Riemann-Cartan geometry as a framework for modeling dispersive waves in solids

We discuss some concept from the Riemann-Caran geometry such as tetrads and torsion in application to modeling propagation of dispersive waves in microstructured solids. The governing PDEs represent non-classical dispersive equations of hyperbolic type with reversible relaxation source terms. A plane-wave analysis reveals a complete frequency band-gap in such a model. A possible application of the equations to modeling acoustic metamaterials is discussed.