  Hyperelastic transformation theory has proven shear-wave manipulation devices
with various functions can be designed by utilizing neo-Hookean material with
appropriate pre-deformation. However, it is still elusive that how can such
devices match with the background medium in which they embedded. In this work,
we present a systematic formulation of the transmission and reflection of
elastic waves at the interface between un-deformed and pre-deformed
hyperelastic materials. With the combination of theoretical analyses and
numerical simulations, we specifically investigate the shear-wave propagation
from an un-deformed neo-Hookean material to the one subject to different
homogeneous deformations. Among three typical deformation modes, we found
"constrained" uniaxial tension and simple shear guarantee total transmission,
whereas "ordinary" uniaxial tension and hydrostatic compression cause wave
reflection. On this basis, three embedded shear-wave manipulation devices,
including a unidirectional cloak, a splicable beam bend, and a concave lens,
are proposed and verified through numerical simulations. This work may pave the
way for the design and realization of soft-matter-based wave control devices.
Potential applications can be anticipated in nondestructive testing, structure
impact protection, biomedical imaging, and soft robotics.
