  Hyperelastic transformation method provides a promising approach to
manipulate elastic waves by utilizing soft materials. However, no existing
constitutive model can rigorously achieve the requirement of such method. In
this Letter, a linear strain energy function (SEF) which is valid for small
deformation is proposed, which can be implemented to control the longitudinal
and shear elastic waves simultaneously. In comparison with the neo-Hookean and
the semi-linear SEFs, the wave propagation and the impedance of pre-deformed
linear hyperelastic material are exploited. Numerical simulations are performed
to validate the theoretical results. The investigation may pave the ways for
the design and realization of soft transformation devices.
