Covariant gradient continua applied to wave propagation within defective material

Abstract

Riemann–Cartan geometry is used to model continuum with defects. In order to illustrate the differences induced by two possible definitions for the strain (spatial or material) in this framework, propagation of waves is studied for a simple example of infinite continuum with uniform and stationary defects density. Anisotropy and attenuation are caught by both models even if these effects are quite different. Furthermore, the spatial strain does not allow some polarizations, whereas the material one induces chirality and uniform breathing vibrations.