Determining material constants in micromorphic theory through phonon dispersion relations

This paper aims to determine the material constants for micromorphic isotropic elastic solid through the phonon dispersion relations from atomistic calculations or experimental measurements. A specialized micromorphic theory for crystal without external modes, such as covalent and ionic crystals, is introduced. The constitutive relations for cubic crystal are derived, and the phonon dispersion relations are obtained. The numerical algorithm to determine the material constants is presented. The material constants for single crystal silicon and diamond are determined and presented