Harnessing Multiple Folding Mechanisms in Soft Periodic Structures for Tunable Control of Elastic Waves

wileyonlinelibrary.com determined by the deformation mechanisms of the ligaments, which buckle under compression at relatively low values of strain. In elasto-plastic porous materials buckling of the beam-like ligaments results in collapse bands that progress at relatively constant stress, providing an efficient energy absorbing mechanism. [ 8–12 ] However, this deformation process cannot be exploited to dynamically tune the macroscopic response of the system, since it is irreversible. By contrast, in periodic porous elastic structures, buckling of the ligaments may trigger dramatic homogeneous and reversible pattern transformations. [ 13,14 ] Remarkably, it has been demonstrated that this parallel, cooperative buckling— a kind of “phase transition” from one to another microstructure—can be instrumental to design materials with tunable properties, including systems with tunable negative Poisson’s ratio, [ 15 ] phononic [ 16–18 ] and photonic [ 19 ] switches and color displays. [ 20 ] Most of the porous systems studied so far are dual-shaped, since mechanical instability is found to trigger only one distinct new buckled pattern. Although different buckling modes have been observed in hexagonal honeycombs under biaxial compression depending on the loading conditions, [ 1,9,10,21–23 ]