A Higher-Order Continuum Model for Elastic Media with Multiphased Microstructure

Abstract

The conventional continuum theory is inadequate for modeling materials with microstructures when the characteristic dimension of the microstructure is comparable to the characteristic length of deformation or wave length. In this paper, a systematic procedure was introduced to construct higher-order microstructure continuum theories. A microstructure continuum theory that employs separate kinematic variables for individual phases of the microstructure was used to study wave propagation in layered media. Further, correction factors were introduced to compensate for the errors resulting from the displacement approximation adopted in developing the high order microstructure continuum theory and to ensure that, at long wave lengths, the phase velocity predicted by the microstructure theory converges to the exact solution. For comparison purposes, dispersion curves for wave propagation in layered media were also calculated using the micromorphic continuum theory which employs only one kinematic variable for materials with multi-phased microstructures.