基于数据驱动的同心Re-entrant负泊松比超材料设计及性能调谐研究

超材料是一种通过自身胞元排布而实现超常物理特性的结构，具有超越常规自然界材料的特性和巨大潜在应用前景。超材料独特物理特性取决于自身的结构设计而非组成他们的物质本身的属性。因此，人为的通过结构胞元层面的结构设计以实现超常物理特性成为近年来备受关注的研究命题。然而，当前超材料胞元层面的设计多来自于经验，缺乏有效的理论指导设计方法与研究范式，并不可避免的受制于设计者的经验喜好和文化背景等干扰，导致难以对所设计的超材料的性能做出精准的调谐和设计。针对这一问题，基于数据驱动的设计方法可实现超材料性能的精准调谐。基于此，本研究以一种具有同心re-entrant的负泊松比超材料（CREAM）为载体，围绕数据驱动设计这一中心，开发了自我演化几何构型算法，建立了基于神经网络CREAM模型和“刚度-负泊松比”多目标优化模型,探究了多物理场下CREAM性能预测模型适用性，并提出了多层次的减振CREAM带隙特性调整策略，最终，实现了CREAM性能可调谐性。本研究主要创新性工作如下：

（1）本研究提出了具有自我演化能力的CREAM几何构型算法，拓展了超材料几何构型的种类。在本研究中，通过结合多种类型的路径生长策略与图像处理技术，提出了三种具有自我演化能力的几何构型算法，即自主生长路径建模、优化路径建模及光滑路径优化建模等，这三种新型算法突破了以往参数化建模情况下超材料构型仅受制于少量参数的弊端，丰富了几何构型的种类，扩展了设计的自由度和设计空间。同时，通过建立求解CREAM泊松比的数值模型，对各种算法的主要影响因素进行了讨论。结果显示，所提出的具有自我演化算法所生成的CREAM均保持了负泊松比特性，这说明这些新算法在CREAM设计中的稳定性，同时为后续机器学习的数据集的获得奠定了基础。

（2）本研究建立了基于数据驱动的CREAM设计方法，解决了其正逆设计需求，并为该结构的“刚度-负泊松比”协调问题提供了策略与流程化研究方法。基于（1）所述的设计方法构建数据集，本研究分别构建了基于反向传播神经网络（BPNN）和遗传算法优化反向传播神经网络（GA-BPNN）的CREAM性能预测模型和结构设计模型，解决了CREAM的正向预测和逆向设计问题。其中，在逆向设计中，遗传算法可以优化神经网络的初始阈值和权重，进而优化网络结构，极大增加了预测精度。结果表明，这两种基于神经网络的模型具有较高的预测精度，可以分别实现对泊松比和几何构型的精准预测。同时，验证了所提出的神经网络模型对自我演化设计方法生成的CREAM性能预测同样具有适用性。针对超材料压缩情况下的屈曲现象，建立了多目标优化模型，为“刚度-负泊松比”协调问题提供了新的设计思路。

（3）本研究建立了基于数据驱动的压电超材料设计方法，并通过试验验证了该方法在压电超材料设计中的适用性，探索了其在多物理场（力场与电场）中的作用，实现了压电超材料“力-电”性能的可调谐性。在本研究中，制备了一种新型的PVDF/TPPC/CNT新型压电超材料。通过搭建压电信号放大电路，测试了不同几何构型的CREAM的输出电压，同时对比了模拟结果和实验测试结果。结果表明，基于数值模型的输出电压预测结果与实验测量值有较高的吻合度。在此基础上，本研究建立了基于BPNN的压电超材料性能预测模型，预测结果证明该模型对泊松比和输出电压等两个不同物理场的性能指标具有较好的预测精度，其在“力-电耦合”设计中具有良好的适用性。这为压电超材料的实际应用提供了现实指导意义。

（4）本研究探究了数据驱动方法在CREAM减振性能预测方面的应用，并借助水泥基超材料（CMs）提出了一种双层次（几何构型、材料属性）的带隙特性调控策略。基于局域共振动力学模型，建立了求解CREAM特征频率的数值模型，并通过有限元法求解了不同构型的样本能带分布。证明了几何构型是调谐CREAM带隙特性的重要手段。在此基础上，构建了基于GA-BPNN的CREAM减振性能预测模型，验证了该模型对自我演化算法生成的CREAM的适用性。这为数据驱动CREAM减振性能预测及结构设计提供了参考。通过设计一种水泥基CREAM减振超材料（CMs），验证了通过调整水泥密度和几何构型均可实现其带隙特性的调谐。基于此，提出在减振设计中应兼顾材料属性和几何构型两个层面，实现对超材料带隙特性的有序调谐。

[1] PENDRY J B, HOLDEN A J, STEWART W J, et al. Extremely Low Frequency Plasmons in Metallic Mesostructures[J]. Physical Review Letters, 1996, 76(25): 4773-4776.
[2] SHELBY R A, SMITH D R, SCHULTZ S. Experimental Verification of a Negative Index of Refraction[J]. Science, 2001, 292(5514): 77-79.
[3] XUE L M, WANG Y J, LIU X J, et al. Propagation characteristics of adjustable abnormal hollow beams in gradient negative refractive index material[J]. Results in Physics, 2022, 43: 106085.
[4] MA J, LUO Z, TAN S, et al. Achieving the low emissivity of graphene oxide based film for micron-level electromagnetic waves stealth application[J]. Carbon, 2024, 218: 118771.
[5] PRATAP V, SONI A K, BASKEY H B, et al. Electromagnetic and radar absorbing properties of γ Fe2O3/Ba4Co2Fe36O60-epoxy polymeric composites for stealth applications[J]. Solid State Sciences, 2021, 113: 106553.
[6] C. GOKCE E, CALISIR M D, SELCUK S, et al. Electromagnetic interference shielding using biomass-derived carbon materials[J]. Materials Chemistry and Physics, 2024, 317: 129165.
[7] LIAO D, GUAN Y, HE Y, et al. Pickering emulsion strategy for high compressive carbon aerogel as lightweight electromagnetic interference shielding material and flexible pressure sensor[J]. Ceramics International, 2021, 47(16): 23433-23443.
[8] PENG Y G, SHEN Y X, GENG Z G, et al. Super-resolution acoustic image montage via a biaxial metamaterial lens[J]. Science Bulletin, 2020, 65(12): 1022-1029.
[9] WANG W, YADAV N P, SHEN Z, et al. Two-stage magnifying hyperlens structure based on metamaterials for super-resolution imaging[J]. Optik, 2018, 174: 199-206.
[10] DU L, SHI T, ZHOU Q, et al. A multi-layer square frustum metamaterial for ultra-broadband electromagnetic absorption based on carbonyl iron powder/carbon fiber composites[J]. Journal of Alloys and Compounds, 2023, 950: 169917.
[11] ZHAO S, MA H, SHAO T, et al. High temperature metamaterial enhanced electromagnetic absorbing coating prepared with alumina ceramic[J]. Journal of Alloys and Compounds, 2021, 874: 159822.
[12] LUO B, WU L, LI D, et al. Novel atomic-scale graphene metamaterials with broadband electromagnetic wave absorption and ultra-high elastic modulus[J]. Carbon, 2022, 196: 146-153.
[13] NAPOLSKII K S, NOYAN A A, KUSHNIR S E. Control of high-order photonic band gaps in one-dimensional anodic alumina photonic crystals[J]. Optical Materials, 2020, 109: 110317.
[14] JIA H, CHEN Z, LIU Z, et al. Photo-induced multi-color fluorescent hydrogels for optical information coding and encryption[J]. European Polymer Journal, 2023, 198: 112406.
[15] LIANG D, CHEN T. Optical modulated graphene metamaterial based on plasmon-induced transparency in the terahertz band: Application for sensing[J]. Diamond and Related Materials, 2023, 131: 109613.
[16] ZHENG D, WEN Y, XU X, et al. Metamaterial grating for colorimetric chemical sensing applications[J]. Materials Today Physics, 2023, 33: 101056.
[17] AMEMIYA T, KANAZAWA T, YAMASAKI S, et al. Metamaterial Waveguide Devices for Integrated Optics[J]. Materials, 2017, 10(9): 1037.
[18] STEIN A, NOUH M, SINGH T. Widening, transition and coalescence of local resonance band gaps in multi-resonator acoustic metamaterials: From unit cells to finite chains[J]. Journal of Sound and Vibration, 2022, 523: 116716.
[19] NEMAT-NASSER S. Inherent negative refraction on acoustic branch of two dimensional phononic crystals[J]. Mechanics of Materials, 2019, 132: 1-8.
[20] AREPOLAGE T, VERDY C, SYLVESTRE T, et al. Controlling heat capacity in a thermal concentrator using metamaterials: Numerical and experimental studies[J]. International Journal of Heat and Mass Transfer, 2024, 220: 124909.
[21] DU W, YANG J, ZHANG S, et al. Super-Planckian near-field heat transfer between hyperbolic metamaterials[J]. Nano Energy, 2020, 78: 105264.
[22] LI Z, WU L, ZHANG H, et al. Dual-functional metamaterial with vibration isolation and heat flux guiding[J]. Journal of Sound and Vibration, 2020, 469: 115122.
[23] HU R, XI W, LIU Y, et al. Thermal camouflaging metamaterials[J]. Materials Today, 2021, 45: 120-141.
[24] YU H, WANG H, GUO X, et al. Building block design for composite metamaterial with an ultra-low thermal expansion and high-level specific modulus[J]. Composite Structures, 2022, 300: 116131.
[25] ZHANG K, WANG K, CHEN J, et al. Design and additive manufacturing of 3D-architected ceramic metamaterials with programmable thermal expansion[J]. Additive Manufacturing, 2021, 47: 102338.
[26] YU R, LUO W, YUAN H, et al. Experimental and numerical research on foam filled re-entrant cellular structure with negative Poisson’s ratio[J]. Thin-Walled Structures, 2020, 153: 106679.
[27] DONG Z, LI Y, ZHAO T, et al. Experimental and numerical studies on the compressive mechanical properties of the metallic auxetic reentrant honeycomb[J]. Materials & Design, 2019, 182: 108036.
[28] HA N S, PHAM T M, TRAN T T, et al. Mechanical properties and energy absorption of bio-inspired hierarchical circular honeycomb[J]. Composites Part B: Engineering, 2022, 236: 109818.
[29] JIANG Y, LI Y. 3D Printed Chiral Cellular Solids with Amplified Auxetic Effects Due to Elevated Internal Rotation[J]. Advanced Engineering Materials, 2017, 19(2): 1600609.
[30] HAMZEHEI R, REZAEI S, KADKHODAPOUR J, et al. 2D triangular anti-trichiral structures and auxetic stents with symmetric shrinkage behavior and high energy absorption[J]. Mechanics of Materials, 2020, 142: 103291.
[31] COULAIS C, TEOMY E, DE REUS K, et al. Combinatorial design of textured mechanical metamaterials[J]. Nature, 2016, 535(7613): 529-532.
[32] FLORIJN B, COULAIS C, VAN HECKE M. Programmable Mechanical Metamaterials[J]. Physical Review Letters, 2014, 113(17): 175503.
[33] BERTOLDI K, VITELLI V, CHRISTENSEN J, et al. Flexible mechanical metamaterials[J]. Nature Reviews Materials, 2017, 2(11): 17066.
[34] ZHOU X, TAO C, LIANG X, et al. Design and Mechanical Properties of Maximum Bulk Modulus Microstructures Based on a Smooth Topology with Grid Point Density[J]. Aerospace, 2024, 11(2): 145.
[35] JIAO P, MUELLER J, RANEY J R, et al. Mechanical metamaterials and beyond[J]. Nature Communications, 2023, 14(1): 6004.
[36] BARCHIESI E, SPAGNUOLO M, PLACIDI L. Mechanical metamaterials: a state of the art[J]. Mathematics and Mechanics of Solids, 2019, 24(1): 212-234.
[37] NOVAK N, STARČEVIČ L, VESENJAK M, et al. Blast response study of the sandwich composite panels with 3D chiral auxetic core[J]. Composite Structures, 2019, 210: 167-178.
[38] ZHANG X G, REN X, JIANG W, et al. A novel auxetic chiral lattice composite: Experimental and numerical study[J]. Composite Structures, 2022, 282: 115043.
[39] MOHSENIZADEH S, ALIPOUR R, SHOKRI RAD M, et al. Crashworthiness assessment of auxetic foam-filled tube under quasi-static axial loading[J]. Materials & Design, 2015, 88: 258-268.
[40] DUDEK K K, GATT R, GRIMA J N. 3D composite metamaterial with magnetic inclusions exhibiting negative stiffness and auxetic behaviour[J]. Materials & Design, 2020, 187: 108403.
[41] CHENG X, ZHANG Y, REN X, et al. Design and mechanical characteristics of auxetic metamaterial with tunable stiffness[J]. International Journal of Mechanical Sciences, 2022, 223: 107286.
[42] DA D, CHAN Y C, WANG L, et al. Data-driven and topological design of structural metamaterials for fracture resistance[J]. Extreme Mechanics Letters, 2022, 50: 101528.
[43] MO S, HUANG X, HUANG Z, et al. Continuously tunable mechanical metamaterials based on gear cells[J]. Extreme Mechanics Letters, 2024, 67: 102133.
[44] FLEISCH M, THALHAMER A, MEIER G, et al. Chiral-based mechanical metamaterial with tunable normal-strain shear coupling effect[J]. Engineering Structures, 2023, 284: 115952.
[45] ZADPOOR A A, MIRZAALI M J, VALDEVIT L, et al. Design, material, function, and fabrication of metamaterials[J]. APL Materials, 2023, 11(2): 020401.
[46] XU R J, LIN Y S. Actively MEMS-Based Tunable Metamaterials for Advanced and Emerging Applications[J]. Electronics, 2022, 11(2): 243.
[47] ZHANG X, WANG J, SUN Q, et al. Mechanical design and analysis of bio-inspired reentrant negative Poisson’s ratio metamaterials with rigid-flexible distinction[J]. International Journal of Smart and Nano Materials, 2024, 15(1): 1-20.
[48] LIU J Y, LIU H T. Energy absorption characteristics and stability of novel bionic negative Poisson’s ratio honeycomb under oblique compression[J]. Engineering Structures, 2022, 267: 114682.
[49] ZHANG Z, TIAN R, ZHANG X, et al. A novel butterfly-shaped auxetic structure with negative Poisson’s ratio and enhanced stiffness[J]. Journal of Materials Science, 2021, 56(25): 14139-14156.
[50] LIM T C. An Auxetic System Based on Interconnected Y-Elements Inspired by Islamic Geometric Patterns[J]. Symmetry, 2021, 13(5): 865.
[51] TIAN R, GUAN H, LU X, et al. Dynamic crushing behavior and energy absorption of hybrid auxetic metamaterial inspired by Islamic motif art[J]. Applied Mathematics and Mechanics, 2023, 44(3): 345-362.
[52] WANG M, SUN S, ZHANG T Y. Machine learning accelerated design of auxetic structures[J]. Materials & Design, 2023, 234: 112334.
[53] CHALLAPALLI A, PATEL D, LI G. Inverse machine learning framework for optimizing lightweight metamaterials[J]. Materials & Design, 2021, 208: 109937.
[54] GAO J, CAO X, XIAO M, et al. Rational designs of mechanical metamaterials: Formulations, architectures, tessellations and prospects[J]. Materials Science and Engineering: R: Reports, 2023, 156: 100755.
[55] CHANG Y, WANG H, DONG Q. Machine learning-based inverse design of auxetic metamaterial with zero Poisson’s ratio[J]. Materials Today Communications, 2022, 30: 103186.
[56] HOU R, DONG P, LIU Y. Novel lozenge-chiral auxetic metamaterials (LCAMs): Design and numerical studies[J]. Materials Letters, 2023, 331: 133440.
[57] HOU R, DONG P, HU J, et al. An optimized lozenge-chiral auxetic metamaterial with tunable auxeticity and stiffness[J]. Materials & Design, 2024, 237: 112530.
[58] NIAN Y, WAN S, LI M, et al. Crashworthiness design of self-similar graded honeycomb-filled composite circular structures[J]. Construction and Building Materials, 2020, 233: 117344.
[59] LUO Y M, HUANG T T, ZHANG Y, et al. Novel meter-scale seismic metamaterial with low-frequency wide bandgap for Lamb waves[J]. Engineering Structures, 2023, 275: 115321.
[60] TAO Z, REN X, ZHAO A G, et al. A novel auxetic acoustic metamaterial plate with tunable bandgap[J]. International Journal of Mechanical Sciences, 2022, 226: 107414.
[61] HU J, DONG P, HOU R, et al. Functionally graded IWP reinforced cementitious composites: Design, fabrication, and the enhanced ductility[J]. Thin-Walled Structures, 2023, 192: 111199.
[62] HAN D, ZHANG Y, ZHANG X Y, et al. Mechanical characterization of a novel thickness gradient auxetic tubular structure under inclined load[J]. Engineering Structures, 2022, 273: 115079.
[63] JIN S, KORKOLIS Y P, LI Y. Shear resistance of an auxetic chiral mechanical metamaterial[J]. International Journal of Solids and Structures, 2019, 174-175: 28-37.
[64] ZHANG X, HAO H, TIAN R, et al. Quasi-static compression and dynamic crushing behaviors of novel hybrid re-entrant auxetic metamaterials with enhanced energy-absorption[J]. Composite Structures, 2022, 288: 115399.
[65] JIANG X, LIU F, WANG L. Machine learning-based stiffness optimization of digital composite metamaterials with desired positive or negative Poisson’s ratio[J]. Theoretical and Applied Mechanics Letters, 2023, 13(6): 100485.
[66] QIU Y, YE H, ZHANG H, et al. Machine learning-driven optimization design of hydrogel-based negative hydration expansion metamaterials[J]. Computer-Aided Design, 2024, 166: 103631.
[67] XIAO L, CAO Z, LU H, et al. Optimal design of one-dimensional elastic metamaterials through deep convolutional neural network and genetic algorithm[J]. Structures, 2023, 57: 105349.
[68] WANG L, CHAN Y C, AHMED F, et al. Deep generative modeling for mechanistic-based learning and design of metamaterial systems[J]. Computer Methods in Applied Mechanics and Engineering, 2020, 372: 113377.
[69] SIGMUND O. Materials with prescribed constitutive parameters: An inverse homogenization problem[J]. International Journal of Solids and Structures, 1994, 31(17): 2313-2329.
[70] DONG H W, ZHAO S D, MIAO X B, et al. Customized broadband pentamode metamaterials by topology optimization[J]. Journal of the Mechanics and Physics of Solids, 2021, 152: 104407.
[71] LU F, LIN B, LING X, et al. Controllable design of bi-material metamaterials with programmable thermal expansion and Poisson’s ratio[J]. Composite Structures, 2023, 322: 117417.
[72] ZHANG X, ZHANG J, XU C, et al. Inverse-designed flexural wave metamaterial beams with thermally induced tunability[J]. International Journal of Mechanical Sciences, 2024, 267: 109007.
[73] ZENG Q, ZHAO Z, LEI H, et al. A deep learning approach for inverse design of gradient mechanical metamaterials[J]. International Journal of Mechanical Sciences, 2023, 240: 107920.
[74] ZHANG Y, HUANG J, GU L, et al. Inverse design of slow light devices at telecommunication band based on metamaterials using a deep learning attempt[J]. Optics Communications, 2023, 537: 129456.
[75] JIANG W, ZHU Y, YIN G, et al. Dispersion relation prediction and structure inverse design of elastic metamaterials via deep learning[J]. Materials Today Physics, 2022, 22: 100616.
[76] JORDAN M I, MITCHELL T M. Machine learning: Trends, perspectives, and prospects[J]. Science, 2015, 349(6245): 255-260.
[77] MAHESH B. Machine Learning Algorithms - A Review[J]. 2018, 9(1).
[78] LECUN Y, BENGIO Y, HINTON G. Deep learning[J]. Nature, 2015, 521(7553): 436-444.
[79] RUSK N. Deep learning[J]. Nature Methods, 2016, 13(1): 35-35.
[80] ZHOU M, DUAN N, LIU S, et al. Progress in Neural NLP: Modeling, Learning, and Reasoning[J]. Engineering, 2020, 6(3): 275-290.
[81] KANG Y, CAI Z, TAN C W, et al. Natural language processing (NLP) in management research: A literature review[J]. Journal of Management Analytics, 2020, 7(2): 139-172.
[82] KEYSERS D, DESELAERS T, GOLLAN C, et al. Deformation Models for Image Recognition[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2007, 29(8): 1422-1435.
[83] HE K, ZHANG X, REN S, et al. Deep Residual Learning for Image Recognition[C]//2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR). Las Vegas, NV, USA: IEEE, 2016: 770-778.
[84] CHANG Y, WANG H, DONG Q. Machine learning-based inverse design of auxetic metamaterial with zero Poisson’s ratio[J]. Materials Today Communications, 2022, 30: 103186.
[85] ZHANG C, XIE J, SHANIAN A, et al. A hybrid deep learning approach for the design of 2D low porosity auxetic metamaterials[J]. Engineering Applications of Artificial Intelligence, 2023, 123: 106413.
[86] BRONDER S, HERTER F, BÄHRE D, et al. Optimized design for modified auxetic structures based on a neural network approach[J]. Materials Today Communications, 2022, 32: 103931.
[87] YU J, SHI X, FENG Y, et al. Machine learning-based design and optimization of double curved beams for multi-stable honeycomb structures[J]. Extreme Mechanics Letters, 2023, 65: 102109.
[88] XIAO L, CAO Z, LU H, et al. Optimal design of one-dimensional elastic metamaterials through deep convolutional neural network and genetic algorithm[J]. Structures, 2023, 57: 105349.
[89] WANG M, SUN S, ZHANG T Y. Machine learning accelerated design of auxetic structures[J]. Materials & Design, 2023, 234: 112334.
[90] VYAVAHARE S, TERAIYA S, KUMAR S. FDM manufactured auxetic structures: An investigation of mechanical properties using machine learning techniques[J]. International Journal of Solids and Structures, 2023, 265-266: 112126.
[91] CHALLAPALLI A, PATEL D, LI G. Inverse machine learning framework for optimizing lightweight metamaterials[J]. Materials & Design, 2021, 208: 109937.
[92] FENG Q, MAIER W, MÖHRING H C. Application of machine learning to optimize process parameters in fused deposition modeling of PEEK material[J]. Procedia CIRP, 2022, 107: 1-8.
[93] SUZUKI A, SHIBA Y, IBE H, et al. Machine-learning assisted optimization of process parameters for controlling the microstructure in a laser powder bed fused WC/Co cemented carbide[J]. Additive Manufacturing, 2022, 59: 103089.
[94] VEEMAN D, SUDHARSAN S, SURENDHAR G J, et al. Machine learning model for predicting the hardness of additively manufactured acrylonitrile butadiene styrene[J]. Materials Today Communications, 2023, 35: 106147.
[95] FARHAN KHAN M, ALAM A, ATEEB SIDDIQUI M, et al. Real-time defect detection in 3D printing using machine learning[J]. Materials Today: Proceedings, 2021, 42: 521-528.
[96] ROSSI A, MORETTI M, SENIN N. Layer inspection via digital imaging and machine learning for in-process monitoring of fused filament fabrication[J]. Journal of Manufacturing Processes, 2021, 70: 438-451.
[97] XIAO R, LI X, JIA H, et al. 3D printing of dual phase-strengthened microlattices for lightweight micro aerial vehicles[J]. Materials & Design, 2021, 206: 109767.
[98] CAO X, HUANG Z, HE C, et al. In-situ synchrotron X-ray tomography investigation of the imperfect smooth-shell cylinder structure[J]. Composite Structures, 2021, 267: 113926.
[99] ZHENG X, SMITH W, JACKSON J, et al. Multiscale metallic metamaterials[J]. Nature Materials, 2016, 15(10): 1100-1106.
[100] MALONEY K J, ROPER C S, JACOBSEN A J, et al. Microlattices as architected thin films: Analysis of mechanical properties and high strain elastic recovery[J]. APL MATERIALS, 2013, 1(2): 022106.
[101] MIZZI L, SALVATI E, SPAGGIARI A, et al. 2D auxetic metamaterials with tuneable micro-/nanoscale apertures[J]. Applied Materials Today, 2020, 20: 100780.
[102] SCHAEDLER T A, JACOBSEN A J, TORRENTS A, et al. Ultralight Metallic Microlattices[J]. Science, 2011, 334(6058): 962-965.
[103] PERERA A T K, WU K, WAN W Y, et al. Modified polymer 3D printing enables the formation of functionalized micro-metallic architectures[J]. Additive Manufacturing, 2023, 61: 103317.
[104] WANG Z, CHENG J, XIE Y, et al. Lead‐Free Piezoelectric Composite Based on a Metamaterial for Electromechanical Energy Conversion[J]. Advanced Materials Technologies, 2022, 7(12): 2200650.
[105] TAO R, SHI J, GRANIER F, et al. Multi-material fused filament fabrication of flexible 3D piezoelectric nanocomposite lattices for pressure sensing and energy harvesting applications[J]. Applied Materials Today, 2022, 29: 101596.
[106] HE Y, ZHOU Z, HUANG Y, et al. An antibacterial ε-poly- L -lysine-derived bioink for 3D bioprinting applications[J]. Journal of Materials Chemistry B, 2022, 10(40): 8274-8281.
[107] CORNOCK R, BEIRNE S, THOMPSON B, et al. Coaxial additive manufacture of biomaterial composite scaffolds for tissue engineering[J]. Biofabrication, 2014, 6(2): 025002.
[108] CAO E, JIA B, GUO D, et al. Bionic design and numerical studies of spider web-inspired membrane-type acoustic metamaterials[J]. Composite Structures, 2023, 315: 117010.
[109] ZHANG Z, ZHANG L, SONG B, et al. Bamboo-inspired, simulation-guided design and 3D printing of light-weight and high-strength mechanical metamaterials[J]. Applied Materials Today, 2022, 26: 101268.
[110] SILVA B, GOVAN J, CRISTÓBAL ZAGAL J, et al. A biomimetic smart kirigami soft metamaterial with multimodal remote locomotion mechanisms[J]. Materials & Design, 2023, 233: 112262.
[111] ZHANG S, JIANG P, QI J, et al. Adjustable indentation and vibration isolation performances of nacre-like metamaterial[J]. International Journal of Smart and Nano Materials, 2023, 14(3): 303-320.
[112] PRANNO A, GRECO F, LEONETTI L, et al. Band gap tuning through microscopic instabilities of compressively loaded lightened nacre-like composite metamaterials[J]. Composite Structures, 2022, 282: 115032.
[113] WANG P, YANG F, ZHENG B, et al. Breaking the Tradeoffs between Different Mechanical Properties in Bioinspired Hierarchical Lattice Metamaterials[J]. Advanced Functional Materials, 2023, 33(45): 2305978.
[114] YANG H, ZHANG Y, WANG Z, et al. Bioinspired dual-phase composite metamaterial for customized deformation behavior and performance characteristic[J]. Materials Today Communications, 2024, 38: 107655.
[115] ALOMARAH A, YUAN Y, RUAN D. A bio-inspired auxetic metamaterial with two plateau regimes: Compressive properties and energy absorption[J]. Thin-Walled Structures, 2023, 192: 111175.
[116] SADEGHI F, BANIASSADI M, SHAHIDI A, et al. TPMS metamaterial structures based on shape memory polymers: Mechanical, thermal and thermomechanical assessment[J]. Journal of Materials Research and Technology, 2023, 23: 3726-3743.
[117] ZHAN Z, CHEN L, DUAN H, et al. 3D printed ultra-fast photothermal responsive shape memory hydrogel for microrobots[J]. International Journal of Extreme Manufacturing, 2022, 4(1): 015302.
[118] WAN M, YU K, SUN H. 4D printed programmable auxetic metamaterials with shape memory effects[J]. Composite Structures, 2022, 279: 114791.
[119] XU P, LAN X, ZENG C, et al. Compression behavior of 4D printed metamaterials with various Poisson’s ratios[J]. International Journal of Mechanical Sciences, 2024, 264: 108819.
[120] YAO H, YU M, FU J, et al. Shape memory polymers enable versatile magneto-active structure with 4D printability, variable stiffness, shape-morphing and effective grasping[J]. Smart Materials and Structures, 2023, 32(9): 095005.
[121] XIAO L, CAO Z, LU H, et al. Controllable and scalable gradient-driven optimization design for two-dimensional metamaterials based on deep learning[J]. Composite Structures, 2024, 337: 118072.
[122] BROWN N K, DESHPANDE A, GARLAND A, et al. Deep reinforcement learning for the design of mechanical metamaterials with tunable deformation and hysteretic characteristics[J]. Materials & Design, 2023, 235: 112428.
[123] BROWN N K, GARLAND A P, FADEL G M, et al. Deep reinforcement learning for the rapid on-demand design of mechanical metamaterials with targeted nonlinear deformation responses[J]. Engineering Applications of Artificial Intelligence, 2023, 126: 106998.
[124] SONG C, WANG X, XU S, et al. Inverse design of laminated plate-type acoustic metamaterials for sound insulation based on deep learning[J]. Applied Acoustics, 2024, 218: 109906.
[125] LIU W, WANG N, LUO T, et al. In-plane dynamic crushing of re-entrant auxetic cellular structure[J]. Materials & Design, 2016, 100: 84-91.
[126] JIANG H, REN Y, JIN Q, et al. Crashworthiness of novel concentric auxetic reentrant honeycomb with negative Poisson’s ratio biologically inspired by coconut palm[J]. Thin-Walled Structures, 2020, 154: 106911.
[127] SHIM J, SHAN S, KOŠMRLJ A, et al. Harnessing instabilities for design of soft reconfigurable auxetic/chiral materials[J]. Soft Matter, 2013, 9(34): 8198.
[128] PRAWOTO Y. Seeing auxetic materials from the mechanics point of view: A structural review on the negative Poisson’s ratio[J]. Computational Materials Science, 2012, 58: 140-153.
[129] BRONDER S, ADORNA M, FÍLA T, et al. Hybrid Auxetic Structures: Structural Optimization and Mechanical Characterization[J]. Advanced Engineering Materials, 2021, 23(5): 2001393.
[130] FU M H, CHEN Y, HU L L. A novel auxetic honeycomb with enhanced in-plane stiffness and buckling strength[J]. Composite Structures, 2017, 160: 574-585.
[131] CHEN Y, FU M H. A novel three-dimensional auxetic lattice meta-material with enhanced stiffness[J]. Smart Materials and Structures, 2017, 26(10): 105029.
[132] XUE Y, GAO P, ZHOU L, et al. An Enhanced Three-Dimensional Auxetic Lattice Structure with Improved Property[J]. Materials, 2020, 13(4): 1008.
[133] JAFARI NEDOUSHAN R, YU W R. A new auxetic structure with enhanced stiffness via stiffened elliptical perforations[J]. Functional Composites and Structures, 2020, 2(4): 045006.
[134] BUDARAPU P R, Y B S S, NATARAJAN R. Design concepts of an aircraft wing: composite and morphing airfoil with auxetic structures[J]. Frontiers of Structural and Civil Engineering, 2016, 10(4): 394-408.
[135] HONG W, KUMAR N A, PATRICK S, et al. Empirical Validation of an Auxetic Structured Foot With the Powered Transfemoral Prosthesis[J]. IEEE Robotics and Automation Letters, 2022, 7(4): 11228-11235.
[136] ZHANG X Y, REN X, ZHANG Y, et al. A novel auxetic metamaterial with enhanced mechanical properties and tunable auxeticity[J]. Thin-Walled Structures, 2022, 174: 109162.
[137] QI C, JIANG F, REMENNIKOV A, et al. Quasi-static crushing behavior of novel re-entrant circular auxetic honeycombs[J]. Composites Part B: Engineering, 2020, 197: 108117.
[138] GAO D, WANG S, ZHANG M, et al. Experimental and numerical investigation on in-plane impact behaviour of chiral auxetic structure[J]. Composite Structures, 2021, 267: 113922.
[139] TAN H, HE Z, LI E, et al. Crashworthiness design and multi-objective optimization of a novel auxetic hierarchical honeycomb crash box[J]. Structural and Multidisciplinary Optimization, 2021, 64(4): 2009-2024.
[140] GAO Q, ZHAO X, WANG C, et al. Multi-objective crashworthiness optimization for an auxetic cylindrical structure under axial impact loading[J]. Materials & Design, 2018, 143: 120-130.
[141] NAJAFI M, AHMADI H, LIAGHAT G. Experimental investigation on energy absorption of auxetic structures[J]. Materials Today: Proceedings, 2021, 34: 350-355.
[142] CHOUDHRY N K, PANDA B, KUMAR S. In-plane energy absorption characteristics of a modified re-entrant auxetic structure fabricated via 3D printing[J]. Composites Part B: Engineering, 2022, 228: 109437.
[143] TAO J, WANG Y, ZHENG X, et al. A review: Polyacrylonitrile as high-performance piezoelectric materials[J]. Nano Energy, 2023, 118: 108987.
[144] FADHLINA H, ATIQAH A, ZAINUDDIN Z. A review on lithium doped lead-free piezoelectric materials[J]. Materials Today Communications, 2022, 33: 104835.
[145] KAUR S, KUMAR R, KAUR R, et al. Piezoelectric materials in sensors: Bibliometric and visualization analysis[J]. Materials Today: Proceedings, 2022, 65: 3780-3786.
[146] GUO H, WANG Y S, YANG C, et al. Vehicle interior noise active control based on piezoelectric ceramic materials and improved fuzzy control algorithm[J]. Applied Acoustics, 2019, 150: 216-226.
[147] YING H, DING G, ZHAO J, et al. Properties of PSN-PZT piezoelectric ceramic powder prepared by fast solid-phase reaction method[J]. Materials Today Communications, 2023, 35: 106086.
[148] GUERIN S, TOFAIL S A M, THOMPSON D. Organic piezoelectric materials: milestones and potential[J]. NPG Asia Materials, 2019, 11(1): 10.
[149] YU S, TAI Y, MILAM-GUERRERO J, et al. Electrospun organic piezoelectric nanofibers and their energy and bio applications[J]. Nano Energy, 2022, 97: 107174.
[150] SHETTY D, CAMPANA C, NAZARYAN N. Modeling and Experimental Evaluation of Monocrystalline Piezoelectric Materials for Electromechanical Actuation[C]//Volume 3: Design, Materials and Manufacturing, Parts A, B, and C. Houston, Texas, USA: American Society of Mechanical Engineers, 2012: 1657-1663.
[151] VIJAYAKANTH T, LIPTROT D J, GAZIT E, et al. Recent Advances in Organic and Organic–Inorganic Hybrid Materials for Piezoelectric Mechanical Energy Harvesting[J]. Advanced Functional Materials, 2022, 32(17): 2109492.
[152] HABIB M, LANTGIOS I, HORNBOSTEL K. A review of ceramic, polymer and composite piezoelectric materials[J]. Journal of Physics D: Applied Physics, 2022, 55(42): 423002.
[153] LU L, DING W, LIU J, et al. Flexible PVDF based piezoelectric nanogenerators[J]. Nano Energy, 2020, 78: 105251.
[154] KALIMULDINA G, TURDAKYN N, ABAY I, et al. A Review of Piezoelectric PVDF Film by Electrospinning and Its Applications[J]. Sensors, 2020, 20(18): 5214.
[155] TAO R, SHI J, RAFIEE M, et al. Fused filament fabrication of PVDF films for piezoelectric sensing and energy harvesting applications[J]. Materials Advances, 2022, 3(12): 4851-4860.
[156] SIMUNEC D P, BREEDON M, MUHAMMAD F U R, et al. Electrical capability of 3D printed unpoled polyvinylidene fluoride (PVDF)/thermoplastic polyurethane (TPU) sensors combined with carbon black and barium titanate[J]. Additive Manufacturing, 2023, 73: 103679.
[157] ZHAO J, HU N, WU J, et al. A review of piezoelectric metamaterials for underwater equipment[J]. Frontiers in Physics, 2022, 10: 1068838.
[158] SHI J, AKBARZADEH A H. Architected cellular piezoelectric metamaterials: Thermo-electro-mechanical properties[J]. Acta Materialia, 2019, 163: 91-121.
[159] KHAN K A, AL-MANSOOR S, KHAN S Z, et al. Piezoelectric Metamaterial with Negative and Zero Poisson’s Ratios[J]. Journal of Engineering Mechanics, 2019, 145(12): 04019101.
[160] SUGINO C, RUZZENE M, ERTURK A. Nonreciprocal piezoelectric metamaterial framework and circuit strategies[J]. Physical Review B, 2020, 102(1): 014304.
[161] PEI H, JING J, CHEN Y, et al. 3D printing of PVDF-based piezoelectric nanogenerator from programmable metamaterial design: Promising strategy for flexible electronic skin[J]. Nano Energy, 2023, 109: 108303.
[162] CUI H, HENSLEIGH R, YAO D, et al. Three-dimensional printing of piezoelectric materials with designed anisotropy and directional response[J]. Nature Materials, 2019, 18(3): 234-241.
[163] CHEN S, FAN Y, FU Q, et al. A Review of Tunable Acoustic Metamaterials[J]. Applied Sciences, 2018, 8(9): 1480.
[164] HABERMAN M R, GUILD M D. Acoustic metamaterials[J]. Physics Today, 2016, 69(6): 42-48.
[165] LI J, WEN X, SHENG P. Acoustic metamaterials[J]. Journal of Applied Physics, 2021, 129(17): 171103.
[166] GAO N, ZHANG Z, DENG J, et al. Acoustic Metamaterials for Noise Reduction: A Review[J]. Advanced Materials Technologies, 2022, 7(6): 2100698.
[167] MA G, SHENG P. Acoustic metamaterials: From local resonances to broad horizons[J]. Science Advances, 2016, 2(2): e1501595.
[168] CUMMER S A, CHRISTENSEN J, ALÙ A. Controlling sound with acoustic metamaterials[J]. Nature Reviews Materials, 2016, 1(3): 16001.
[169] HUANG H H, SUN C T, HUANG G L. On the negative effective mass density in acoustic metamaterials[J]. International Journal of Engineering Science, 2009, 47(4): 610-617.
[170] MAN X, LUO Z, LIU J, et al. Hilbert fractal acoustic metamaterials with negative mass density and bulk modulus on subwavelength scale[J]. Materials & Design, 2019, 180: 107911.
[171] CHEN H, ZHAI S, DING C, et al. Acoustic metamaterial with negative mass density in water[J]. Journal of Applied Physics, 2015, 118(9): 094901.
[172] LEE S H, PARK C M, SEO Y M, et al. Acoustic metamaterial with negative density[J]. Physics Letters A, 2009, 373(48): 4464-4469.
[173] LEE S H, WRIGHT O B. Origin of negative density and modulus in acoustic metamaterials[J]. Physical Review B, 2016, 93(2): 024302.
[174] HOU Z, ASSOUAR B M. Tunable solid acoustic metamaterial with negative elastic modulus[J]. Applied Physics Letters, 2015, 106(25): 251901.
[175] DING C, HAO L, ZHAO X. Two-dimensional acoustic metamaterial with negative modulus[J]. Journal of Applied Physics, 2010, 108(7): 074911.
[176] FAN L, YU W wei, ZHANG S yi, et al. Zak phases and band properties in acoustic metamaterials with negative modulus or negative density[J]. Physical Review B, 2016, 94(17): 174307.
[177] GAO H, YAN Q, LIU X, et al. Low-Frequency Bandgaps of the Lightweight Single-Phase Acoustic Metamaterials with Locally Resonant Archimedean Spirals[J]. Materials, 2022, 15(1): 373.
[178] NING S, YANG F, LUO C, et al. Low-frequency tunable locally resonant band gaps in acoustic metamaterials through large deformation[J]. Extreme Mechanics Letters, 2020, 35: 100623.
[179] SONG G Y, CHENG Q, HUANG B, et al. Broadband fractal acoustic metamaterials for low-frequency sound attenuation[J]. Applied Physics Letters, 2016, 109(13): 131901.
[180] LI Y, SHEN H, ZHANG L, et al. Control of low-frequency noise for piping systems via the design of coupled band gap of acoustic metamaterials[J]. Physics Letters A, 2016, 380(29-30): 2322-2328.
[181] LIAO G, LUAN C, WANG Z, et al. Acoustic Metamaterials: A Review of Theories, Structures, Fabrication Approaches, and Applications[J]. Advanced Materials Technologies, 2021, 6(5): 2000787.
[182] WANG X, LUO X, ZHAO H, et al. Acoustic perfect absorption and broadband insulation achieved by double-zero metamaterials[J]. Applied Physics Letters, 2018, 112(2): 021901.
[183] ZHANG C, HU X. Three-Dimensional Single-Port Labyrinthine Acoustic Metamaterial: Perfect Absorption with Large Bandwidth and Tunability[J]. Physical Review Applied, 2016, 6(6): 064025.
[184] QU S, SHENG P. Microwave and Acoustic Absorption Metamaterials[J]. Physical Review Applied, 2022, 17(4): 047001.
[185] SONG H, DING X, CUI Z, et al. Research Progress and Development Trends of Acoustic Metamaterials[J]. 2021.
[186] DAI H, ZHANG X, ZHENG Y, et al. Review and prospects of metamaterials used to control elastic waves and vibrations[J]. Frontiers in Physics, 2022, 10: 1069454.
[187] KRUSHYNSKA A O, JANBAZ S, OH J H, et al. Fundamentals and applications of metamaterials: Breaking the limits[J]. Applied Physics Letters, 2023, 123(24): 240401.
[188] ZHENG Y, DAI H, WU J, et al. Research progress and development trend of smart metamaterials[J]. Frontiers in Physics, 2022, 10: 1069722.
[189] HUO J, WANG Y, WANG N, et al. Data-driven design and optimization of ultra-tunable acoustic metamaterials[J]. Smart Materials and Structures, 2023, 32(5): 05LT01.
[190] LEE D, CHEN W (Wayne), WANG L, et al. Data‐Driven Design for Metamaterials and Multiscale Systems: A Review[J]. Advanced Materials, 2024, 36(8): 2305254.
[191] BOSTANABAD R, CHAN Y C, WANG L, et al. Globally Approximate Gaussian Processes for Big Data With Application to Data-Driven Metamaterials Design[J]. Journal of Mechanical Design, 2019, 141(11): 111402.
[192] BAALI H, ADDOUCHE M, BOUZERDOUM A, et al. Design of acoustic absorbing metasurfaces using a data-driven approach[J]. Communications Materials, 2023, 4(1): 40.
[193] DONG P, LIU J, WANG H, et al. Sustainable municipal solid waste incineration fly ash (MSWIFA) alkali-activated materials in construction: Fabrication and performance[J]. Nanotechnologies in Construction A Scientific Internet-Journal, 2022, 14(1): 43-52.
[194] MÜLLER U, RÜBNER K. The microstructure of concrete made with municipal waste incinerator bottom ash as an aggregate component[J]. Cement and Concrete Research, 2006, 36(8): 1434-1443.
[195] WANG Y S, ALREFAEI Y, DAI J G. Roles of hybrid activators in improving the early-age properties of one-part geopolymer pastes[J]. Construction and Building Materials, 2021, 306: 124880.
[196] WANG P, CASADEI F, SHAN S, et al. Harnessing Buckling to Design Tunable Locally Resonant Acoustic Metamaterials[J]. Physical Review Letters, 2014, 113(1): 014301.