  Bianisotropy is common in electromagnetics whenever a cross-coupling between
electric and magnetic responses exists. However, the analogous concept for
elastic waves in solids, termed as Willis coupling, is more challenging to
observe. It requires coupling between stress and velocity or momentum and
strain fields, which is difficult to induce in non-negligible levels, even when
using metamaterial structures. Here, we report the experimental realization of
a Willis metamaterial for flexural waves. Based on a cantilever bending
resonance, we demonstrate asymmetric reflection amplitudes and phases due to
Willis coupling. We also show that, by introducing loss in the metamaterial,
the asymmetric amplitudes can be controlled and can be used to approach an
exceptional point of the non-Hermitian system, at which unidirectional zero
reflection occurs. The present work extends conventional propagation theory in
plates and beams to include Willis coupling, and provides new avenues to tailor
flexural waves using artificial structures.
