Dispersion Analysis of Wave Propagation in Cubic--Tetrahedral Assembly by Doublet Mechanics

Based on elongation and shear microstrains between the doublet particles, we present the dynamic scaling equations of plane wave propagation in a cubic-tetrahedral assembly (lattice type H₄) in accordance with the formalism of doublet mechanics (DM). The relations between the micro-moduli of DM constitutions and the macro-parameters of the Cosserat continuum model are obtained by a mapping process and a non-scale approximation of the DM model. With multi-scale characteristics, the frequency dispersion curves from DM reflect the effect of granule inhomogeneity and the anisotropic nature of the micro-structure on the wave propagation in the H₄ medium.