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The band structure in phononic crystals (PCs) is usually affected by thedeformations of their soft components. In this work, hyperelastictransformation media is proposed to be integrated in the PCs'design, to achievestable elastic band-gaps which is independent with finite mechanicaldeformations. For a one-dimensional (1D) PC, we demonstrate the semi-linearsoft component can keep all elastic wave bands unchanged with the externaldeformation field. While for neo-Hookean soft component, only S-wave bands canbe precisely retained. The change of the P-wave bands can be predicted by usinga lumped mass method. Numerical simulations are performed to validate ourtheory predictions and the robustness of the proposed PCs.

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