  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
Dirac-like cone. We separate the low frequencies guided modes (typically 100 Hz
for a centimetre 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 the more interesting as they make most of
the biological tissues.
