Yıl 2023,
Cilt: 11 Sayı: 4, 893 - 902, 28.12.2023
İsmail Erdoğan
,
İhsan Toktas
Kaynakça
- [1] A.V. Mazaev, O. Ajeneza, M.V. Shitikova, Auxetics materials: classification, mechanical properties, and applications, IOP Conference Series: Materials Science and Engineering, 747 (2020) 012008.
- [2] N. Novak, L. Biasetto, P. Rebesan, F. Zanini, S. Carmignato, L. Krstulovic-Opara, M. Vesenjak, Z. Ren, Experimental and computational evaluation of tensile properties of additively manufactured hexa- and tetrachiral auxetic cellular structures, Additive Manufacturing 45 (2021) 102022.
- [3] S. Gohar, G. Hussain, M. Ilyas, A. Ali, Performance of 3D printed topologically optimized novel auxetic structures under compressive loading: experimental and FE analyses, Journal of Materials Research and Technology 15 (2021) 394–408.
- [4] K. Gunaydin, F.G. Gallina, A. Airoldi, G. Sala, A.M. Grande, Numerical and experimental crushing behaviour investigation of EBM printed auxetic chiral lattices, II International Conference on Simulation for Additive Manufacturing - Sim-AM 2019 (2019).
- [5] I.K. Türkoğlu, H. Kasım, M. Yazıcı, Experimental investigation of 3D-printed auxetic core sandwich structures under quasi-static and dynamic compression and bending loads. International Journal of Protective Structures 14(1) (2023) 63-86.
- [6] S. Gök, Structural design and analysis of an impact resistant auxetic metamaterial. M.Sc. Thesis, Istanbul Technical University, (2021).
- [7] K. Meena, S. Singamneni, A new auxetic structure with significantly reduced stress concentration effects. Materials & Design 173 (2019) 107779.
- [8] C. Luo, C. Zhen, X. Zhang, G. Zhang, X. Ren, Design, manufacturing and applications of auxetic tubular structures: A review, Thin-Walled Structures 163 (2021) 107682.
- [9] M. Najafi, H. Ahmadi, L. Gholamhossein, Experimental investigation on energy absorption of auxetic structures, Materials Today: Proceedings 34(1) (2020) 350–355.
- [10] Y. Shao, J. Meng, G. Mab, S. Ren, L. Fang, X. Cao, L. Liu, H. Li, W. Wua, D. Xiao, Insight into the negative Poisson’s ratio effect of the gradient auxetic reentrant honeycombs, Composite Structures 274 (2021) 114366.
- [11] R. Nedoushan, Y. An, W. Yu, M. Abghary, Novel triangular auxetic honeycombs with enhanced stiffness, Composite Structures 277 (2021) 114605.
- [12] S. Tabacu, N.D. Stanescu, A theoretical model for the estimate of the reaction force for 3D auxetic anti-tetra chiral tubular structures under tensile loads, Thin-Walled Structures 168 (2021) 108304.
- [13] J. Shena, K. Liua, O. Zenga, J. Gea, Z. Donga, Design and mechanical property studies of 3D re-entrant lattice auxetic structure, Aerospace Science and Technology 118 (2021) 106998.
- [14] Y. Gao, X. Wei, X. Han, Z. Zhou, J. Xiong, Novel 3D auxetic lattice structures developed based on the rotating rigid mechanism, International Journal of Solids and Structures 233 (2021) 111232.
- [15] S. Bronder, M. Adorna, T. Fíla, P. Koudelka, J. Falta, O. Jiroušek, A. Jung, Hybrid auxetic structures: Structural optimization and mechanical characterization, Advanced Engineering Materials 23 (2021) 2001393.
- [16] A.R. Sangsefidi, S. H. Dibajian, J. Kadkhodapour, A. P. Anaraki, S. Schmauder, Y. Schneider, An Abaqus plugin for evaluation of the Auxetic structure performance, Engineering with Computers 38(2) (2022) 1681–1704.
- [17] W. Wu, P. Liu, Z. Kang, A novel mechanical metamaterial with simultaneous stretching- and compression-expanding property, Materials & Design 208 (2021) 109930.
- [18] G.Z. Fan, X. Ren, S.L. Wang, C. Luo, Y.M. Xie, A novel cement-based auxetic foam composite: Experimental study, Case Studies in Construction Materials 17 (2022) e01159.
- [19] M. Wallbanks, M. F. Khan, M. Bodaghi, A. Triantaphyllou, A. Serjouei, On the design workflow of auxetic metamaterials for structural applications, Smart Materials and Structures 31 (2022) 023002.
- [20] U. Kemiklioglu, Novel design and comparison of structural and modal analyses of auxetic geometry versus honeycomb geometry, Journal of Applied Mechanical Engineering 10 (2) (2021) 1000349.
- [21] S. Wang, C. Deng, O. Ojo, B. Akinrinlola, J. Kozub, L. Wu, Design and modeling of a novel three-dimensional auxetic reentrant honeycomb structure for energy absorption, Composite Structures 280 (2022) 114882.
- [22] D. Photiou, S. Avraam, F. Sillani, F. Verga, O. Jay, L. Papadakis, Experimental and numerical analysis of 3D printed polymer tetra-petal auxetic structures under compression, Appl. Sci. 11(21) (2021) 10362.
- [23] G. Zhang, X. Ren, W. Jiang, X. Zhang, C. Luo, Y. Zhang, M. Xie, A novel auxetic chiral lattice composite: Experimental and numerical study, Composite Structures 282 (2022) 110956.
- [24] C. Yang, H.D. Vora, Y. Chang, Behavior of auxetic structures under compression and impact forces, Smart Materials and Structures 27 (2018) 025012.
- [25] J. Lawrensen, A. Nazir, C.P. Hsu, Comparison between 3D printed auxetic and non-auxetic structures: Simulation and experimental validation, International Journal of Innovative Science and Research Technology 6(9) (2021) 2456–2165.
- [26] A. Alomarah, S.H. Masood, I. Sbarski, B. Faisal, Z. Gao, D. Ruan, Compressive properties of 3D printed auxetic structures: experimental and numerical studies, Virtual and Physical Prototyping 15(1) (2020) 1–21.
- [27] O. Gülcan, K. Günaydın, Distortion and dimensional deviation of Inconel 718 auxetic structures produced by DMLM, Journal of Additive Manufacturing Technologies 1(3) (2021) 563.
- [28] D. Gürkan, B. Sağbaş, Additively manufactured Ti6Al4V lattice Structures for biomedical applications, Int. J. of 3D Printing Tech. Dig. Ind. 5(2) (2021) 155–163.
- [29] A. Joseph, V. Mahesh, D. Harursampath, On the application of additive manufacturing methods for auxetic structures: A review, Adv. Manuf. 9 (2021) 342–368.
- [30] A. Hosseinkhani, D. Younesian, M. Ranjbar, F. Scarpa, Enhancement of the vibro-acoustic performance of anti-tetra-chiral auxetic sandwich panels using topologically optimized local resonators, Applied Acoustics 177 (2021) 107930.
- [31] M.S. Mazloomi, M. Ranjbar, L. Boldrin, F. Scarpa, S. Patsias, N. Ozada, Vibroacoustics of 2D gradient auxetic hexagonal honeycomb sandwich panels, Composite Structures 187 (2018) 593–603.
- [32] M.S. Mazloomi, M. Ranjbar, Hybrid design optimization of sandwich panels with gradient shape anti-tetrachiral auxetic core for vibroacoustic applications, Transport in Porous Media 142 (2022) 5–22.
- [33] X. C. Teng, X. Ren, Y. Zhang, W. Jiang, Y. Pan, X.G. Zhang, X.Y. Zhang, Y.M. Xie, A simple 3D re-entrant auxetic metamaterial with enhanced energy absorption, International Journal of Mechanical Sciences 229 (2022) 107524.
- [34] T.Wang, Z. Li, L. Wang, X. Zhang, Z. Ma, In-plane elasticity of a novel arcwall-based double-arrowed auxetic honeycomb design: Energy-based theoretical analysis and simulation, Aerospace Science and Technology 127 (2022) 107715.
- [35] W.M. Zhang, Z.Y. Li, J.S. Yang, L. Ma, Z. Lin, R. Schmidt, K.U. Schröder, A lightweight rotationally arranged auxetic structure with excellent energy absorption performance, Mechanics of Materials 166 (2022) 104244.
[36] T. Wang, Y. Xie, L. Wang, X. Zhang, Z. Ma, Size effects of elastic properties for auxetic cellular structures: bending energy-based method, Materials Today Communications 31 (2022) 103585.
- [37] Y. Zhang, X. Ren, D. Han, X. Cheng, W. Jiang, X.G. Zhang, X.Y. Zhang, Y.M. Xie, Static and dynamic properties of a perforated metallic auxetic metamaterial with tunable stiffness and energy absorption, International Journal of Impact Engineering 164 (2022) 104193.
- [38] M.F. Guo, H. Yang, L. Ma, 3D lightweight double arrow-head plate-lattice auxetic structures with enhanced stiffness and energy absorption performance, Composite Structures 290 (2022) 115484.
- [39] R.P. Bohara, S. Linforth, T. Nguyen, A. Ghazlan, T. Ngo, Novel lightweight high-energy absorbing auxetic structures guided by topology optimisation, International Journal of Mechanical Sciences 211 (2021) 106793.
[40] Y. Zhou, Y. Li, D. Jiang, Y. Chen, Y.M. Xie, L.J. Jia, In-plane impact behavior of 3D-printed auxetic stainless honeycombs, Engineering Structures 266 (2022) 114656.
- [41] W. Yang, R. Huang, J. Liu, J. Liu, W. Huang, Ballistic impact responses and failure mechanism of composite double-arrow auxetic structure, Thin-Walled Structures 174 (2022) 109087.
- [42] D. Han, X. Ren, Y. Zhang, X.Y. Zhang, X.G. Zhang, C. Luo, Y.M. Xie, Lightweight auxetic metamaterials: Design and characteristic study, Composite Structures 293 (2022) 115706.
- [43] D. Kalubadanage, A. Remennikov, T. Ngo, C. Qi, Experimental study on damage magnification effect of lightweight auxetic honeycomb protective panels under close-in blast loads, Thin-Walled Structures 178 (2022) 109509.
- [44] I.P. Seetoh, B. Leong, E.L. Yi, K. Markandan, P. K. Kanaujia, C.Q. Lai, Extremely stiff and lightweight auxetic metamaterial designs enabled by asymmetric strut cross-sections, Extreme Mechanics Letters 52 (2022) 101677.
- [45] A. Sorrentino, D. Castagnetti, L. Mizzi, A. Spaggiari, Bio-inspired auxetic mechanical metamaterials evolved from rotating squares unit, Mechanics of Materials 173 (2022) 104421.
- [46] J. Li, Z.Y. Zhang, H.T. Liu, Y.B. Wang, Design and characterization of novel bi-directional auxetic cubic and cylindrical metamaterials, Composite Structures 299 (2022) 116015.
- [47] Z.Y. Li, X.T. Wang, L. Ma, L.Z. Wu, Study on the mechanical properties of CFRP composite auxetic structures consist of corrugated sheets and tubes, Composite Structures 292 (2022) 115655.
- [48] C. Luo, X. Ren, D. Han, X.G. Zhang, R. Zhong, X.Y. Zhang, Y.M. Xie, A novel concrete-filled auxetic tube composite structure: Design and compressive characteristic study, Engineering Structures 268 (2022) 114759.
- [49] W. Jiang, X. Ren, S.L. Wang, X.G. Zhang, X.Y. Zhang, C. Luo, Y.M. Xie, F. Scarpa, A. Alderson, K.E. Evans, Manufacturing, characteristics and applications of auxetic foams: A state-of-the-art review, Composites Part B: Engineering 235 (2022) 109733.
- [50] C. Mercer, T. Speck, J. Lee, D.S. Balint, M. Thielen, Effects of geometry and boundary constraint on the stiffness and negative Poisson’s ratio behaviour of auxetic metamaterials under quasi-static and impact loading, International Journal of Impact Engineering 169 (2022) 104315.
- [51] I. Zhilyaev, D. Krushinsky, M. Ranjbar, A. O. Krushynska, Hybrid machine-learning and finite-element design for flexible metamaterial wings, Materials & Design 218 (2022) 110709.
- [52] I. Zhilyaev, N. Anerao, A.G.P. Kottapalli, M.C. Yilmaz, M. Murat, M. Ranjbar, A. Krushynska, Fully-printed metamaterial-type flexible wings with controllable flight characteristics, Bioinspir. Biomim. 17 (2022) 025002.
- [53] İ. Erdoğan, İ. Toktaş, Investigation of the effect of geometry ınner thickness on new designed auxetic structure, Journal of Polytechnic, early view.
- [54] R. Penrose, Islamic Geometric Patterns, Nature 2017 USA.
- [55] Standard Test Methods for Tension Testing of Metallic Materials, Designation: E8/E8M − 16a. 2016.
- [56] Ansys Analysis Software, Material Library, ANSYS 2020 R1.
Investigation of the Auxetic of a novel geometric structure and improvement of Poisson’s ratio at different inner thicknesses
Yıl 2023,
Cilt: 11 Sayı: 4, 893 - 902, 28.12.2023
İsmail Erdoğan
,
İhsan Toktas
Öz
Poisson’s ratio, one of the important mechanical properties of materials and structures, is positive for almost all of the known materials and structures. However, auxetic materials or structures has negative Poisson’s ratios. Characteristics of the auxetic structures are very important to be used in design of a new structure. Computational or experimental studies on auxetic structures have been increasing in literature. In this study, a new auxetic lattice structure with different Poisson’s ratios was designed and studied by finite element analysis. Mechanical properties of the newly designed auxetic lattice structures were analyzed with different lattice inner thickness. Results showed that change in inner thickness affects the Poisson’s ratio, mass, volume and surface area of the newly designed Auxetic lattice structures.
Kaynakça
- [1] A.V. Mazaev, O. Ajeneza, M.V. Shitikova, Auxetics materials: classification, mechanical properties, and applications, IOP Conference Series: Materials Science and Engineering, 747 (2020) 012008.
- [2] N. Novak, L. Biasetto, P. Rebesan, F. Zanini, S. Carmignato, L. Krstulovic-Opara, M. Vesenjak, Z. Ren, Experimental and computational evaluation of tensile properties of additively manufactured hexa- and tetrachiral auxetic cellular structures, Additive Manufacturing 45 (2021) 102022.
- [3] S. Gohar, G. Hussain, M. Ilyas, A. Ali, Performance of 3D printed topologically optimized novel auxetic structures under compressive loading: experimental and FE analyses, Journal of Materials Research and Technology 15 (2021) 394–408.
- [4] K. Gunaydin, F.G. Gallina, A. Airoldi, G. Sala, A.M. Grande, Numerical and experimental crushing behaviour investigation of EBM printed auxetic chiral lattices, II International Conference on Simulation for Additive Manufacturing - Sim-AM 2019 (2019).
- [5] I.K. Türkoğlu, H. Kasım, M. Yazıcı, Experimental investigation of 3D-printed auxetic core sandwich structures under quasi-static and dynamic compression and bending loads. International Journal of Protective Structures 14(1) (2023) 63-86.
- [6] S. Gök, Structural design and analysis of an impact resistant auxetic metamaterial. M.Sc. Thesis, Istanbul Technical University, (2021).
- [7] K. Meena, S. Singamneni, A new auxetic structure with significantly reduced stress concentration effects. Materials & Design 173 (2019) 107779.
- [8] C. Luo, C. Zhen, X. Zhang, G. Zhang, X. Ren, Design, manufacturing and applications of auxetic tubular structures: A review, Thin-Walled Structures 163 (2021) 107682.
- [9] M. Najafi, H. Ahmadi, L. Gholamhossein, Experimental investigation on energy absorption of auxetic structures, Materials Today: Proceedings 34(1) (2020) 350–355.
- [10] Y. Shao, J. Meng, G. Mab, S. Ren, L. Fang, X. Cao, L. Liu, H. Li, W. Wua, D. Xiao, Insight into the negative Poisson’s ratio effect of the gradient auxetic reentrant honeycombs, Composite Structures 274 (2021) 114366.
- [11] R. Nedoushan, Y. An, W. Yu, M. Abghary, Novel triangular auxetic honeycombs with enhanced stiffness, Composite Structures 277 (2021) 114605.
- [12] S. Tabacu, N.D. Stanescu, A theoretical model for the estimate of the reaction force for 3D auxetic anti-tetra chiral tubular structures under tensile loads, Thin-Walled Structures 168 (2021) 108304.
- [13] J. Shena, K. Liua, O. Zenga, J. Gea, Z. Donga, Design and mechanical property studies of 3D re-entrant lattice auxetic structure, Aerospace Science and Technology 118 (2021) 106998.
- [14] Y. Gao, X. Wei, X. Han, Z. Zhou, J. Xiong, Novel 3D auxetic lattice structures developed based on the rotating rigid mechanism, International Journal of Solids and Structures 233 (2021) 111232.
- [15] S. Bronder, M. Adorna, T. Fíla, P. Koudelka, J. Falta, O. Jiroušek, A. Jung, Hybrid auxetic structures: Structural optimization and mechanical characterization, Advanced Engineering Materials 23 (2021) 2001393.
- [16] A.R. Sangsefidi, S. H. Dibajian, J. Kadkhodapour, A. P. Anaraki, S. Schmauder, Y. Schneider, An Abaqus plugin for evaluation of the Auxetic structure performance, Engineering with Computers 38(2) (2022) 1681–1704.
- [17] W. Wu, P. Liu, Z. Kang, A novel mechanical metamaterial with simultaneous stretching- and compression-expanding property, Materials & Design 208 (2021) 109930.
- [18] G.Z. Fan, X. Ren, S.L. Wang, C. Luo, Y.M. Xie, A novel cement-based auxetic foam composite: Experimental study, Case Studies in Construction Materials 17 (2022) e01159.
- [19] M. Wallbanks, M. F. Khan, M. Bodaghi, A. Triantaphyllou, A. Serjouei, On the design workflow of auxetic metamaterials for structural applications, Smart Materials and Structures 31 (2022) 023002.
- [20] U. Kemiklioglu, Novel design and comparison of structural and modal analyses of auxetic geometry versus honeycomb geometry, Journal of Applied Mechanical Engineering 10 (2) (2021) 1000349.
- [21] S. Wang, C. Deng, O. Ojo, B. Akinrinlola, J. Kozub, L. Wu, Design and modeling of a novel three-dimensional auxetic reentrant honeycomb structure for energy absorption, Composite Structures 280 (2022) 114882.
- [22] D. Photiou, S. Avraam, F. Sillani, F. Verga, O. Jay, L. Papadakis, Experimental and numerical analysis of 3D printed polymer tetra-petal auxetic structures under compression, Appl. Sci. 11(21) (2021) 10362.
- [23] G. Zhang, X. Ren, W. Jiang, X. Zhang, C. Luo, Y. Zhang, M. Xie, A novel auxetic chiral lattice composite: Experimental and numerical study, Composite Structures 282 (2022) 110956.
- [24] C. Yang, H.D. Vora, Y. Chang, Behavior of auxetic structures under compression and impact forces, Smart Materials and Structures 27 (2018) 025012.
- [25] J. Lawrensen, A. Nazir, C.P. Hsu, Comparison between 3D printed auxetic and non-auxetic structures: Simulation and experimental validation, International Journal of Innovative Science and Research Technology 6(9) (2021) 2456–2165.
- [26] A. Alomarah, S.H. Masood, I. Sbarski, B. Faisal, Z. Gao, D. Ruan, Compressive properties of 3D printed auxetic structures: experimental and numerical studies, Virtual and Physical Prototyping 15(1) (2020) 1–21.
- [27] O. Gülcan, K. Günaydın, Distortion and dimensional deviation of Inconel 718 auxetic structures produced by DMLM, Journal of Additive Manufacturing Technologies 1(3) (2021) 563.
- [28] D. Gürkan, B. Sağbaş, Additively manufactured Ti6Al4V lattice Structures for biomedical applications, Int. J. of 3D Printing Tech. Dig. Ind. 5(2) (2021) 155–163.
- [29] A. Joseph, V. Mahesh, D. Harursampath, On the application of additive manufacturing methods for auxetic structures: A review, Adv. Manuf. 9 (2021) 342–368.
- [30] A. Hosseinkhani, D. Younesian, M. Ranjbar, F. Scarpa, Enhancement of the vibro-acoustic performance of anti-tetra-chiral auxetic sandwich panels using topologically optimized local resonators, Applied Acoustics 177 (2021) 107930.
- [31] M.S. Mazloomi, M. Ranjbar, L. Boldrin, F. Scarpa, S. Patsias, N. Ozada, Vibroacoustics of 2D gradient auxetic hexagonal honeycomb sandwich panels, Composite Structures 187 (2018) 593–603.
- [32] M.S. Mazloomi, M. Ranjbar, Hybrid design optimization of sandwich panels with gradient shape anti-tetrachiral auxetic core for vibroacoustic applications, Transport in Porous Media 142 (2022) 5–22.
- [33] X. C. Teng, X. Ren, Y. Zhang, W. Jiang, Y. Pan, X.G. Zhang, X.Y. Zhang, Y.M. Xie, A simple 3D re-entrant auxetic metamaterial with enhanced energy absorption, International Journal of Mechanical Sciences 229 (2022) 107524.
- [34] T.Wang, Z. Li, L. Wang, X. Zhang, Z. Ma, In-plane elasticity of a novel arcwall-based double-arrowed auxetic honeycomb design: Energy-based theoretical analysis and simulation, Aerospace Science and Technology 127 (2022) 107715.
- [35] W.M. Zhang, Z.Y. Li, J.S. Yang, L. Ma, Z. Lin, R. Schmidt, K.U. Schröder, A lightweight rotationally arranged auxetic structure with excellent energy absorption performance, Mechanics of Materials 166 (2022) 104244.
[36] T. Wang, Y. Xie, L. Wang, X. Zhang, Z. Ma, Size effects of elastic properties for auxetic cellular structures: bending energy-based method, Materials Today Communications 31 (2022) 103585.
- [37] Y. Zhang, X. Ren, D. Han, X. Cheng, W. Jiang, X.G. Zhang, X.Y. Zhang, Y.M. Xie, Static and dynamic properties of a perforated metallic auxetic metamaterial with tunable stiffness and energy absorption, International Journal of Impact Engineering 164 (2022) 104193.
- [38] M.F. Guo, H. Yang, L. Ma, 3D lightweight double arrow-head plate-lattice auxetic structures with enhanced stiffness and energy absorption performance, Composite Structures 290 (2022) 115484.
- [39] R.P. Bohara, S. Linforth, T. Nguyen, A. Ghazlan, T. Ngo, Novel lightweight high-energy absorbing auxetic structures guided by topology optimisation, International Journal of Mechanical Sciences 211 (2021) 106793.
[40] Y. Zhou, Y. Li, D. Jiang, Y. Chen, Y.M. Xie, L.J. Jia, In-plane impact behavior of 3D-printed auxetic stainless honeycombs, Engineering Structures 266 (2022) 114656.
- [41] W. Yang, R. Huang, J. Liu, J. Liu, W. Huang, Ballistic impact responses and failure mechanism of composite double-arrow auxetic structure, Thin-Walled Structures 174 (2022) 109087.
- [42] D. Han, X. Ren, Y. Zhang, X.Y. Zhang, X.G. Zhang, C. Luo, Y.M. Xie, Lightweight auxetic metamaterials: Design and characteristic study, Composite Structures 293 (2022) 115706.
- [43] D. Kalubadanage, A. Remennikov, T. Ngo, C. Qi, Experimental study on damage magnification effect of lightweight auxetic honeycomb protective panels under close-in blast loads, Thin-Walled Structures 178 (2022) 109509.
- [44] I.P. Seetoh, B. Leong, E.L. Yi, K. Markandan, P. K. Kanaujia, C.Q. Lai, Extremely stiff and lightweight auxetic metamaterial designs enabled by asymmetric strut cross-sections, Extreme Mechanics Letters 52 (2022) 101677.
- [45] A. Sorrentino, D. Castagnetti, L. Mizzi, A. Spaggiari, Bio-inspired auxetic mechanical metamaterials evolved from rotating squares unit, Mechanics of Materials 173 (2022) 104421.
- [46] J. Li, Z.Y. Zhang, H.T. Liu, Y.B. Wang, Design and characterization of novel bi-directional auxetic cubic and cylindrical metamaterials, Composite Structures 299 (2022) 116015.
- [47] Z.Y. Li, X.T. Wang, L. Ma, L.Z. Wu, Study on the mechanical properties of CFRP composite auxetic structures consist of corrugated sheets and tubes, Composite Structures 292 (2022) 115655.
- [48] C. Luo, X. Ren, D. Han, X.G. Zhang, R. Zhong, X.Y. Zhang, Y.M. Xie, A novel concrete-filled auxetic tube composite structure: Design and compressive characteristic study, Engineering Structures 268 (2022) 114759.
- [49] W. Jiang, X. Ren, S.L. Wang, X.G. Zhang, X.Y. Zhang, C. Luo, Y.M. Xie, F. Scarpa, A. Alderson, K.E. Evans, Manufacturing, characteristics and applications of auxetic foams: A state-of-the-art review, Composites Part B: Engineering 235 (2022) 109733.
- [50] C. Mercer, T. Speck, J. Lee, D.S. Balint, M. Thielen, Effects of geometry and boundary constraint on the stiffness and negative Poisson’s ratio behaviour of auxetic metamaterials under quasi-static and impact loading, International Journal of Impact Engineering 169 (2022) 104315.
- [51] I. Zhilyaev, D. Krushinsky, M. Ranjbar, A. O. Krushynska, Hybrid machine-learning and finite-element design for flexible metamaterial wings, Materials & Design 218 (2022) 110709.
- [52] I. Zhilyaev, N. Anerao, A.G.P. Kottapalli, M.C. Yilmaz, M. Murat, M. Ranjbar, A. Krushynska, Fully-printed metamaterial-type flexible wings with controllable flight characteristics, Bioinspir. Biomim. 17 (2022) 025002.
- [53] İ. Erdoğan, İ. Toktaş, Investigation of the effect of geometry ınner thickness on new designed auxetic structure, Journal of Polytechnic, early view.
- [54] R. Penrose, Islamic Geometric Patterns, Nature 2017 USA.
- [55] Standard Test Methods for Tension Testing of Metallic Materials, Designation: E8/E8M − 16a. 2016.
- [56] Ansys Analysis Software, Material Library, ANSYS 2020 R1.