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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., Comment: 6 pages, 4 figures

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.

Elastic topological states have been receiving increased intention in numerous scientific and engineering fields due to their defect-immune nature, resulting in applications of vibration control and information processing. Here, we present the data-driven discovery of elastic topological states using dynamic mode decomposition (DMD). The DMD spectrum and DMD modes are retrieved from the propagation of the relevant states along the topological boundary, where their nature is learned by DMD. Applications such as classification and prediction can be achieved by the underlying characteristics from DMD. We demonstrate the classification between topological and traditional metamaterials using DMD modes. Moreover, the model enabled by the DMD modes realizes the prediction of topological state propagation along the given interface. Our approach to characterizing topological states using DMD can pave the way towards data-driven discovery of topological phenomena in material physics and more broadly lattice systems., Comment: 32 pages, 10 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.

Elastic valley metamaterials offer an excellent platform to manipulate elastic waves and have potential applications in energy harvesting and elastography. Here we introduce a series of strategies to realize topological transition in spiral elastic valley metamaterials by parameter modulations. We show the evolution of Berry curvature and valley Chern number as a function of inherent parameters of spiral, which further results in a general scheme to achieve topological valley edge states. Our strategy leverages multiple degrees of freedom in spiral elastic valley metamaterials to provide enhanced opportunities for desired topological states.

Automated Fiber Placement (AFP) technology provides a great ability to efficiently produce large carbon fiber reinforced composite structures with complex surfaces. AFP has a wide range of tow placement angles, and the users can design layup angles so that they can tailor the performance of the structure. However, despite the design freedom, the industry generally adopts a layering of 0 deg, 90 deg, and plus-minus 45 deg ply-drop angles. Here, we demonstrate the optimization of ply-drop angles of non-conventional composites. Specifically, we use classical laminate theory and Bayesian optimization to achieve better layup angles in terms of stiffness, Tsai-Wu failure criteria, and manufacturing time. Our approach shows its effectiveness in designing carbon fiber composite structures using unconventional angles in terms of both mechanical properties and production efficiency. Our method has the potential to be used for more complex scenarios, such as the production of curved surfaces and the utilization of finite element analysis.

Spin-1 Weyl point is formed by three bands touching at a single point in the three dimensional (3D) momentum space, with two of which show cone-like dispersion while the third band is flat. Such a triply degenerate point carries higher topological charge $\pm2$2 and can be described by a three-band Hamiltonian. We first propose a tight-binding model of a 3D Lieb lattice with chiral interlayer coupling to form the Spin-1 Weyl point. Then we design a chiral phononic crystal that carries these spin-1 Weyl points and special straight-type acoustic Fermi arcs. We also computationally demonstrate the robust propagation of the topologically protected surface states that can travel around a corner or defect without reflection. Our results pave a new way to manipulate acoustic waves in 3D structures and provide a platform for exploring energy transport properties in 3D spin-1 Weyl systems.

The study of Weyl points in electronic systems has inspired many recent researches in classical systems such as photonic and acoustic lattices. Here we show how the Weyl physics can also inspire the design of novel elastic structures. We construct a single-phase 3D structure, an analogue of the AA-stacked honeycomb lattice, and predict the existence of Weyl points with opposite topological charges (${\pm 1}$), elastic Fermi arcs, and the associated gapless topologically protected surface states. We employ full-scale numerical simulations on the elastic 3D structure, and present a clear visualization of topological surface states that are directional and robust. Such designed lattices can pave the way for novel vibration control and energy harvesting on structures that are ubiquitous in many engineering applications.

We present a gradient-index crystal that offers extreme tunability in terms of manipulating the propagation of elastic waves. For small-amplitude excitations, we achieve control over wave transmission depth into the crystal. We numerically and experimentally demonstrate a boomerang-like motion of wave packet injected into the crystal. For large-amplitude excitations on the same crystal, we invoke nonlinear effects. We numerically and experimentally demonstrate asymmetric wave transmission from two opposite ends of the crystal. Such tunable systems can thus inspire a novel class of designed materials to control linear and nonlinear elastic wave propagation in multi-scales., Comment: 9 pages with Supporting Information, 7 figures

Valley, as a new degree of freedom, raises the valleytronics in fundamental and applied science. The elastic analogs of valley states have been proposed by mimicking the symmetrical structure of either two-dimensional materials or photonic valley crystals. However, the asymmetrical valley construction remains unfulfilled. Here, we present the valley anisotropy by introducing asymmetrical design into elastic metamaterials. The elastic valley metamaterials are composed of bio-inspired hard spirals and soft materials. The anisotropic topological nature of valley is verified by asymmetrical distribution of the Berry curvature. We show the high tunability of the Berry curvature both in magnitude and sign enabled by our anisotropic valley metamaterials. Finally, we demonstrate the creation of valley topological insulators and show topologically protected propagation of transverse elastic waves relying on operating frequency. The proposed topological properties of elastic valley metamaterials pave the way to better understanding the valley topology and to creating a new type of topological insulators enabled by an additional valley degree of freedom., Comment: 22 pages, 7 figures

In this study, we investigate experimentally and numerically the mode I intra-laminar fracture and size effect of Discontinuous Fiber Composites (DFCs) as a function of the structure thicknesses. By testing geometrically-scaled Single Edge Notch Tension (SENT) specimens a notable structure size effect on the nominal strength of DFCs is identified. As the specimen size increases, the nominal strength decreases. For small specimens, we find a limited size effect with enhanced pseudo-ductility and a strong divergence from Linear Elastic Fracture Mechanics (LEFM). For sufficiently large specimen sizes, the scaling of the nominal strength follows closely LEFM with a strong brittle failure. As the thickness increases, the size effect decreases. We identify the fracture energy and the effective size of the fracture process zone as a function of the thickness of the structure. To do so, we integrate equivalent fracture mechanics and stochastic finite element modeling. Experimentally, we collect the nominal strength of geometrically-scaled Single Edge Notch Tension (SENT) specimens. The numerical stochastic model captures the complex, inhomogeneous mesostructure of DFCs by explicitly generating the platelets. From the integrated analysis, it is found that the fracture energy depends significantly on the structure thickness. It is shown to increase gradually up to 2 mm and saturates after 3 mm to a value of 57.77 N/mm, which is 4.81 times larger than a typical aluminum alloy.

This study investigates the mode I intra-laminar fracture and size effect in Discontinuous Fiber Composites (DFCs). Towards this goal, the results of fracture tests on geometrically-scaled Single Edge Notch Tension (SENT) specimens are presented and critically discussed for three platelet sizes. The results clearly show a decrease in nominal strength as the specimen size increases. This effect becomes more important as the structure size increases. It is found that, when the specimen is sufficiently large, the structural strength scales according to Linear Elastic Fracture Mechanics (LEFM) and the failure occurs in a very brittle way. In contrast, small specimens exhibit a more pronounced pseudo-ductility with a limited scaling effect and a significant deviation from LEFM. To characterize the fracture energy and the effective length of the fracture process zone, an approach combining equivalent fracture mechanics and stochastic finite element modeling is proposed. The model accounts for the complex random mesostructure of the material by modeling the platelets explicitly. Thanks to this theoretical framework, the mode I fracture energy of DFCs is estimated for the first time and it is shown to depend significantly on the platelet size. In particular, the fracture energy is shown to increase linearly with the platelet size in the range investigated in this work., Comment: 42 pages, 16 figures

We study the Bloch oscillation of elastic waves in a chain composed of hollow elliptical cylinders (HECs). These HECs are 3D-printed in different wall thicknesses and are arranged to form a graded chain. We find that the frequency band structure of this lattice can be manipulated in a way to create a narrow strip of transmission range sandwiched between slanted stop bands. This enables the trapping of elastic waves at a specific location of the chain, which depends on the input frequency of the propagating elastic waves. This elastic Bloch oscillation in a tailorable 3D-printed system enables the control of energy localization in solids, potentially leading to engineering applications for vibration filtering, energy harvesting, and structural health monitoring., Comment: 18 pages, 8 figures, 2 appendices

We propose a 3D-printed graded lattice made of hollow elliptical cylinders (HECs) as a new way to design impact mitigation systems. We observe asymmetric dynamics in the graded HEC chains with increasing and decreasing stiffness. Specifically, the increasing stiffness chain shows an acceleration of the propagating waves, while the decreasing stiffness chain shows the opposite. From the standpoint of impact mitigation, the decreasing stiffness chain combined with the strain-softening behavior of HECs results in an order-of-magnitude improvement in force attenuation compared to the increasing stiffness chain. We extend this finding to the graded 2D arrays and demonstrate a similar trend of wave transmission efficiency contrast between the increasing and decreasing stiffness lattices. The 3D-printed HEC lattices shown in this study can lead to the development of a new type of impact mitigating and shock absorbing structures., Comment: 22 pages, 11 figures, 4 appendices