We investigate nonlinear wave dynamics in origami-based mechanical metamaterials composed of origami-based structures, specifically the Triangulated Cylindrical Origami (TCO). The TCO structure shows coupling behavior between longitudinal and rotational motions. One of the unique features of the TCO is that the unit cell can exhibit mono- or bistable behavior selectively, which is determined by initial configurations such as height and rotational angle. In this study, we first fabricate physical prototypes made of paper sheets, and conduct compression tests on the prototypes to verify this unique tunable mono-/bistable features. By utilizing this tunability, we design a 1D chain of the TCO unit cells in which mono-/bistable behaviors of each unit cell can be altered by geometric parameters. Then, we analyze wave propagation in this origami-based system numerically by applying impact to the end of the chain. When the monostable configuration is selected for all of the unit cells, our numerical analysis shows that the application of compressive impact creates a tensile solitary wave propagating ahead of the initial compressive wave. In addition, the wave speed of this tensile solitary wave can be manipulated by the configurations of the TCO unit cells. These unique tunable static/dynamic behaviors can be exploited to design engineering devices which can mitigate impact in an efficient manner.
The discovery of topological insulators in materials science revolutionized the concept of wave propagation by giving rise to the existence of edge modes that are immune to backscattering. Similarly, the tunability in waveguiding – including in-situ frequency modifications and path designation – can be highly useful in manipulating energy flow, which still remains an open challenge. Here we investigate topologically tunable mechanical metamaterials based on the quantum valley hall effect (QVHE) by utilizing the bi-stable Stewart platform (SP). Generally, topologically protected wave propagation can leverage two physical mechanisms: the quantum hall effect (QHE) and the quantum spin hall effect (QSHE). Compared to the QHE and the QSHE, the QVHE exploited in this study maintains the time reversal symmetry and can be achieved by using a relatively simple, passive system with one degree-of-freedom. The tunable system we propose and investigate in this study is made of a two-dimensional hexagon crystal and is composed of SPs at nodes connected by linear springs. Each building block can exhibit one of the two stable states of the SP, so that the C6 inversion symmetry of the lattice is broken while C3 symmetry is reserved. By changing the sequence of the bi-stable state in the SP, we can formulate two kinds of unit cells – marked as A and B – with different topological properties. Berry curvatures as well as corresponding eigenmodes are obtained to demonstrate the topological conversion between the two lattices. Then we conduct super-cell analysis by forming a 1-by-20 array of A and B unit cells. Band structure of the super-cell indicates the existence of edge modes over the while band gap, which appear at the interface of A and B unit cells. Based on this tunable property of bi-stable SP, we can easily form S-type and L-type (60 and 120 degree bents) topological paths in the 40-by-40 lattices without breaking the original geometry parameters. We then conduct the numerical simulations with these topological wave guides to verify the topological protection of the valley hall edge states from backscattering. The tunable system we proposed in this paper may pave a possible way to achieving tunability of topological metamaterials.
In this presentation, we propose a novel design of elastic metamaterial that possesses unique anisotropic mass density and hyperbolic dispersion, which enables subwavelength-scale flexural wave manipulation. The metamaterial unit cell is inspired by kirigami, an ancient art of paper cutting and folding. A three-dimensional kirigami microstructure can be obtained by simply cutting and folding a thin metallic plate. By attaching the resonant kirigami microstructures periodically on the top of a host plate, a hyperbolic metamaterial plate can be manufactured without any perforation that degrades the strength of the pristine plate. A theoretical model based on the classic plate theory and mass-spring model is developed to understand the working mechanism of the elastic metamaterial. Dispersion curves are obtained by using an extended plane wave expansion method. An anisotropic effective mass density tensor is retrieved based on effective medium theory, which explains the different couplings between the local resonance of kirigami microstructure and the global flexural wave propagations in the host plate along two in-plane principal directions. Finally, numerical simulation on an elastic hyperlens is conducted to demonstrate the subwavelength-scale flexural wave control and super-resolution imaging abilities. The advantages of the proposed kirigami-based elastic hyperbolic metamaterial are twofold: (i) simple manufacturing process without perforation in the pristine plate and (ii) subwavelength flexural wave manipulation providing a high signal-to-noise ratio in plate-like engineering structures. Therefore, the proposed elastic hyperbolic metamaterial could be highly promising for high resolution damage imaging in nondestructive evaluation and structural health monitoring.
We investigate wave dynamics in origami-based mechanical metamaterials composed of bellows-like origami structures, specifically the Tachi-Miura Polyhedron (TMP). One of the unique features of the TMP is that its structural deformations take place only along the crease lines, therefore the structure can be made of rigid plates and hinges. By utilizing this feature, we introduce linear torsional springs to model the crease lines and derive the force and displacement relationship of the TMP structure along the longitudinal direction. Our analysis shows strain softening/hardening behaviors in compression/tensile regions respectively, and the force-displacement curve can be manipulated by altering the initial configuration of the TMP (e.g., the initial folding angle). We also fabricate physical prototypes and measure the force-displacement behavior to verify our analytical model. Based on this static analysis on the TMP, we simplify the TMP structure into a linkage model, preserving the tunable strain softening/hardening behaviors. Dynamic analysis is also conducted numerically to analyze the frequency response of the simplified TMP unit cell under harmonic excitations. The simplified TMP exhibits a transition between linear and nonlinear behaviors, which depends on the amplitude of the excitation and the initial configuration. In addition, we design a 1D system composed of simplified TMP unit cells and analyze the relationship between frequency and wave number. If two different configurations of the unit cell (e.g., different initial folding angles) are connected in an alternating arrangement, the system develops frequency bandgaps. These unique static/dynamic behaviors can be exploited to design engineering devices which can handle vibrations and impact in an efficient manner.