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1. Manipulating elastic waves via engineered spatial curvature profiles

   https://doi.org/10.1117/12.2612573  

   Mazzotti, Matteo; Gupta, Mohit; Santangelo, Christian; Ruzzene, Massimo (April 2022, SPIE Smart Structures + Nondestructive Evaluation)

   Fromme, Paul; Su, Zhongqing (Ed.)

   We investigate curved surfaces operating as geodesic lenses for elastic waves. Consistently with findings in optics, we show that wave propagation occurs along rays that correspond to the geodesics of the curved surfaces, and we establish the geometric equivalence between Gaussian curvature and refractive index. This equivalence is formulated for flexural waves in curved shells by showing that, in the short wavelength limit, the ray equation corresponds to the classical equation of geodesics. We leverage this result to identify a non-Euclidean transformation that maps the geometric profile of a isotropic curved waveguide into a spatially varying refractive index distribution for a planar waveguide. These theoretical predictions are validated first through numerical simulations, and subsequently through experiments on 3D printed curved membranes with different curvature distributions. Numerical and experimental findings confirm that focal regions and caustic networks are correctly predicted based on geodesic evaluations. Our results form the basis for the design of curved profiles that correspond to spatial distributions of the refractive index and induce focal points by forcing waves to propagate along predefined trajectories. The findings of this study also suggest curvature as an attractive alternative to strategies based on the local tailoring of material properties and geometrical patterns that have gained in popularity for gradient-index lens design. 

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2. Baseline-Free Structural Damage Identification for Beam-Like Structures Using Curvature Waveforms of Propagating Flexural Waves

   https://doi.org/10.3390/s21072453  

   Xu, Y. F.; Kim, J. S. (April 2021, Sensors)

   null (Ed.)

   Curvatures in mode shapes and operating deflection shapes have been extensively studied for vibration-based structural damage identification in recent decades. Curvatures of mode shapes and operating deflection shapes have proved capable of localizing and manifesting local effects of damage on mode shapes and operating deflection shapes in forms of local anomalies. The damage can be inversely identified in the neighborhoods of the anomalies that exist in the curvatures. Meanwhile, propagating flexural waves have also been extensively studied for structural damage identification and proved to be effective, thanks to their high damage-sensitivity and long range of propagation. In this work, a baseline-free structural damage identification method is developed for beam-like structures using curvature waveforms of propagating flexural waves. A multi-resolution local-regression temporal-spatial curvature damage index (TSCDI) is defined in a pointwise manner. A two-dimensional auxiliary TSCDI and a one-dimensional auxiliary damage index are developed to further assist the identification. Two major advantages of the proposed method are: (1) curvature waveforms of propagating flexural waves have relatively high signal-to-noise ratios due to the use of a multi-resolution central finite difference scheme, so that the local effects of the damage can be manifested, and (2) the proposed method does not require quantitative knowledge of a pristine structure associated with a structure to be examined, such as its material properties, waveforms of propagating flexural waves and boundary conditions. Numerical and experimental investigations of the proposed method are conducted on damaged beam-like structures, and the effectiveness of the proposed method is verified by the results of the investigations. 

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3. Electronically Reconfigurable Virtual Joints by Shape Memory Alloy-Induced Buckling of Curved Sheets

   https://doi.org/10.1109/SoutheastCon48659.2022.9763962  

   Bupe, Paul; Jackson, Douglas J.; Harnett, C. K. (March 2022, Proceedings of IEEE SoutheastCon 2022)

   This paper presents the concept of creating virtual joints in soft robotic structures by modifying the local curvature of non-stretchable thin-walled structures through shape memory alloy (SMA)-based surface actuation. A thin planar flexible material can be stiffened by curving it along one axis, which increases stiffness by increasing the effective thickness. Locally deforming the curved sheet by making a flat region reduces this thickness, creating a defect. The material buckles and bends in a controlled manner at that location under an external force, producing a virtual compliant joint. We use tailored wire placement techniques to embed a continuous SMA wire in a serpentine pattern into denim cloth stiffened by a thin plastic film. When curved, joints can be created in this structure by activating small segments of the SMA wire using Joule heating which induces local curvature, with each of these segments able to exert up to 1.6 N of force. Finally, we present a circuit and algorithm for routing current through any desired SMA wire segment(s). Experimental results show that compliant joints can be created anywhere along the structure, resulting in a reconfigurable system. 

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4. Geometric control of topological dynamics in a singing saw

   https://doi.org/10.1073/pnas.2117241119  

   Shankar, Suraj; Bryde, Petur; Mahadevan, L. (April 2022, Proceedings of the National Academy of Sciences)

   Significance The ability to sustain notes or vibrations underlies the design of most acoustic devices, ranging from musical instruments to nanomechanical resonators. Inspired by the singing saw that acquires its musical quality from its blade being unusually bent, we ask how geometry can be used to trap and insulate acoustic modes from dissipative decay in a continuum elastic medium. By using experiments and theoretical and numerical analysis, we demonstrate that spatially varying curvature in a thin shell can localize topologically protected modes at inflection lines, akin to exotic edge states in topological insulators. A key feature is the ability to geometrically control both spatial localization and the dynamics of oscillations in thin shells. Our work uncovers an unusual mechanism for designing robust, yet reconfigurable, high-quality resonators across scales. 

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5. Substrate curvature induces fallopian tube epithelial cell invasion via cell–cell tension in a model of ovarian cortical inclusion cysts

   https://doi.org/10.1093/intbio/zyz028  

   Fleszar, Andrew J; Walker, Alyssa; Kreeger, Pamela K; Notbohm, Jacob (November 2019, Integrative Biology)

   Abstract Throughout the body, epithelial tissues contain curved features (e.g. cysts, ducts and crypts) that influence cell behaviors. These structures have varied curvature, with flat structures having zero curvature and structures such as crypts having large curvature. In the ovary, cortical inclusion cysts (CICs) of varying curvatures are found, and fallopian tube epithelial (FTE) cells have been found trapped within these cysts. FTE are the precursor for ovarian cancer, and the CIC niche has been proposed to play a role in ovarian cancer progression. We hypothesized that variations in ovarian CIC curvature that occur during cyst resolution impact the ability of trapped FTE cells to invade into the surrounding stroma. Using a lumen model in collagen gels, we determined that increased curvature resulted in more invasions of mouse FTE cells. To isolate curvature as a system parameter, we developed a novel technique to pattern concave curvatures into collagen gels. When FTE cells were seeded to confluency on curved substrates, increases in curvature increased the number of invading FTE cells and the invasion distance. FTE invasion into collagen substrates with higher curvature depended on matrix metalloproteinases (MMPs), but expression of collagen I degrading Mmps was not different on curved and flat regions. A finite-element model predicted that contractility and cell–cell connections were essential for increased invasion on substrates with higher curvature, while cell–substrate interactions had minimal effect. Experiments supported these predictions, with invasion decreased by blebbistatin, ethylene glycol-bis(β-aminoethyl ether)-N,N,N’,N’-tetraacetic acid (EGTA) or N-cadherin-blocking antibody, but with no effect from a focal adhesion kinase inhibitor. Finally, experimental evidence supports that cell invasion on curved substrates occurs in two phases—a cell–cell-dependent initiation phase where individual cells break away from the monolayer and an MMP-dependent phase as cells migrate further into the collagen matrix. 

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