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1. Frustration propagation in tubular foldable mechanisms

   https://doi.org/10.3389/fphy.2023.1296661  

   Reddy, A.; Karami, A.; Nassar, H. (December 2023, Frontiers in Physics)

   Shell mechanisms are patterned surface-like structures with compliant deformation modes that allow them to change shape drastically. Examples include many origami and kirigami tessellations as well as other periodic truss mechanisms. The deployment paths of a shell mechanism are greatly constrained by the inextensibility of the constitutive material locally and by the compatibility requirements of surface geometry globally. With notable exceptions (e.g., Miura-ori), the deployment of a shell mechanism often couples in-plane stretching and out-of-plane bending. Here, we investigate the repercussions of this kinematic coupling in the presence of geometric confinement, specifically in tubular states. We demonstrate that the confinement in the hoop direction leads to a frustration that propagates axially, as if by buckling. We fully characterize this phenomenon in terms of amplitude, wavelength, and mode shape in the asymptotic regime, where the size of the unit cell of the mechanismris small compared to the typical radius of curvatureρ. In particular, we conclude that the amplitude and wavelength of the frustration are of order $\sqrt{r/\rho }$and that the mode shape is an elastica solution. Derivations are carried out for a particular pyramidal truss mechanism. The findings are supported by numerical solutions of the exact kinematics. 

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2. Perfect reflection by dielectric subwavelength particle arrays: causes, implications, and technology

   https://doi.org/10.1117/12.2578953  

   Magnusson, Robert; Ko, Yeong H.; Lee, Kyu J.; Bootpakdeetam, Pawarat; Razmjooei, Nasrin; Simlan, Fairooz A.; Chen, Ren-Jie; Buchanan-Vega, Joseph; Carney, Daniel J.; Hemmati, Hafez; et al (April 2021, Proc. SPIE, Integrated Optics: Devices, Materials, and Technologies XXV)

   García-Blanco, Sonia M.; Cheben, Pavel (Ed.)

   Periodic arrays of resonant dielectric nano- or microstructures provide perfect reflection across spectral bands whose extent is controllable by design. At resonance, the array yields this result even in a single subwavelength layer fashioned as a membrane or residing on a substrate. The resonance effect, known as guided-mode resonance, is basic to modulated films that are periodic in one dimension (1D) or in two dimensions (2D). It has been known for 40 years that these remarkable effects arise as incident light couples to leaky Bloch-type waveguide modes that propagate laterally while radiating energy. Perfect reflection by periodic lattices derives from the particle assembly and not from constituent particle resonance. We show that perfect reflection is independent of lattice particle shape in the sense that it arises for all particle shapes. The resonance wavelength of the Bloch-mode-mediated zero-order reflectance is primarily controlled by the period for a given lattice. This is because the period has direct, dominant impact on the homogenized effective-medium refractive index of the lattice that controls the effective mode index experienced by the mode generating the resonance. In recent years, the field of metamaterials has blossomed with a flood of attendant publications. A significant fraction of this output is focused on reflectors with claims that local Fabry-Perot or Mie resonance causes perfect reflection with the leaky Bloch-mode viewpoint ignored. In this paper, we advance key points showing the essentiality of lateral leaky Bloch modes while laying bare the shortcomings of the local mode explanations. The state of attendant technology with related applications is summarized. The take-home message is that it is the assembly of particles that delivers all the important effects including perfect reflection. 

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3. Periodic deformation of semiflexible colloidal chains in eccentric time-varying magnetic fields

   https://doi.org/10.1088/1361-648X/ac533a  

   Spatafora-Salazar, Aldo; Cunha, Lucas H. P.; Biswal, Sibani Lisa (March 2022, Journal of Physics: Condensed Matter)

   Abstract Elastic filaments driven out of equilibrium display complex phenomena that involve periodic changes in their shape. Here, the periodic deformation dynamics of semiflexible colloidal chains in an eccentric magnetic field are presented. This field changes both its magnitude and direction with time, leading to novel nonequilibrium chain structures. Deformation into S-, Z-, and 4-mode shapes arises via the propagation and growth of bending waves. Transitions between these morphologies are governed by an interplay among magnetic, viscous, and elastic forces. Furthermore, the periodic behavior leading to these structures is described by four distinct stages of motion that include rotation, arrest, bending, and stretching of the chain. These stages correspond to specific intervals of the eccentric field’s period. A scaling analysis that considers the relative ratio of viscous to magnetic torques via a critical frequency illustrates how to maximize the bending energy. These results provide new insights into controlling colloidal assemblies by applying complex magnetic fields. 

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4. A High-Fidelity Dynamic Model for Origami Based on Iso-Parametric Absolute Nodal Coordinate Formulation (Iso-ANCF)

   https://doi.org/10.1115/SMASIS2019-5534  

   Tao, Jiayue; Li, Suyi (December 2019, ASME 2019 Conference on Smart Materials, Adaptive Structures and Intelligent Systems)

   Origami-inspired structures and material systems have been used in many engineering applications because of their unique kinematic and mechanical properties induced by folding. However, accurately modeling and analyzing origami folding and the associated mechanical properties are challenging, especially when large deformation and dynamic responses need to be considered. In this paper, we formulate a high-fidelity model — based on the iso-parametric Absolute Nodal Coordinate Formulation (ANCF) — for simulating the dynamic folding behaviors of origami involving large deformation. The centerpiece of this new model is the characterization of crease deformation. To this end, we model the crease using rotational spring at the nodes. The corresponding folding angle is calculated based on the local surface normal vectors. Compared to the currently popular analytical methods for analyzing origami, such as the rigid-facet and equivalent bar-hinge approach, this new model is more accurate in that it can describe the large crease and facet deformation without imposing many assumptions. Meanwhile, the ANCF based origami model can be more efficient computationally compared to the traditional finite element simulations. Therefore, this new model can lay down the foundation for high-fidelity origami analysis and design that involves mechanics and dynamics. 

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5. Inflatable Origami: Multimodal Deformation via Multistability

   https://doi.org/10.1002/adfm.202201891  

   Melancon, David; Forte, Antonio_Elia; Kamp, Leon_M; Gorissen, Benjamin; Bertoldi, Katia (June 2022, Advanced Functional Materials)

   Abstract Inflatable structures have become essential components in the design of soft robots and deployable systems as they enable dramatic shape change from a single pressure inlet. This simplicity, however, often brings a strict limitation: unimodal deformation upon inflation. Here, multistability is embraced to design modular, inflatable structures that can switch between distinct deformation modes as a response to a single input signal. This system comprises bistable origami modules in which pressure is used to trigger a snap‐through transition between a state of deformation characterized by simple deployment to a state characterized by bending deformation. By assembling different modules and tuning their geometry to cause snapping at different pressure thresholds, structures capable of complex deformations that can be pre‐programmed and activated using only one pressure source are created. This approach puts forward multistability as a paradigm to eliminate a one‐to‐one relation between input signal and deformation mode in inflatable systems. 

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