Dirac cones and chiral selection of elastic waves in a soft strip

Maxime Lanoy (1) , Fabrice Lemoult (1) , Antonin Eddi (2) , Claire Prada (1)

1 IL - Institut Langevin - Ondes et Images (UMR7587)
2 PMMH - Physique et mécanique des milieux hétérogenes (UMR 7636)

Significance We monitor the propagation of in-plane elastic waves in an incompressible thin strip and observe a Dirac cone in a soft material. Additional remarkable wave features such as negative phase velocities, pseudo-zero group velocity, and one-way chiral selection are highlighted. These results are universal: Any thin strip made of any soft elastomer will display the same behavior. Dirac cones have inspired many developments in the condensed-matter field over the last decade. Our findings enable the search for analogs in the realm of soft matter, leading to a wide range of potential applications. Additionally, they are of practical interest for biologists since soft strips are ubiquitous among human tissues and organs. Abstract We study the propagation of in-plane elastic waves in a soft thin strip, a specific geometrical and mechanical hybrid framework which we expect to exhibit a Dirac-like cone. We separate the low frequencies guided modes (typically 100 Hz for a 1-cm-wide strip) and obtain experimentally the full dispersion diagram. Dirac cones are evidenced together with other remarkable wave phenomena such as negative wave velocity or pseudo-zero group velocity (ZGV). Our measurements are convincingly supported by a model (and numerical simulation) for both Neumann and Dirichlet boundary conditions. Finally, we perform one-way chiral selection by carefully setting the source position and polarization. Therefore, we show that soft materials support atypical wave-based phenomena, which is all of the more interesting as they make most of the biological tissues.

Mots clés: Dirac cone; soft matter; elastic waves; chiral waves

Domaines: Physique [physics]

Maxime Lanoy, Fabrice Lemoult, Antonin Eddi, Claire Prada. Dirac cones and chiral selection of elastic waves in a soft strip. Proceedings of the National Academy of Sciences of the United States of America, 2020, pp.202010812. ⟨10.1073/pnas.2010812117⟩. ⟨hal-03014230⟩