Stable Band-Gaps in Phononic Crystals by Harnessing Hyperelastic Transformation Media

TL;DR

This paper introduces a novel design for phononic crystals using hyperelastic transformation media to maintain stable elastic band-gaps despite mechanical deformations, enhancing their robustness and potential applications.

Contribution

The work proposes integrating hyperelastic transformation media into phononic crystals to achieve deformation-independent band-gaps, a significant advancement over traditional designs.

Findings

Semi-linear soft components keep all elastic wave bands unchanged under deformation.

Neo-Hookean soft components precisely retain S-wave bands.

Numerical simulations validate the stability and robustness of the proposed design.

Abstract

The band structure in phononic crystals (PCs) is usually affected by the deformations of their soft components. In this work, hyperelastic transformation media is proposed to be integrated in the PCs'design, to achieve stable elastic band-gaps which is independent with finite mechanical deformations. For a one-dimensional (1D) PC, we demonstrate the semi-linear soft component can keep all elastic wave bands unchanged with the external deformation field. While for neo-Hookean soft component, only S-wave bands can be precisely retained. The change of the P-wave bands can be predicted by using a lumped mass method. Numerical simulations are performed to validate our theory predictions and the robustness of the proposed PCs.