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In this study, we present a method for generating a synthetic gauge field in origami metamaterials with continuously varying geometrical parameters. By modulating the mass term in the Dirac equation linearly, we create a synthetic gauge field in the vertical direction, which allows for the quantization of Landau levels through the generated pseudomagnetic field. Furthermore, we demonstrate the existence and robustness of the chiral zeroth Landau level. The unique elastic snake state is realized using the coupling between the zeroth and the first Landau levels. Our results, supported by theory and simulations, establish a feasible framework for generating pseudomagnetic fields in origami metamaterials with potential applications in waveguides and cloaking., 6 pages, 4 figures

Origami structures often serve as the building block of mechanical systems due to their rich static and dynamic behaviors. Experimental observation and theoretical modeling of origami dynamics have been reported extensively, whereas the data-driven modeling of origami dynamics is still challenging due to the intrinsic nonlinearity of the system. In this study, we show how the dynamic mode decomposition (DMD) method can be enhanced by integrating geometry information of the origami structure to model origami dynamics in an efficient and accurate manner. In particular, an improved version of DMD with control, that we term geometry-informed dynamic mode decomposition~(giDMD), is developed and evaluated on the origami chain and dual Kresling origami structure to reveal the efficacy and interpretability. We show that giDMD can accurately predict the dynamics of an origami chain across frequencies, where the topological boundary state can be identified by the characteristics of giDMD. Moreover, the periodic intrawell motion can be accurately predicted in the dual origami structure. The type of dynamics in the dual origami structure can also be identified. The model learned by the giDMD also reveals the influential geometrical parameters in the origami dynamics, indicating the interpretability of this method. The accurate prediction of chaotic dynamics remains a challenge for the method. Nevertheless, we expect that the proposed giDMD approach will be helpful towards the prediction and identification of dynamics in complex origami structures, while paving the way to the application to a wider variety of lightweight and deployable structures., 11 pages, 7 figures

In this study, we experimentally and numerically investigate the evolution of the tensile material properties of Discontinuous Fiber Composites (DFCs) with an increasing average number of platelets through the thickness for two different platelet widths. The results show that both the number of platelets and the platelet width have significant effects on the tensile modulus and strength. We find that not only the average mechanical properties but also their coefficients of variation change according to the different DFC mesostructures. To understand the relationship between material morphology at the mesoscale and corresponding material properties, we developed a random platelet mesostructure generation algorithm combined with explicit finite element models. Leveraging the computational tools, we find that moduli and strength increase with increasing average number of platelets through the thickness. The increasing trend continues until reaching an asymptotic limit at about 45 layers through the thickness for the narrow platelets and 27 layers for the square platelets. In the study, we address the importance of having accurate simulations of the mesostructure to match not only the average modulus and strength but also their associated coefficients of variation. We show that it is possible to accurately predict the tensile material properties of DFCs, including their B-basis design values. This is a quintessential condition for the adoption of DFCs in structural applications.

We investigate the effect of disorder on topologically nontrivial states in a two dimension (2D) mechanical system. We first propose a quantum spin Hall (QSH) insulator based on an out-of-plane spring-mass model and analytically study the interplay between the disorder and topology in both topologically trivial and nontrivial systems. We adopt the spin Bott index to characterize the topological property in disordered mechanical systems. By tracking the evolution of the spin Bott index with the increase of disorders, we quantitatively demonstrate the disorder induced transition from a topologically nontrivial QSH insulator to a trivial insulator. We then validate the topological phase transition through transient analysis in discrete lattices. Finally, we design a phononic crystal based on the discrete spring-mass model and numerically verify the topologically protected states along the boundary between the trivial insulator and disordered topological QSH insulator in a continuous system. This work puts a step forward in understanding the role of disorder in a 2D topological classical system.

We investigate infinite-broadband of graded one-dimensional local resonant granular chains, i.e., a graded woodpile lattice. A woodpile lattice is a type of granular crystal, consisting of horizontally-stacked cylindrical rods, whose natural modes strongly interfere with excitation waves. This phenomenon is a local resonance that results in a locally resonant bandgap in low-frequencies regimes, prohibiting wave propagation. To describe wave physics like local resonance, from linear to nonlinear regime in complex geometries, the discrete element or reduced-order model has been highly preferred. Here, we introduce a new method for a discrete element model (DEM), considering countable-infinity local resonance mode based on continuum mechanics. This approach can replicate a theoretical DEM for complex structures of geometric building blocks, which exploits a desired functional wave dynamic. Then, we characterize never-ending broadband in a graded woodpile structure based on the superposition principle, which demonstrates numerically graded local resonance effects by a newly developed analytical DEM. Regarding these results, we also verify experimentally. These findings could open a new way for broadband filtering using a graded local resonance mechanism, where performance can be functionally inverse designed into a discretization model., Comment: 36 pages, 8 figures

We numerically investigate the topological phase transition induced purely by disorder in a spring-mass chain. We employ two types of disorders - chiral and random types - to explore the interplay between topology and disorder. By tracking the evolution of real space topological invariants, we obtain the topological phase diagrams and demonstrate the bilateral capacity of disorder to drive topological transitions, from topologically nontrivial to trivial and vice versa. The corresponding transition is accompanied by the realization of a mechanical Topological Anderson Insulator. The findings from this study hint that the combination of disorder and topology can serve as an efficient control knob to manipulate the transfer of mechanical energy.

We numerically investigate the topological phase transition induced purely by disorder in a spring-mass chain. We employ two types of disorders-chiral and random types-to explore the interplay between topology and disorder. By tracking the evolution of real-space topological invariants, we obtain the topological phase diagrams and demonstrate the bilateral capacity of disorder to drive topological transitions, from topologically nontrivial to trivial and vice versa. The corresponding transition is accompanied by the realization of a mechanical topological Anderson insulator. The findings from this study hint that the combination of disorder and topology can serve as an efficient control knob to manipulate the transfer of mechanical energy.

We numerically and experimentally study corner states in a continuous elastic plate with em-bedded bolts in a hexagonal pattern. While preserving C6 crystalline symmetry, the system can transition from a topologically trivial to a non-trivial configuration. We create interfacial corners of 60{\deg} and 120{\deg} by adjoining trivial and non-trivial topological configurations. Due to the rich interaction between the bolts and the continuous elastic plate, we find a variety of corner states with and without topological origin. Notably, some of the corner states are highly localized and tunable. By taking advantage of this property, we experimentally demonstrate one-way corner localization in a Z-shaped domain wall., Comment: 6 pages, 5 figures