Mapping acoustical activity in 3D chiral mechanical metamaterials onto micropolar continuum elasticity

Abstract

We compare the phonon band structures and chiral phonon eigenmodes of a recently experimentally realized three-dimensional (3D) cubic chiral metamaterial architecture to results from linear micropolar elasticity, an established generalization of classical linear Cauchy elasticity. We achieve very good qualitative agreement concerning the anisotropies of the eigenfrequencies, the anisotropies of the eigenmode properties of the acoustic branches, as well as with respect to the observed pronounced sample-size dependence of acoustical activity and of the static push-to-twist conversion effects. The size dependence of certain properties, that is, the loss of scale invariance, is a fingerprint of micropolar elasticity. We also discuss quantitative shortcomings and conceptual limitations of mapping the properties of finite-size 3D chiral mechanical metamaterials onto micropolar continuum elasticity.