A characteristic length scale in confined elastic buckling of a force chain

We examine the confined elastic buckling of a single N-particle force chain. For a given set of material parameters, a characteristic load-carrying capacity is attained for a clearly defined range of force chain lengths N a parts per thousand yen L*. The rotation and translation of particles along periodically located segments of the critical buckling mode, each of length L*, are on average consistent with those for particles inside the shear band. Preliminary results from postbuckling analysis show that the critical buckling mode is unstable and that buckling culminates in a localized response over one of these segments where observed shear band kinematics prevail. Thus, the localized buckling response is characterized by the rotation of a finite number of particles with a clearly defined length L*. For a wide range of material properties, L* is around eight particle diameters-the observed shear band thickness for many granular materials, most notably sand.