Effect of Variation of Coefficient of Thermal Expansion on Thermomechanical Deformation of Cylindrical In-plane Auxetics Based on Re-Entrant Cells

Anastasia S. Tarasova, Mikhail A. Tashkinov

Author details

Anastasia S. Tarasova
Perm National Research Polytechnic University, Perm, Russian Federation
Mikhail A. Tashkinov
Perm National Research Polytechnic University, Perm, Russian Federation

https://doi.org/10.15593/perm.mech/2024.6.06

The active development of mechanical metamaterials has recently led to the widespread use of auxetic structures in various applications with different loading conditions. This study examines the thermomechanical behavior of new cylindrical auxetic lattice structures by analyzing the relationship between their deformation characteristics and the coefficient of thermal expansion (CTE) of the material. Unlike traditional auxetic cylinders, the auxeticity plane of the developed models is perpendicular to the cylinder axis, which determines the specifics of their behavior. To understand the behavior of auxetic lattices under combined thermal and mechanical loads, computational experiments based on the finite element method (FEM) were carried out. Differentiations of both rectangular and cylindrical lattice structures were studied. The dependences of transverse strain on CTE were obtained and compared. The influence of CTE on the structural Poisson's ratio of rectangular auxetic lattices, which is a key parameter characterizing the auxetic behavior of the structure under thermomechanical loading, was evaluated. The possibility of modeling the mechanical behavior of auxetic cylinders using an orthotropic mechanical material model with effective properties was tested. The constants for specifying such a material model were obtained by modeling a numerical experiment on tension and shear of rectangular auxetic lattices along the coordinate axes. Using an example with artificial material properties, it was shown that the predominant deformation mechanism caused by the counteracting influence of mechanical and thermal loads can be controlled by choosing a material with a suitable CTE. This allows controlling the structure response to temperature change and mechanical load. Such results can be used to create cylindrical auxetic lattice structures subjected to mechanical and thermal deformations in applications requiring a controlled thermomechanical response.

Keywords

mechanical metamaterialscylindrical lattice structuresauxeticsnegative Poisson's ratiothermoelasticityre-entrant cell

Влияние изменения коэффициента термического расширения на термомеханическую деформацию цилиндров с ауксетичностью в плоскости на основе повторно-входящих ячеек

Активное развитие механических метаматериалов в настоящее время привело к широкому применению ауксетичных структур в различных приложениях, отличающихся условиями нагружения. В данном исследовании изучается термомеханическое поведение новых цилиндрических ауксетичных решетчатых структур путем анализа взаимосвязи между их деформационными характеристиками и коэффициентом термического расширения (КТР) материала. В отличие от традиционных ауксетичных цилиндров, плоскость ауксетичности разработанных моделей расположена перпендикулярно оси цилиндра, что определяет специфику их поведения. Для понимания поведения ауксетичных решеток под комбинированными термическими и механическими нагрузками были проведены вычислительные эксперименты на основе метода конечных элементов (МКЭ). Исследовались дифференциации как прямоугольных, так и цилиндрических решетчатых структур. Получены и сравнены зависимости поперечной деформации от КТР. Оценено влияние КТР на структурный коэффициент Пуассона прямоугольных ауксетичных решеток, являющегося ключевым параметром, характеризующим ауксетичное поведение структуры при термомеханическом нагружении. Проверена возможность моделирования механического поведения ауксетичных цилиндров с помощью ортотропной механической модели материала с эффективными свойствами. Константы для задания такой модели материала получены путем моделирования численного эксперимента на растяжение и сдвиг прямоугольных ауксетичных решеток вдоль осей координат. Используя пример с искусственными свойствами материала, было показано, что преобладающий механизм деформации, вызванный противодействующим влиянием механической и термической нагрузки, может контролироваться путем выбора материала с подходящим КТР. Это позволяет регулировать отклик структуры на изменение температуры и механическую нагрузку. Такие результаты могут быть использованы для создания цилиндрических ауксетичных решетчатых структур, подверженных механическим и термическим деформациям, в приложениях, где требуется контролируемый термомеханический отклик.

Ключевые слова

механические метаматериалыцилиндрические решетчатые структурыакустикиотрицательный коэффициент Пуассонатермоупругостьповторно-входящая ячейка

Bibliography

1.Skripnyak V. V., Chirkov M.O., Skripnyak V.A. Modeling the mechanical response of auxetic metamaterials to dynamic effects. PNRPU Mechanics Bulletin, 2021, 2021(2), pp. 144-152. DOI: 10.15593/PERM.MECH/2021.2.13 Scholar
2.Qin Q., Dayyani I., Webb P. Structural Mechanics of cylindrical fish-cell zero Poisson's ratio metamaterials. Compos. Struct., 2022, 289, pp. 115455. DOI: 10.1016/J.COMPSTRUCT.2022.115455 Scholar
3.Yu X., Zhou J., Liang H., Jiang Z., Wu L. Mechanical metamaterials associated with stiffness, rigidity and compressibility: A brief review. Prog. Mater. Sci., 2018, 94, pp. 114-173. DOI: 10.1016/j.pmatsci.2017.12.003 Scholar
4.Yao Y. et al. A multifunctional three-dimensional lattice material integrating auxeticity, negative compressibility and negative thermal expansion. Compos. Struct., 2024, 337 (March). DOI: 10.1016/j.compstruct.2024.118032 Scholar
5.Montazeri A., Saeedi A., Bahmanpour E., Mahnama M. Auxetic mechanical metamaterials with symmetry-broken Re-entrant units. Int. J. Mech. Sci., 2024, 266, pp. 108917. DOI: 10.1016/J.IJMECSCI.2023.108917 Scholar
6.Balan P. M., Mertens A. J., Bahubalendruni M.V.A.R. Auxetic mechanical metamaterials and their futuristic developments: A state-of-art review. Mater. Today Commun., 2023, 34 (October 2022), pp. 105285. DOI: 10.1016/j.mtcomm.2022.105285 Scholar
7.Zheng X., Guo X., Watanabe I. A mathematically defined 3D auxetic metamaterial with tunable mechanical and conduction properties. Mater. Des., 2021, 198, pp. 109313. DOI: 10.1016/J.MATDES.2020.109313 Scholar
8.Qi C., Jiang F., Remennikov A., Pei L.Z., Liu J., Wang J.S., Liao X.W., Yang S. Quasi-static crushing behavior of novel re-entrant circular auxetic honeycombs. Compos. Part B Eng., 2020, 197, pp. 108117. DOI: 10.1016/J.COMPOSITESB.2020.108117 Scholar
9.Gorodtsov V.A., Lisovenko D.S. Auxetics among Materials with Cubic Anisotropy. Mech. Solids, 2020, 55(4), pp. 461-474. DOI: 10.3103/S0025654420040044. Scholar
10.Wu X., Su Y., Shi J. In-plane impact resistance enhancement with a graded cell-wall angle design for auxetic metamaterials. Compos. Struct., 2020, 247, pp. 112451. DOI: 10.1016/J.COMPSTRUCT.2020.112451 Scholar
11.Li T., Liu F., Wang L. Enhancing indentation and impact resistance in auxetic composite materials. Compos. Part B Eng., 2020, 198(July), pp. 108229. DOI: 10.1016/j.compositesb.2020.108229 Scholar
12.Ivanova S.Y., Osipenko K.Y., Kuznetsov V.A., Solovyov N.G., Banichuk N. V., Lisovenko D.S. Experimental Investigation of the Properties of Auxetic and Non-Auxetic Metamaterials Made of Metal During Penetration of Rigid Strikers. Mech. Solids, 2023, 58(2), pp. 524-528. DOI: 10.3103/S0025654422061016 Scholar
13.Ivanova S.Y., Osipenko K.Y., Demin A.I., Banichuk N. V., Lisovenko D.S. Studying the Properties of Metamaterials with a Negative Poisson's Ratio when Punched by a Rigid Impactor. Mech. Solids, 2023, 58(5), pp. 1536-1544. DOI: 10.3103/S0025654423600897 Scholar
14.Teng X.C., Ren X., Zhang Y., Jiang W., Pan Y., Zhang X.G., Zhang X.Y., Xie Y.M. A simple 3D re-entrant auxetic metamaterial with enhanced energy absorption. Int. J. Mech. Sci., 2022, 229 (July), pp. 107524. DOI: 10.1016/j.ijmecsci.2022.107524 Scholar
15.Jin S., Korkolis Y.P., Li Y. Shear resistance of an auxetic chiral mechanical metamaterial. Int. J. Solids Struct., 2019, 174-175, pp. 28-37. DOI: 10.1016/j.ijsolstr.2019.06.005 Scholar
16.Airoldi A., Bettini P., Panichelli P., Sala G. Chiral topologies for composite morphing structures - Part II: Novel configurations and technological processes. Phys. Status Solidi Basic Res., 2015, 252(7), pp. 1446-1454. DOI: 10.1002/pssb.201584263 Scholar
17.Duncan O., Shepherd T., Moroney C., Foster L., Venkatraman P.D., Winwood K., Allen T., Alderson A. Review of auxetic materials for sports applications: Expanding options in comfort and protection. Appl. Sci., 2018, 8(6). DOI: 10.3390/app8060941 Scholar
18.Weng L., Zhou J., Cai R. Analytical model of Li-ion diffusion-induced stress in nanowire and negative Poisson's ratio electrode under different operations. Int. J. Mech. Sci., 2018, 141, pp. 245-261. DOI: 10.1016/J.IJMECSCI.2018.04.013 Scholar
19.Wang C.Y., Wang W.W., Zhao W.Z., Wang Y., Zhou G. Structure design and multi-objective optimization of a novel NPR bumper system. Compos. Part B Eng., 2018, 153 (April), pp. 78-96. DOI: 10.1016/j.compositesb.2018.07.024 Scholar
20.Kolken H.M.A., Janbaz S., Leeflang S.M.A., Lietaert K., Weinans H.H., Zadpoor A.A. Rationally designed meta-implants: A combination of auxetic and conventional meta-biomaterials. Mater. Horizons, 2018, 5(1), pp. 28-35. DOI: 10.1039/c7mh00699c Scholar
21.Iantaffi C., Bele E., McArthur D., Lee P.D., Leung C.L.A. Auxetic response of additive manufactured cubic chiral lattices at large plastic strains. Mater. Des., 2023, 233 (May), pp. 112207. DOI: 10.1016/j.matdes.2023.112207 Scholar
22.Li X., Fan R., Fan Z., Lu Y. Programmable mechanical metamaterials based on hierarchical rotating structures. Int. J. Solids Struct., 2021, 216, pp. 145-155. DOI: 10.1016/j.ijsolstr.2021.01.028 Scholar
23.Gao Y., Wei X., Han X., Zhou Z., Xiong J. Novel 3D auxetic lattice structures developed based on the rotating rigid mechanism. Int. J. Solids Struct., 2021, 233, pp. 111232. DOI: 10.1016/J.IJSOLSTR.2021.111232 Scholar
24.Gao Q., Ge C., Zhuang W., Wang L., Ma Z. Crashworthiness analysis of double-arrowed auxetic structure under axial impact loading. Mater. Des., 2019, 161, pp. 22-34. DOI: 10.1016/j.matdes.2018.11.013 Scholar
25.Carneiro V.H., Puga H. Axisymmetric auxetics. Compos. Struct., 2018, 204(April), pp. 438-444. DOI: 10.1016/j.compstruct.2018.07.116 Scholar
26.Carneiro V.H., Puga H. Enhanced mechanical properties in cellular solids using axisymmetric configurations. Compos. Struct., 2021, 255 (May 2020), pp. 112972. DOI: 10.1016/j.compstruct.2020.112972 Scholar
27.Yang H., Ma L. Design and characterization of axisymmetric auxetic metamaterials. Compos. Struct. 2020, 249 (May). DOI: 10.1016/j.compstruct.2020.112560 Scholar
28.Novak N., Mauko A., Ulbin M., Krstulović-Opara L., Ren Z., Vesenjak M. Development and characterisation of novel three-dimensional axisymmetric chiral auxetic structures. J. Mater. Res. Technol., 2022, 17, pp. 2701-2713. DOI: 10.1016/j.jmrt.2022.02.025 Scholar
29.Gomes R.A., de Oliveira L.A., Francisco M.B., Gomes G.F. Tubular auxetic structures: A review. Thin-Walled Struct., 2023, 188 (February), pp. 110850. DOI: 10.1016/j.tws.2023.110850 Scholar
30.Gao Q., Liao W.H. Energy absorption of thin walled tube filled with gradient auxetic structures-theory and simulation. Int. J. Mech. Sci., 2021, 201, pp. 106475. DOI: 10.1016/J.IJMECSCI.2021.106475 Scholar
31.Li J., Zhang Z.Y., Liu H.T., Wang Y.B. Design and characterization of novel bi-directional auxetic cubic and cylindrical metamaterials. Compos. Struct., 2022, 299(June), pp. 116015. DOI: 10.1016/j.compstruct.2022.116015 Scholar
32.Gao Q., Zhao X., Wang C., Wang L., Ma Z. Multi-objective crashworthiness optimization for an auxetic cylindrical structure under axial impact loading. Mater. Des., 2018, 143, pp. 120-130. DOI: 10.1016/j.matdes.2018.01.063 Scholar
33.Guo Y., Zhang J., Chen L., Du B., Liu H., Chen L., Li W., Liu Y. Deformation behaviors and energy absorption of auxetic lattice cylindrical structures under axial crushing load. Aerosp. Sci. Technol., 2020, 98, pp. 105662. DOI: 10.1016/j.ast.2019.105662 Scholar
34.Lee W., Jeong Y., Yoo J., Huh H., Park S.J., Park S.H., Yoon J. Effect of auxetic structures on crash behavior of cylindrical tube. Compos. Struct., 2019, 208 (October 2018), pp. 836-846. DOI: 10.1016/j.compstruct.2018.10.068 Scholar
35.Han D., Zhang Y., Zhang X.Y., Xie Y.M., Ren X. Lightweight auxetic tubular metamaterials: Design and mechanical characteristics. Compos. Struct., 2023, 311 (February), pp. 116849. DOI: 10.1016/j.compstruct.2023.116849 Scholar
36.Huo R.Y. et al. Mechanical properties of auxetic circular and square tubes filled with aluminum foam. Eng. Struct., 2023, 281 (February), pp. 115732. DOI: 10.1016/j.engstruct.2023.115732 Scholar
37.Gao Q., Liao W.H., Huang C. Theoretical predictions of dynamic responses of cylindrical sandwich filled with auxetic structures under impact loading. Aerosp. Sci. Technol., 2020, 107, pp. 106270. DOI: 10.1016/J.AST.2020.106270 Scholar
38.Li C., Yang J., Shen H.S. Postbuckling of pressure-loaded auxetic sandwich cylindrical shells with FG-GRC facesheets and 3D double-V meta-lattice core. Thin-Walled Struct., 2022, 177 (March), pp. 109440. DOI: 10.1016/j.tws.2022.109440 Scholar
39.Allam M.N.M., Radwan A.F., Sobhy M. Hygrothermal deformation of spinning FG graphene sandwich cylindrical shells having an auxetic core. Eng. Struct., 2022, 251(PA), pp. 113433. DOI: 10.1016/j.engstruct.2021.113433 Scholar
40.Cong P.H., Long P.T., Van Nhat N., Duc N.D. Geometrically nonlinear dynamic response of eccentrically stiffened circular cylindrical shells with negative poisson’s ratio in auxetic honeycombs core layer. Int. J. Mech. Sci., 2019, 152 (December 2018), pp. 443-453. DOI: 10.1016/j.ijmecsci.2018.12.052 Scholar
41.Tashkinov M., Tarasova A., Vindokurov I., Silberschmidt V. V., Behaviour A., Tashkinov M., Tarasova A., Vindokurov I. Composites with Re-Entrant Lattice: Effect of Filler on Auxetic Behaviour. Polymers (Basel), 2023, 15(20), pp. 4076. DOI: 10.3390/polym15204076 Scholar
42.Nielson G.M. Dual marching cubes. IEEE Visualization 2004, IEEE Comput. Soc, 2004, pp. 489-496. DOI: 10.1109/VISUAL.2004.28 Scholar
43.Cohen-Or D., Kadosh A., Levin D., Yagel R. Smooth Boundary Surfaces from Binary 3D Datasets. Volume Graphics, 2000. DOI: 10.1007/978-1-4471-0737-8_4 Scholar

1.Skripnyak, V.V. Modeling the mechanical response of auxetic metamaterials to dynamic effects / V.V. Skripnyak, M.O. Chirkov, V.A. Skripnyak // PNRPU Mech. Bull. - 2021. - Vol. 2021, no. 2. - P. 144-152. DOI: 10.15593/PERM.MECH/2021.2.13 Scholar
2.Qin, Q. Structural Mechanics of cylindrical fish-cell zero Poisson's ratio metamaterials / Q. Qin, I. Dayyani, P. Webb // Compos. Struct. - 2022. - Vol. 289. - P. 115455. DOI: 10.1016/J.COMPSTRUCT.2022.115455 Scholar
3.Mechanical metamaterials associated with stiffness, rigidity and compressibility: A brief review / X. Yu [et al.] // Prog. Mater. Sci. - 2018. - Vol. 94. - P. 114-173. DOI: 10.1016/j.pmatsci.2017.12.003 Scholar
4.A multifunctional three-dimensional lattice material integrating auxeticity, negative compressibility and negative thermal expansion / Y. Yao [et al.] // Compos. Struct. - 2024. - Vol. 337, no. March. DOI: 10.1016/j.compstruct.2024.118032 Scholar
5.Auxetic mechanical metamaterials with symmetry-broken Re-entrant units / A. Montazeri [et al.] // Int. J. Mech. Sci. - 2024. - Vol. 266. - P. 108917. DOI: 10.1016/J.IJMECSCI.2023.108917 Scholar
6.Balan, P.M. Auxetic mechanical metamaterials and their futuristic developments: A state-of-art review / P.M. Balan, A.J. Mertens, M.V.A.R. Bahubalendruni // Mater. Today Commun. - 2023. - Vol. 34, no. October 2022. - P. 105285. DOI: 10.1016/j.mtcomm.2022.105285 Scholar
7.Zheng, X. A mathematically defined 3D auxetic metamaterial with tunable mechanical and conduction properties / X. Zheng, X. Guo, I. Watanabe // Mater. Des. - 2021. - Vol. 198. - P. 109313. DOI: 10.1016/J.MATEDS.2020.109313 Scholar
8.Quasi-static crushing behavior of novel re-entrant circular auxetic honeycombs / C. Qi [et al.] // Compos. Part B Eng. - 2020. - Vol. 197. - P. 108117. DOI: 10.1016/J.COMPOSITESB.2020.108117 Scholar
9.Gorodtsov, V.A. Auxetics among Materials with Cubic Anisotropy / V.A. Gorodtsov, D.S. Lisovenko // Mech. Solids. - 2020. - Vol. 55, no. 4. - P. 461-474. DOI: 10.3103/S0025654420040044 Scholar
10.Wu, X. In-plane impact resistance enhancement with a graded cell-wall angle design for auxetic metamaterials / X. Wu, Y. Su, J. Shi // Compos. Struct. - 2020. - Vol. 247. - P. 112451. DOI: 10.1016/J.COMPSTRUCT.2020.112451 Scholar
11.Li, T. Enhancing indentation and impact resistance in auxetic composite materials / T. Li, F. Liu, L. Wang // Compos. Part B Eng. - 2020. - Vol. 198, no. July. - P. 108229. DOI: 10.1016/j.compositesb.2020.108229 Scholar
12.Experimental Investigation of the Properties of Auxetic and Non-Auxetic Metamaterials Made of Metal During Penetration of Rigid Strikers / S.Y. Ivanova [et al.] // Mech. Solids. - 2023. - Vol. 58, no. 2. - P. 524-528. DOI: 10.3103/S0025654422601616 Scholar
13.Studying the Properties of Metamaterials with a Negative Poisson's Ratio when Punched by a Rigid Impactor / S.Y. Ivanova [et al.] // Mech. Solids. - 2023. - Vol. 58, no. 5. - P. 1536-1544. DOI: 10.3103/S0025654423600897 Scholar
14.A simple 3D re-entrant auxetic metamaterial with enhanced energy absorption / X.C. Teng [et al.] // Int. J. Mech. Sci. - 2022. - Vol. 229, no. July. - P. 107524. DOI: 10.1016/j.ijmecsci.2022.107524 Scholar
15.Jin, S. Shear resistance of an auxetic chiral mechanical metamaterial / S. Jin, Y.P. Korkolis, Y. Li // Int. J. Solids Struct. - 2019. - Vol. 174-175. - P. 28-37. DOI: 10.1016/j.ijsolstr.2019.06.005 Scholar
16.Chiral topologies for composite morphing structures - Part II: Novel configurations and technological processes / A. Airoldi [et al.] // Phys. Status Solidi Basic Res. - 2015. - Vol. 252, no. 7. - P. 1446-1454. DOI: 10.1002/pssb.201584263 Scholar
17.Review of auxetic materials for sports applications: Expanding options in comfort and protection / O. Duncan [et al.] // Appl. Sci. - 2018. - Vol. 8, no. 6. DOI: 10.3390/app8060941 Scholar
18.Weng, L. Analytical model of Li-ion diffusion-induced stress in nanowire and negative Poisson's ratio electrode under different operations / L. Weng, J. Zhou, R. Cai // Int. J. Mech. Sci. - 2018. - Vol. 141. - P. 245-261. DOI: 10.1016/J.IJMECSCI.2018.04.013 Scholar
19.Structure design and multi-objective optimization of a novel NPR bumper system / C.Y. Wang [et al.] // Compos. Part B Eng. - 2018. - Vol. 153, no. April. - P. 78-96. DOI: 10.1016/j.compositesb.2018.07.024 Scholar
20.Rationally designed meta-implants: A combination of auxetic and conventional meta-biomaterials / H.M.A. Kolken [et al.] // Mater. Horizons. - 2018. - Vol. 5, no. 1. - P. 28-35. DOI: 10.1039/c7mh00699c Scholar
21.Auxetic response of additive manufactured cubic chiral lattices at large plastic strains / C. Iantaffi [et al.] // Mater. Des. - 2023. - Vol. 233, no. May. - P. 112207. DOI: 10.1016/j.matdes.2023.112207 Scholar
22.Programmable mechanical metamaterials based on hierarchical rotating structures / X. Li [et al.] // Int. J. Solids Struct. - 2021. - Vol. 216. - P. 145-155. DOI: 10.1016/j.ijsolstr.2021.01.028 Scholar
23.Novel 3D auxetic lattice structures developed based on the rotating rigid mechanism / Y. Gao [et al.] // Int. J. Solids Struct. - 2021. - Vol. 233. - P. 111232. DOI: 10.1016/J.IJSOLSTR.2021.111232 Scholar
24.Crashworthiness analysis of double-arrowed auxetic structure under axial impact loading / Q. Gao [et al.] // Mater. Des. - 2019. - Vol. 161. - P. 22-34. DOI: 10.1016/j.matdes.2018.11.013 Scholar
25.Carneiro, V.H. Axisymmetric auxetics / V.H. Carneiro, H. Puga // Compos. Struct. - 2018. - Vol. 204, no. April. - P. 438-444. DOI: 10.1016/j.compstruct.2018.07.116 Scholar
26.Carneiro, V.H. Enhanced mechanical properties in cellular solids using axisymmetric configurations / V.H. Carneiro, H. Puga // Compos. Struct. - 2021. - Vol. 255, no. May 2020. - P. 112972. DOI: 10.1016/j.compstruct.2020.112972 Scholar
27.Yang, H. Design and characterization of axisymmetric auxetic metamaterials / H. Yang, L. Ma // Compos. Struct. - 2020. - Vol. 249, no. May. DOI: 10.1016/j.compstruct.2020.112560 Scholar
28.Development and characterisation of novel three-dimensional axisymmetric chiral auxetic structures / N. Novak [et al.] // J. Mater. Res. Technol. - 2022. - Vol. 17. - P. 2701-2713. DOI: 10.1016/j.jmrt.2022.02.025 Scholar
29.Tubular auxetic structures: A review / R.A. Gomes [et al.] // Thin-Walled Struct. - 2023. - Vol. 188, no. February. - P. 110850. DOI: 10.1016/j.tws.2023.110850 Scholar
30.Gao, Q. Energy absorption of thin walled tube filled with gradient auxetic structures-theory and simulation / Q. Gao, W.H. Liao // Int. J. Mech. Sci. - 2021. - Vol. 201. - P. 106475. DOI: 10.1016/J.IJMECSCI.2021.106475 Scholar
31.Design and characterization of novel bi-directional auxetic cubic and cylindrical metamaterials / Li J. [et al.] // Compos. Struct. - 2022. - Vol. 299, no. June. - P. 116015. DOI: 10.1016/j.compstruct.2022.116015 Scholar
32.Multi-objective crashworthiness optimization for an auxetic cylindrical structure under axial impact loading / Q. Gao [et al.] // Mater. Des. - 2018. - Vol. 143. - P. 120-130. DOI: 10.1016/j.matdes.2018.01.063 Scholar
33.Deformation behaviors and energy absorption of auxetic lattice cylindrical structures under axial crushing load / Y. Guo [et al.] // Aerosp. Sci. Technol. - 2020. - Vol. 98. - P. 105662. DOI: 10.1016/j.ast.2019.105662 Scholar
34.Effect of auxetic structures on crash behavior of cylindrical tube / W. Lee [et al.] // Compos. Struct. - 2019. - Vol. 208, no. October 2018. - P. 836-846. DOI: 10.1016/j.compstruct.2018.10.068 Scholar
35.D. Han [et al.] Lightweight auxetic tubular metamaterials: Design and mechanical characteristics // Compos. Struct. - 2023. - Vol. 311, no. February. - P. 116849. DOI: 10.1016/j.compstruct.2023.116849 Scholar
36.Mechanical properties of auxetic circular and square tubes filled with aluminum foam / R.Y. Huo [et al.] // Eng. Struct. - 2023. - Vol. 281, no. February. - P. 115732. DOI: 10.1016/j.engstruct.2023.115732 Scholar
37.Gao, Q. Theoretical predictions of dynamic responses of cylindrical sandwich filled with auxetic structures under impact loading / Q. Gao, W.H. Liao, C. Huang // Aerosp. Sci. Technol. - 2020. - Vol. 107. - P. 106270. DOI: 10.1016/J.AST.2020.106270 Scholar
38.Li, C. Postbuckling of pressure-loaded auxetic sandwich cylindrical shells with FG-GRC facesheets and 3D double-V meta-lattice core / C. Li, J. Yang, H.S. Shen // Thin-Walled Struct. - 2022. - Vol. 177, no. March. - P. 109440. DOI: 10.1016/j.tws.2022.109440 Scholar
39.Allam, M.N.M. Hygrothermal deformation of spinning FG graphene sandwich cylindrical shells having an auxetic core / M.N.M. Allam, A.F. Radwan, M. Sobhy // Eng. Struct. - 2022. - Vol. 251, no. PA. - pp. 113433. DOI: 10.1016/j.engstruct.2021.113433 Scholar
40.Geometrically nonlinear dynamic response of eccentrically stiffened circular cylindrical shells with negative poisson's ratio in auxetic honeycombs core layer / P.H. Cong [et al.] // Int. J. Mech. Sci. - 2019. - Vol. 152, no. December 2018. - P. 443-453. DOI: 10.1016/j.ijmecsci.2018.12.052 Scholar
41.Composites with Re-Entrant Lattice: Effect of Filler on Auxetic Behaviour / M. Tashkinov [et al.] // Polymers (Basel). - 2023. - Vol. 15, no. 20. - P. 4076. DOI: 10.3390/polym15204076 Scholar
42.Nielson, G.M. Dual marching cubes / G.M. Nielson // IEEE Visualization 2004. - 2004. - P. 489-496. DOI: 10.1109/VISUAL.2004.28 Scholar
43.Smooth Boundary Surfaces from Binary 3D Datasets / D. Cohen-Or [et al.] // Volume Graphics. - 2000. DOI: 10.1007/978-1-4471-0737-8_4 Scholar

Article information

Published: 26 December 2024
Issue date: 26 December 2024
Issue: No. 6 (2024)

Effect of Variation of Coefficient of Thermal Expansion on Thermomechanical Deformation of Cylindrical In-plane Auxetics Based on Re-Entrant Cells

Abstract

Keywords

Ключевые слова

Bibliography

Other articles in this issue

Article information