Examining the physical foundation of continuum theories from the viewpoint of phonon dispersion relation

Abstract

An overview of crystal types and their interatomic force models are given and the basic feature of the dynamics of atoms in crystal is introduced. Elastic waves described by classical continuum theory, phonon dispersion relations by micromorphic theory, micropolar theory, couple stress theories and nonlocal theory are calculated and presented. The physical foundation and the applicability are examined from the viewpoint of phonon dispersion relation. Two physical examples, including the apparent change of material constants at different length scales and the macroscopic phenomenon of piezoelectricity are discussed.