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Soft mechanical metamaterials with hinge-like elements can undergo multi-step reconfiguration through folding and contacts, and thus exhibit highly nonlinear responses. Numerical simulation of the nonlinear behaviors is essential for the design and control of the mechanical metamaterials, but it remains a challenge due to complicated nonlinear effects. Here, we report the finite element modeling of multi-step reconfiguration of a shape-changing metamaterial, and elucidate the underlying mechanism of soft elasticity. The predicted stress–strain curve together with the folding angles of hinge elements shows excellent agreement with experimental data reported in the literature. Moreover, we explore the influence of reconfiguration and folding-induced internal stress on the bandgap distribution of the mechanical metamaterials. Our efforts provide useful guidelines for the design and application of mechanical metamaterials for both static and dynamic situations.

When exposed to a solvent, a gel bilayer beam can bend due to different swelling abilities of the two layers. In this work, an analytical model is derived to obtain the curvature of the bilayer beam. The model is further linearized to obtain an explicit expression for the curvature. The finite element model is used to verify the above analytical solutions. The results show the curvature predicted by the analytical model is in excellent agreement with the finite element results. The linear model predicts a smaller curvature at large swelling ratio. These results suggest the analytical models can provide a design metric for self-folding 3D structures.

In recent years, 4D printing has gained increasing attention in the tissue engineering field since this advanced manufacturing platform can create stimulus-responsive structures, which can change their shapes, functions, and/or properties when appropriate external stimulus/stimuli is/are applied. A number of hydrogels with swellable/shrinkable abilities have been explored for 4D printing to fabricate different shape-morphing structures for tissue engineering. Among them, gelatin methacryloyl (GelMA) has been 4D printed, which can self-fold into microtubular structures. Currently, the self-folding ability of 4D printed GelMA hydrogels is mainly based on the different cross-linking degrees (which control and govern the swelling degrees) across the thickness of hydrogels. However, this strategy alone can only form self-folding GelMA tubes with diameters at the micrometer level and cannot create self-folding GelMA tubes with diameters at the millimeter level, which is mainly due to the insufficient internal force generated in 4D printed GelMA hydrogels when they are exposed to water. To overcome this limitation, this study has investigated a new strategy to fabricate self-folding GelMA tubes with large diameters at the millimeter level for tissue engineering applications. The new strategy introduced a cross-linking degree gradient across the GelMA plane in addition to its thickness by printing a second layer of strips on the first 4D printed GelMA film. In the aqueous environment, under the current fabrication condition, such bilayer GelMA hydrogels could self-fold into tubes of larger diameters up to 6mm. The in vitro release behavior of heparin incorporated into the 4D printed GelMA was also studied. It was shown that heparin release could be controlled by the GelMA concentration and heparin content in 4D printed GelMA. The 4D printed GelMA hydrogels with the improved self-folding ability and controlled release of a drug are promising for targeted tissue engineering applications.