demonstrated, using 2D and 3D models with interparticle harmonic interactions, that such departures are expected at small scales [below $\mathcal{O}(100)$ particle diameters], at which continuum elasticity is invalid, and vanish at large scales. The models exhibit force chains on small scales, and force and stress distributions which agree with experimental findings. Effects of anisotropy, disorder, and boundary conditions are discussed as well.