In-Situ Reconfigurability and Stiffness Tunability of Origami-Based Mechanical Metamaterial

We investigate the programmable mechanical properties of the origami-based mechanical metamaterials, namely Tachi-Miura Polyhedron (TMP). The TMP is a space-filling bellows-like rigid origami derived from well-known Miura-ori. Therefore, the kinematics and corresponding constitutive relation of the TMP are determined by the underlying geometrical parameters of the crease pattern. This makes the TMP suitable for the three-dimensional structural modules with certain design requirements. In this study, we particularly focus on the stiffness tunability of the TMP-based multi-cellular structure. The conventional multi-cellular structures have preconfigured mechanical properties, and it is extremely difficult to alter them after assembly. By employing the TMP as a building block, our multi-cellular structure exhibits the shape modulation accompanied by the change of its mechanical property, specifically the stiffness. The shape modulation of the tessellation is performed via the transition of the TMP unit cells between distinct postures or states. One crease pattern for the TMP can be folded into three distinct tubular shapes: one conventional TMP and two parallelopipeds. The resultant tubular configuration can be shifted shuttlewise even after the assembly. Moreover, since they are all derived from the same crease pattern, different states can coexist within the same tessellation yet preserving the effectiveness of unit-by-unit state transition. One the other hand, the stiffness variation can be achieved by introducing the self-locking unit cells into the tessellation. The self-locking can be induced by the intracellular vertex collision and further deformation of the rigid facets. In theory, the rigid origami assumption neglects the facet deformation. However, in practice, the facets are free to deform according to the external load. During the intracellular collision phase, the interferences of rigid facet vertices are intentionally provoked by tailoring the crease pattern. The collision causes a structural deformation of the facets, which is not assumed in rigid origami theory. By allowing the intracellular collision, the transition from rigid-foldable deformation to non-rigid facet deformation occurs during the overall deformation process. Within the rigid-foldable regime, the unit cell is easily folded along the crease lines. Once reached the intracellular collision phase, the facet bending becomes the dominant deformation process. Here, the structural stiffness increases abruptly because the facet deformation requires an external force larger than crease folding. Given that the presence of intracellular collision depends upon how the facets are arranged within the unit cell, this self-locking mechanism is unique to the aforementioned conventional TMP state, but not to the other two parallelopiped states. Hence, in the combination of these transformability and intracellular collision, we can program the overall stiffness of the TMP-based multi-cellular structure by selecting the number of self-locking unit cells. For instance, if all unit cells are chosen to be in conventional TMP state with self-locking, the structure becomes stiff. However, the tessellation solely composed of parallelopiped is fully collapsible, or less stiff. We experimentally verify this stiffness programmability through the compression test, which clearly shows a linear relationship between the structural stiffness and the number of self-locking units. This in-situ programmability of the structural stiffness can be leveraged in the diverse mechanical systems including soft-robotics, architectures, and aerospace structures.