Waves in continua with extreme microstructures

Abstract

The effective properties of a material may be generally defined as those that describe the limiting case where the wavelength of propagation is infinite compared to the characteristic scale of the microstructure. Generally, the limit of vanishingly small microstructural scale in a heterogeneous elastic medium results in an effective homogeneous medium that is again elastic. We show that for materials with extreme microstructures, the limiting effective medium can be quite exotic, including polar materials, or multiphase continuum. These continuum models naturally give rise to unusual effective properties including negative or anisotropic mass. Though unusual, these properties have straightforward interpretations in terms of the laws of classical mechanics. Finally, we discuss wave propagation in these structures and find dispersion curves with multiple branches.