NONLINEAR DISPERSION OF PLANE-WAVE IN GRANULAR MEDIA

A high-gradient elastic stress-strain model that accounts for the effects of gradient of strain and gradient of rigid body rotation is presented. The present model is distinct from its micromechanics approach; the constitutive coefficients are expressed as explicit functions of inter-particle stiffness and particle size. The stress-strain model is then applied to analyze the propagation of plane waves in granular media. The present stress-strain model leads to a phenomenon of non-linear dispersion of waves. The dispersion relations derived from the present high-gradient model for granular media are compared with those from crystal lattice models and non-local models. Links among the present model, crystal lattice model. and non-local model are discussed. According to the derived dispersion relations, the granular material is a natural filter, in which short-length waves and high-frequency waves cannot transmit through. The effects of inter-particle stiffness and particle size on the admissible range of wave lengths and frequencies are also discussed.