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1. Auxetic Regions in Large Deformations of Periodic Frameworks

   https://doi.org/10.1007/978-3-030-16423-2_18  

   Borcea, Ciprian S.; Streinu, Ileana (May 2019, Interdisciplinary Applications of Kinematics. Mechanisms and Machine Science)

   In materials science, auxetic behavior refers to lateral widening upon stretching. We investigate the problem of finding domains of auxeticity in global deformation spaces of periodic frameworks. Case studies include planar periodic mechanisms constructed from quadrilaterals with diagonals as periods and other frameworks with two vertex orbits. We relate several geometric and kinematic descriptions. 

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2. Auxetic interval determination and experimental validation for a three-dimensional periodic framework

   https://doi.org/10.1177/10812865211041390  

   Borcea, Ciprian S.; Broeren, Freek G.; Herder, Just L.; Streinu, Ileana; van der Wijk, Volkert (May 2022, Mathematics and Mechanics of Solids)

   Auxetic behavior refers to lateral widening upon stretching or, in reverse, lateral shrinking upon compression. When an initially auxetic structure is actuated by compression or extension, it will not necessarily remain auxetic for larger deformations. In this paper, we investigate the auxetic range in the deformation of a periodic framework with one degree of freedom. We use geometric criteria to identify the interval where the deformation is auxetic and validate these theoretical findings with compression experiments on sample structures with [Formula: see text] unit cells. 

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3. Auxetics Abounding

   https://doi.org/10.1109/REMAR.2018.8449905  

   Borcea, Ciprian S.; Streinu, Ileana (August 2018, 2018 International Conference on Reconfigurable Mechanisms and Robots (ReMAR))

   Auxetic behavior refers to lateral widening upon stretching. Although a structural origin for this rather counterintuitive type of deformation was often suggested, a theoretical understanding of the role of geometry in auxetic behavior has been a challenge for a long time. However, for structures modeled as periodic bar-and-joint frameworks, including atom-and-bond frameworks in crystalline materials, there is a complete geometric solution which opens endless possibilities for new auxetic designs. We construct a large family of three-dimensional auxetic periodic mechanisms and discuss the ideas involved in their design. 

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4. Quantum scarring in a spin-boson system: fundamental families of periodic orbits

   https://doi.org/10.1088/1367-2630/abd2e6  

   Pilatowsky-Cameo, Saúl; Villaseñor, David; Bastarrachea-Magnani, Miguel A.; Lerma-Hernández, Sergio; Santos, Lea F.; Hirsch, Jorge G. (March 2021, New Journal of Physics)

   Abstract As the name indicates, a periodic orbit is a solution for a dynamical system that repeats itself in time. In the regular regime, periodic orbits are stable, while in the chaotic regime, they become unstable. The presence of unstable periodic orbits is directly associated with the phenomenon of quantum scarring, which restricts the degree of delocalization of the eigenstates and leads to revivals in the dynamics. Here, we study the Dicke model in the superradiant phase and identify two sets of fundamental periodic orbits. This experimentally realizable atom–photon model is regular at low energies and chaotic at high energies. We study the effects of the periodic orbits in the structure of the eigenstates in both regular and chaotic regimes and obtain their quantized energies. We also introduce a measure to quantify how much scarred an eigenstate gets by each family of periodic orbits and compare the dynamics of initial coherent states close and away from those orbits. 

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5. An autonomous design algorithm to experimentally realize three-dimensionally isotropic auxetic network structures without compromising density

   https://doi.org/10.1038/s41524-024-01281-y  

   Shen, Meng; Reyes-Martinez, Marcos A; Powell, Louise Ahure; Iadicola, Mark A; Sharma, Abhishek; Byléhn, Fabian; Pashine, Nidhi; Chan, Edwin P; Soles, Christopher L; Jaeger, Heinrich M; et al (December 2024, npj Computational Materials)

   Abstract Auxetic materials have a negative Poisson’s ratio and are of significant interest in applications that include impact mitigation, membrane separations and biomedical engineering. While there are numerous examples of structured materials that exhibit auxetic behavior, the examples of engineered auxetic structures is largely limited to periodic lattice structures that are limited to directional or anisotropic auxetic response. Structures that exhibit a three-dimensionally isotropic auxetic response have been, unfortunately, slow to evolve. Here we introduce an inverse design algorithm based on global node optimization to design three-dimensional auxetic metamaterial structures from disordered networks. After specifying the target Poisson’s ratio for a structure, an inverse design algorithm is used to adjust the positions of all nodes in a disordered network structure until the desired mechanical response is achieved. The proposed algorithm allows independent control of shear and bulk moduli, while preserving the density and connectivity of the networks. When the angle bending stiffness in the network is kept low, it is possible to realize optimized structures with a Poisson’s ratios as low as −0.6. During the optimization, the bulk modulus of these networks decreases by almost two orders of magnitude, but the shear modulus remains largely unaltered. The materials designed in this manner are fabricated by dual-material 3D-printing, and are found to exhibit the mechanical responses that were originally encoded in the computational design engine. The approach proposed here provides a materials-by-design platform that could be extended for engineering of optical, acoustic, and electrical properties, beyond the design of auxetic metamaterials. 

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