L. R. Akhmetshin
DEFORMATION PROPERTIES OF A METAMATERIAL UNDER CHANGES
IN THE SIZES OF THE TETRACHIRAL STRUCTURE ELEMENTS
DOI: 10.17804/2410-9908.2024.5.079-087 Due to their special properties, mechanical honeycomb metamaterials, such as tetrachiral ones, have attracted a lot of research. The present study investigates the effect of deflection of a metamaterial sample under uniaxial loading. The mechanical behavior (deviation of the sample from its initial position) reveals an interesting phenomenon to consider, which is influenced by the cross-sectional area of the tetrachiral structure and the ring size. A comparison shows that a larger cross-sectional area results in less deviation for smaller ring sizes. Greater deviation is associated with larger areas as the ring size increases, as opposed to smaller areas. The twisting of the rings causes the lateral dimensions of the sample to change, and this makes it possible to study how changes in the metamaterial structure affect its effective Poisson’s ratio. Although Poisson’s ratio varies only slightly depending on the parameters, it can also take on a negative value. For Poisson’s ratio, an analytical formula is presented, which sufficiently characterizes any graph of dependencies.
Acknowledgement: The study was carried out with financial support from the Russian Science Foundation, Grant No. 23-29-00402, https://rscf.ru/en/project/23-29-00402/. Keywords: mechanical metamaterial, tetrachiral metamaterial, numerical simulation, structure–property relationship, rotating structure, effective Poisson’s ratio References:
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Л. Р. Ахметшин
ДЕФОРМАЦИОННЫЕ СВОЙСТВА МЕТАМАТЕРИАЛА ПРИ ИЗМЕНЕНИИ
РАЗМЕРОВ ЭЛЕМЕНТОВ ТЕТРАХИРАЛЬНОЙ СТРУКТУРЫ
Механические метаматериалы по типу сот, например тетрахиральные, привлекают большое внимание благодаря своим уникальным свойствам. В настоящей работе изучен эффект отклонения образца из метаматериала при одноосном нагружении. В механическом поведении (отклонение от исходного положения) обнаружен интересный эффект, который зависит от площади поперечного сечения тетрахиральной структуры и размера кольца. При сравнении большей и меньшей площадей обнаружено, что для малого размера кольца бόльшая площадь дает меньшее отклонение. При увеличении размера кольца бόльшая площадь дает большее отклонение в сравнении с меньшей площадью. Эффект скручивания связан с изменением линейных размеров образца, что позволило исследовать влияние изменения в структуре метаматериала на его эффективный коэффициент Пуассона. Несмотря на малые отличия при различных случаях варьирования параметров, зафиксировано отрицательное значение коэффициента Пуассона. Предложена аналитическая формула, адекватно описывающая каждый график зависимостей для коэффициента Пуассона.
Благодарность: Исследование выполнено за счет гранта Российского научного фонда № 23-29-00402, https://rscf.ru/project/23-29-00402/. Ключевые слова: механический метаматериал, тетрахиральный метаматериал, численное моделирование, скручивание структуры, коэффициент Пуассона Библиография:
- Special characteristics of tetrachiral honeycombs under large deformation / R. Zhong, M. Fu, Q. Yin, O. Xu, L. Hu // International Journal of Solids and Structures. – 2019. – Vol. 169. – P. 166–176. – DOI: 10.1016/j.ijsolstr.2019.04.020.
- Multi-stiffness topology optimization of zero Poisson’s ratio cellular structures / J. Huang, Q. Zhang, F. Scarpa, Y. Liu, J. Leng // Composites Part B: Engineering. – 2018. – Vol. 140. – P. 35–43. – DOI: 10.1016/j.compositesb.2017.12.014.
- Fu M., Liu F., Hu L. A novel category of 3D chiral material with negative Poisson’s ratio // Composites Science and Technology. – 2018. – Vol. 160. – P. 111–118. – DOI: 10.1016/j.compscitech.2018.03.017.
- Programmable mechanical metamaterials based on hierarchical rotating structures / X. Li, R. Fan, Zh. Fan, Y. Lu // International Journal of Solids and Structures. – 2021. – Vol. 216. – P. 145–155. – DOI: 10.1016/j.ijsolstr.2021.01.028.
- Mechanical design and multifunctional applications of chiral mechanical metamaterials: a review / W. Wu, W. Hu, G. Qian, H. Liao, X. Xu, F. Berto // Materials & Design. – 2019. – Vol. 180. – P. 107950. – DOI: 10.1016/j.matdes.2019.107950.
- Shi H. Y. Y., Tay T. E., Lee H. P. Numerical studies on composite meta-material structure for mid to low frequency elastic wave mitigation // Composite Structures. – 2018. – Vol. 195. – P. 136–146. – DOI: 10.1016/j.compstruct.2018.04.049.
- Spadoni A., Ruzzene M., Scarpa F. Global and local linear buckling behavior of a chiral cellular structure // Physica Status Solidi (b). – 2005. – Vol. 242, No. 3. – P. 695–709. – DOI: 10.1002/pssb.200460387.
- Mizzi L., Spaggiari A. Novel chiral honeycombs based on octahedral and dodecahedral Euclidean polygonal tessellations // International Journal of Solids and Structures. – 2022. – Vol. 238. – Art. 111428. – DOI: 10.1016/j.ijsolstr.2022.111428.
- Kelvin W. T. Baltimore Lectures on Molecular Dynamics and the Wave Theory of Light. – London : C. J. Clay and Sons. – 1904.
- Elastic constants of 3-, 4- and 6-connected chiral and anti-chiral honeycombs subject to uniaxial in-plane loading / A. Alderson, K. L. Alderson, D. Attard, K. E. Evans, R. Gatt, J. N. Grima, W. Miller, N. Ravirala, C. W. Smith, K. Zied // Composites Science and Technology. – 2010. – Vol. 70, No. 7. – P. 1042–1048. – DOI: 10.1016/j.compscitech.2009.07.009.
- Yuan Zh., Cui Zh., Ju J. Micropolar homogenization of wavy tetra-chiral and tetra-achiral lattices to identify axial–shear coupling and directional negative Poisson's ratio // Materials and Design. – 2021. – Vol. 201. – Art. 109483. – DOI: 10.1016/j.matdes.2021.109483.
- Elasticity of anti-tetrachiral anisotropic lattices / Y. J. Chen, F. Scarpa, Y. J. Liu, J. S. Leng // International Journal of Solids and Structures. – 2013. – Vol. 50, No. 6. – P. 996–1004. – DOI: 10.1016/j.ijsolstr.2012.12.004.
- Numerical study of the deformation behavior of a 2D chiral metamaterial / L. R. Akhmetshin, K. V. Iokhim, E. A. Kazantseva, I. Yu. Smolin // Letters on Materials. – 2024. – Vol. 14, No. 1. – P. 9–14. – DOI: 10.48612/letters-2024-1-9-14.
- Эффективные механические свойства двухмерного тетрахирального метаматериала / Л. Р. Ахметшин, К. В. Иохим, Е. А. Казанцева, И. Ю. Смолин // Известия вузов. Физика. – 2024. – T. 67, № 3. – С. 90–99. – DOI: 10.17223/00213411/67/3/10.
Библиографическая ссылка на статью
Akhmetshin L. R. Deformation Properties of a Metamaterial under Changes in the Sizes of the Tetrachiral Structure Elements // Diagnostics, Resource and Mechanics of materials and structures. -
2024. - Iss. 5. - P. 79-87. - DOI: 10.17804/2410-9908.2024.5.079-087. -
URL: http://dream-journal.org/issues/2024-5/2024-5_460.html (accessed: 22.12.2024).
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