Effects of Nonaffinity on Jammed Materials

If an amorphous solid such as a jammed particle system is subjected to an external stress, the induced displacements of internal particles are necessarily nonaffine. Using numerical minimization procedures, we investigate the response to stress of a disordered packing of purely repulsive spheres. We calculate the correlations of the nonaffine part of the displacements of individual particles just above the jamming threshold (point J)\footnote{C.S.~O'Hern, L.E.~Sibert, A.J.~Liu, and S.R.~Nagel, Phys.\ Rev.\ E {\bf 68}, 011306 (2003)}. We find that these correlations are consistent with those predicted by a continuum theory and verified numerically in simple model random elastic systems\footnote{ B.~DiDonna and T.C.~ Lubensky, Phys.Rev.\ E (to be published)}.