  This paper proposes a new metamaterial structure consisting of a periodically
porous elastomer with pore coatings. This design enables us to engender finite
deformation by a contactless load. As a case study, we apply thermal load to
the pore coating and carry out a finite element analysis to probe instabilities
and the associated phononic properties. It turns out that a novel buckling
mode, preserving the nature of surface wrinkling in tubular structures, can be
induced under a plane-strain setup, and a smaller size of the unit cell is
attained compared to the counterpart of traditional buckled profile in soft
porous elastomers. In particular, this buckling pattern is able to produce
several bandgaps in different frequency ranges as the macroscopic mean strain
increases. We further introduce a metallic core as local resonator, and the
updated metamaterial allows a low-frequency bandgap, the bandgap width of which
can be estimated by a simplified theoretical model. As more free parameters are
involved in the structure, we perform a detailed parametric study to elucidate
the influences of the modulus ratio between coating and matrix, the porosity,
the core radius, and the macroscopic mean strain on the buckling initiation and
the evolution of bandgap. Remarkably, a stiffer surface coating is prone to
enhance the stability of the structure, which is contrary to existing results
in film/substrate bilayers. It is expected that the current study could shed
light on new insight into pattern formation and wave manipulation in porous
elastomers.
