Determining material constants in nonlocal micromorphic theory through phonon dispersion relations

This paper aims to determine the material constants in nonlocal micromorphic theory through phonon dispersion relations. The nonlocal constitutive relations for isotropic elastic solids in micromorphic theory are derived. The numerical algorithm to determine the material constants is presented. The material constants for single crystal silicon and diamond in local and nonlocal micromorphic theory are determined by fitting the phonon dispersion relations obtained from atomistic calculations or experimental measurements. The solutions of the local micromorphic theory can only fit those dispersion relations well in half Brillouin zone, while it is found that the nonlocal solutions are in very good agreement with the lattice dynamic results throughout the entire Brillouin zone. The applicability of nonlocal micromorphic theory is discussed.