A Linear Strain Energy Function for Hyperelastic Transformation Method

TL;DR

This paper introduces a new linear strain energy function for hyperelastic materials that enables simultaneous control of longitudinal and shear elastic waves, facilitating the design of soft transformation devices.

Contribution

A novel linear strain energy function valid for small deformations is proposed, addressing limitations of existing models for hyperelastic transformation methods.

Findings

The linear SEF effectively controls elastic wave propagation.

Numerical simulations validate the theoretical model.

The approach compares favorably with neo-Hookean and semi-linear SEFs.

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.