  A novel design of an elastic metamaterial with anisotropic mass density is
proposed to manipulate flexural waves at a subwavelength scale. The
three-dimensional metamaterial is inspired by kirigami, which can be easily
manufactured by cutting and folding a thin metallic plate. By attaching the
resonant kirigami structures periodically on the top of a host plate, a
metamaterial plate can be constructed without any perforation that degrades the
strength of the pristine plate. An analytical model is developed to understand
the working mechanism of the proposed elastic metamaterial and the dispersion
curves are calculated by using an extended plane wave expansion method. As a
result, we verify an anisotropic effective mass density stemming from the
coupling between the local resonance of the kirigami cells and the global
flexural wave propagations in the host plate. Finally, numerical simulations on
the directional flexural wave propagation in a two-dimensional array of
kirigami metamaterial as well as super-resolution imaging through an elastic
hyperlens are conducted to demonstrate the subwavelength-scale flexural wave
control abilities. The proposed kirigami-based metamaterial has the advantages
of no-perforation design and subwavelength flexural wave manipulation
capability, which can be highly useful for engineering applications including
non-destructive evaluations and structural health monitoring.
