A generalized stress-strain relationship is derived for a representative volume of randomly packed particle assembly taking into account the efefct of rigid body rotation. A second-order polynomial function is assumed for the displacement field such that there exists a gradient of rigid body rotation. From the principle of virtual work, the gradient of rigid body rotation is correspondent to a higher-order stress. Along this line, a higher order stress-strain relationship is derived for isotropic packing with equal-sized particles. Material constants for the particulate material are derived in terms of inter-particle particle properties. The highe order stress-strain relationship is useful for mideling material behavior under torsion or bending where the influence of rigid body rotation gradient is significant.
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