A novel buckling pattern in periodically porous elastomers with applications to elastic wave regulations

Abstract

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 a thermal load to pore coatings 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 growth-induced surface wrinkling in tubular structures, can be generated 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.