A nonlinear mechanics model of soft network metamaterials with unusual swelling behavior and tunable phononic band gaps

Abstract Soft mechanical metamaterials with negative swelling responses represent a class of man-made materials with specially engineered micro-architectures, which are attractive for applications in areas such as biomedical engineering, aerospace and microelectronics. These soft mechanical metamaterials are usually constructed with laminated filaments that serve as building block structures in periodic lattices, with capabilities to convert hydraulic deformations of active materials into large bending deformations of the filamentary microstructures. The previous studies mainly relied on massive calculations of finite element analyses (FEA) as the core process of metamaterial designs to achieve targeted mechanical properties. The FEA calculations could, however, be very cumbersome and time-consuming, especially when the micro-architecture involves a large number of complex microstructures. This paper introduces a theoretical model that can predict accurately the swelling-induced deformations in such soft mechanical metamaterials consisting of sandwiched horseshoe microstructures. This model takes into account the evident shape change of sandwiched cross section observed in experiments, during the hydration process. Experimental and computational studies on mechanical metamaterials with a wide range of microstructure geometries were carried out to validate the developed model. These results unveil the significant role of out-of-plane deformations on the swellability of the mechanical metamaterials. The theoretical model sheds light on the essential microstructure-property relationship, which could serve as a reference of metamaterial designs to achieve desired swelling behavior. Furthermore, we leverage the active control of microstructure geometry during hydration to offer tunable phononic band structures, with potential applications in noise/vibration control and wave mitigation.