A Linear Strain Energy Function for Hyperelastic Transformation Method

Abstract

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.