A generalized constitutive relation for a randomly packed particle assembly

Abstract A generalized stress-strain relationship is derived for a randomly packed particle assembly taking into account the effect of particle rotation. A second-order polynomial function is assumed for the field of particle displacement. From the principle of virtual work, stress measures for a granular solid are expressed in terms of contact forces, contact moments, and geometric measures for the particle structure. An explicit stress-strain relationship is derived for isotropic packing with equal-sized particles. Examples of a representative element under torsion and bending are given to demonstrate the applicability of the presently derived higher-order stress-strain relationship.