First lecture on micropolar chiral elasticity

In this lecture, I will introduce some basics of micropolar continuum elastic theory and its applications to the continuum modeling of chiral elastic metamaterials. Due to mirror symmetry breaking, chiral elastic metamaterials can exhibit interesting properties impossible within achiral ones, such as static push-to-twisting coupling and dynamic chiral phonons or acoustical activity. With the examples, one can see micropolar continuum theory can correctly describe the above behavior as well as related size effects. In traditional chiral metamaterials, mostly with cubic symmetry, chiral phonons and acoustical activity are allowed only along several phonon propagation directions. Chiral elastic metamaterials that support isotropic chiral phonons are preferred in practical applications. Here, chiral elastic metamaterials with isotropic properties are designed based on quasicrystalline lattice and periodic cubic lattice. Both designs are verified numerically by phonon band structure calculations.