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Analytical model for large deformation and capacitance of rhomboidal pressure sensors and experimental verification

菱形压力传感器的大变形力学性能及电容性能理论模型与 实验验证

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Abstract

Capacitive pressure sensors which convert pressure into electric signals are a kind of highly efficient and reliable sensor and have wide applications. The flexible structure of capacitive pressure sensors may undergo large deformation, and the sensitivity and linearity with respect to the deformation are two major performance indices of capacitive pressure sensors. Thus, a simple and accurate analytical model to predict the deformation and electromechanical coupling under external pressure is essential for the quantitative design of the sensors. In this paper, we propose an electromechanical analytical model which couples the capacitance change under large deformation of the flexible curved electrodes. The theory is used to predict the deformation and capacitance of a flexible rhomboidal capacitive sensor, and is verified by both numerical simulations and experiments. The electromechanical analytical model can be applied to other cantilever-like capacitors with symmetric flexible/curved electrodes under symmetric loading. The theory can degenerate into the existing analyses in the literature for the case of small deformation. The accurate analytical model can facilitate design and analyses of capacitive pressure sensors and other similar structures.

摘要

电容式压力传感器是一种将压力转换成电信号的高效可靠的传感器, 具有广泛的用途. 柔性电容式压力传感器的结构可能会发 生较大的变形, 大变形下的灵敏度和线性度是柔性压力传感器的主要性能指标, 无法用传统小变形理论进行分析. 因此, 建立能够准确 预测外部压力下柔性压力传感器的变形和力-电耦合性能的理论模型对传感器的定量设计至关重要. 在本文中, 我们提出了一个力-电 耦合理论模型, 分析了柔性电极在弯曲大变形下的电容变化. 该理论被用来预测柔性菱形电容式传感器的变形和电容变化关系, 并通 过数值模拟和实验进行了验证. 该力-电耦合理论可用于对具有对称柔性/弧形电极的悬臂式电容器在对称载荷作用下的力-电性能进 行分析和设计, 并可退化为文献中的小变形理论. 准确的理论分析模型可以促进电容式压力传感器和其他类似结构的研究和设计.

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References

  1. W. A. D. M. Jayathilaka, K. Qi, Y. Qin, A. Chinnappan, W. Serrano-Garcia, C. Baskar, H. Wang, J. He, S. Cui, S. W. Thomas, and S. Ramakrishna, Significance of nanomaterials in wearables: A review on wearable actuators and sensors, Adv. Mater. 31, 1805921 (2019).

    Article  Google Scholar 

  2. X. Wang, Z. Liu, and T. Zhang, Flexible sensing electronics for wearable/attachable health monitoring, Small 13, 1602790 (2017).

    Article  Google Scholar 

  3. Y. H. Jung, J. Lee, Y. Qiu, N. Cho, S. J. Cho, H. Zhang, S. Lee, T. J. Kim, S. Gong, and Z. Ma, Stretchable twisted-pair transmission lines for microwave frequency wearable electronics, Adv. Funct. Mater. 26, 4635 (2016).

    Article  Google Scholar 

  4. T. Chang, Y. Tanabe, C. C. Wojcik, A. C. Barksdale, S. Doshay, Z. Dong, H. Liu, M. Zhang, Y. Chen, Y. Su, T. H. Lee, J. S. Ho, and J. A. Fan, A general strategy for stretchable microwave antenna systems using serpentine mesh layouts, Adv. Funct. Mater. 27, 1703059 (2017).

    Article  Google Scholar 

  5. C. F. Guo, T. Sun, Q. Liu, Z. Suo, and Z. Ren, Highly stretchable and transparent nanomesh electrodes made by grain boundary lithography, Nat. Commun. 5, 3121 (2014).

    Article  Google Scholar 

  6. Y. Yang, J. Liang, F. Pan, Z. Wang, J. Zhang, K. Amin, J. Fang, W. Zou, Y. Chen, X. Shi, and Z. Wei, Macroscopic helical chirality and self-motion of hierarchical self-assemblies induced by enantiomeric small molecules, Nat. Commun. 9, 3808 (2018).

    Article  Google Scholar 

  7. C. R. Yang, M. F. Lin, C. K. Huang, W. C. Huang, S. F. Tseng, and H. H. Chiang, Highly sensitive and wearable capacitive pressure sensors based on PVDF/BaTiO3 composite fibers on PDMS microcylindrical structures, Measurement 202, 111817 (2022).

    Article  Google Scholar 

  8. B. Zhu, Z. Niu, H. Wang, W. R. Leow, H. Wang, Y. Li, L. Zheng, J. Wei, F. Huo, and X. Chen, Microstructured graphene arrays for highly sensitive flexible tactile sensors, Small 10, 3625 (2014).

    Article  Google Scholar 

  9. H. Wu, D. Kong, Z. Ruan, P. C. Hsu, S. Wang, Z. Yu, T. J. Carney, L. Hu, S. Fan, and Y. Cui, A transparent electrode based on a metal nanotrough network, Nat. Nanotech. 8, 421 (2013).

    Article  Google Scholar 

  10. F. Pan, G. Wang, L. Liu, Y. Chen, Z. Zhang, and X. Shi, Bending induced interlayer shearing, rippling and kink buckling of multi-layered graphene sheets, J. Mech. Phys. Solids 122, 340 (2019).

    Article  MathSciNet  Google Scholar 

  11. Y. Chen, F. Pan, Z. Guo, B. Liu, and J. Zhang, Stiffness threshold of randomly distributed carbon nanotube networks, J. Mech. Phys. Solids 84, 395 (2015).

    Article  Google Scholar 

  12. W. Chen, and X. Yan, Progress in achieving high-performance piezoresistive and capacitive flexible pressure sensors: A review, J. Mater. Sci. Tech. 43, 175 (2020).

    Article  Google Scholar 

  13. S. Z. Homayounfar, and T. L. Andrew, Wearable sensors for monitoring human motion: A review on mechanisms, materials, and challenges, SLAS Tech. 25, 9 (2020).

    Article  Google Scholar 

  14. B. Herren, V. Webster, E. Davidson, M. C. Saha, M. C. Altan, and Y. Liu, PDMS sponges with embedded carbon nanotubes as piezo-resistive sensors for human motion detection, Nanomaterials 11, 1740 (2021).

    Article  Google Scholar 

  15. W. Li, X. Jin, X. Han, Y. Li, W. Wang, T. Lin, and Z. Zhu, Synergy of porous structure and microstructure in piezoresistive material for high-performance and flexible pressure sensors, ACS Appl. Mater. Interfaces 13, 19211 (2021).

    Article  Google Scholar 

  16. H. Kim, G. Kim, T. Kim, S. Lee, D. Kang, M. S. Hwang, Y. Chae, S. Kang, H. Lee, H. G. Park, and W. Shim, Transparent, flexible, conformal capacitive pressure sensors with nanoparticles, Small 14, 1703432 (2018).

    Article  Google Scholar 

  17. Y. Luo, J. Shao, S. Chen, X. Chen, H. Tian, X. Li, L. Wang, D. Wang, and B. Lu, Flexible capacitive pressure sensor enhanced by tilted micropillar arrays, ACS Appl. Mater. Interfaces 11, 17796 (2019).

    Article  Google Scholar 

  18. Bijender, and A. Kumar, Flexible and wearable capacitive pressure sensor for blood pressure monitoring, Sens. Bio-Sens. Res. 33, 100434 (2021).

    Article  Google Scholar 

  19. B. Stadlober, M. Zirkl, and M. Irimia-Vladu, Route towards sustainable smart sensors: ferroelectric polyvinylidene fluoride-based materials and their integration in flexible electronics, Chem. Soc. Rev. 48, 1787 (2019).

    Article  Google Scholar 

  20. Y. Chen, Z. Yang, Z. Chen, K. Li, L. Wang, and S. Zhou, Theoretical and experimental investigations of multibifurcated piezoelectric energy harvesters with coupled bending and torsional vibrations, Acta Mech. Sin. 38, 521434 (2022).

    Article  MathSciNet  Google Scholar 

  21. Y. Du, R. Wang, M. Zeng, S. Xu, M. Saeidi-Javash, W. Wu, and Y. Zhang, Hybrid printing of wearable piezoelectric sensors, Nano Energy 90, 106522 (2021).

    Article  Google Scholar 

  22. A. Braun, R. Wichert, A. Kuijper, and D. W. Fellner, Capacitive proximity sensing in smart environments, J. Ambient Intell. Smart Environ. 7, 483 (2015).

    Article  Google Scholar 

  23. Y. Ye, C. Zhang, C. He, X. Wang, J. Huang, and J. Deng, A review on applications of capacitive displacement sensing for capacitive proximity sensor, IEEE Access 8, 45325 (2020).

    Article  Google Scholar 

  24. W. Zhang, W. Sun, W. Xiao, X. Zhong, C. Wu, and W. Guo, Numerical simulation analysis of microstructure of dielectric layers in capacitive pressure sensors, IEEE Sens. J. 19, 3260 (2019).

    Article  Google Scholar 

  25. M. M. Y. B. Elshabasy, M. A. Al-Moghazy, and H. A. El Gamal, Investigation of the enhancement of microelectromechanical capacitive pressure sensor performance using the genetic algorithm optimization technique, Eng. Optim. 53, 1 (2021).

    Article  MathSciNet  Google Scholar 

  26. W. Yang, Y. Liu, W. Xu, and H. Y. Nie, Design and fabrication of flexible capacitive sensor with cellular structured dielectric layer via 3D printing, IEEE Sens. J. 21, 10473 (2021).

    Article  Google Scholar 

  27. C. M. Boutry, M. Negre, M. Jorda, O. Vardoulis, A. Chortos, O. Khatib, and Z. Bao, A hierarchically patterned, bioinspired e-skin able to detect the direction of applied pressure for robotics, Sci. Robot. 3, (2018).

  28. B. C. K. Tee, A. Chortos, R. R. Dunn, G. Schwartz, E. Eason, and Z. Bao, Tunable flexible pressure sensors using microstructured elastomer geometries for intuitive electronics, Adv. Funct. Mater. 24, 5427 (2014).

    Article  Google Scholar 

  29. N. Xue, G. Gao, J. Sun, C. Liu, T. Li, and C. Chi, Systematic study and experiment of a flexible pressure and tactile sensing array for wearable devices applications, J. Micromech. Microeng. 28, 075019 (2018).

    Article  Google Scholar 

  30. Y. Wan, Z. Qiu, Y. Hong, Y. Wang, J. Zhang, Q. Liu, Z. Wu, and C. F. Guo, A highly sensitive flexible capacitive tactile sensor with sparse and high-aspect-ratio microstructures, Adv. Electron. Mater. 4, 1700586 (2018).

    Article  Google Scholar 

  31. J. Yang, S. Luo, X. Zhou, J. Li, J. Fu, W. Yang, and D. Wei, Flexible, tunable, and ultrasensitive capacitive pressure sensor with micro-conformal graphene electrodes, ACS Appl. Mater. Interfaces 11, 14997 (2019).

    Article  Google Scholar 

  32. K. Lee, J. Lee, G. Kim, Y. Kim, S. Kang, S. Cho, S. G. Kim, J. K. Kim, W. Lee, D. E. Kim, S. Kang, D. E. Kim, T. Lee, and W. Shim, Rough-surface-enabled capacitive pressure sensors with 3D touch capability, Small 13, 1700368 (2017).

    Article  Google Scholar 

  33. H. Ding, Z. Wen, E. Qin, Y. Yang, W. Zhang, B. Yan, D. Wu, Z. Shi, Y. Tian, and X. Li, Influence of the pore size on the sensitivity of flexible and wearable pressure sensors based on porous Ecoflex dielectric layers, Mater. Res. Express 6, 066304 (2019).

    Article  Google Scholar 

  34. D. Kwon, T. I. Lee, J. Shim, S. Ryu, M. S. Kim, S. Kim, T. S. Kim, and I. Park, Highly sensitive, flexible, and wearable pressure sensor based on a giant piezocapacitive effect of three-dimensional micro-porous elastomeric dielectric layer, ACS Appl. Mater. Interfaces 8, 16922 (2016).

    Article  Google Scholar 

  35. A. Ettouhami, N. Zahid, and M. Elbelkacemi, A novel capacitive pressure sensor structure with high sensitivity and quasi-linear response, Comptes Rendus Mécanique 332, 141 (2004).

    Article  Google Scholar 

  36. L. Rosengren, J. Söderkvist, and L. Smith, Micromachined sensor structures with linear capacitive response, Sens. Actuat. A-Phys. 31, 200 (1992).

    Article  Google Scholar 

  37. P. R. Scheeper, W. Olthuis, and P. Bergveld, The design, fabrication, and testing of corrugated silicon nitride diaphragms, J. Microelec-tromech. Syst. 3, 36 (1994).

    Article  Google Scholar 

  38. W. Yang, W. Ding, M. Liu, J. Yang, and M. Li, A theoretical model of a flexible capacitive pressure sensor with microstructured electrodes for highly sensitive electronic skin, J. Phys. D-Appl. Phys. 55, 094001 (2022).

    Article  Google Scholar 

  39. A. C. Ugural, Mechanics of Materials (Wiley, Hoboken, 2007).

    Google Scholar 

  40. A. Saxena, and S. N. Kramer, A simple and accurate method for determining large deflections in compliant mechanisms subjected to end forces and moments, J. Mech. Des. 120, 392 (1998).

    Article  Google Scholar 

  41. K. E. Korte, S. E. Skrabalak, and Y. Xia, Rapid synthesis of silver nanowires through a CuCl- or CuCl2-mediated polyol process, J. Mater. Chem. 18, 437 (2008).

    Article  Google Scholar 

  42. R. Shi, Z. Lou, S. Chen, and G. Shen, Flexible and transparent capacitive pressure sensor with patterned microstructured composite rubber dielectric for wearable touch keyboard application, Sci. China Mater. 61, 1587 (2018).

    Article  Google Scholar 

  43. J. C. Yang, J. O. Kim, J. Oh, S. Y. Kwon, J. Y. Sim, D. W. Kim, H. B. Choi, and S. Park, Microstructured porous pyramid-based ultrahigh sensitive pressure sensor insensitive to strain and temperature, ACS Appl. Mater. Interfaces 11, 19472 (2019).

    Article  Google Scholar 

  44. T. Li, H. Luo, L. Qin, X. Wang, Z. Xiong, H. Ding, Y. Gu, Z. Liu, and T. Zhang, Flexible capacitive tactile sensor based on micro-patterned dielectric layer, Small 12, 5042 (2016).

    Article  Google Scholar 

  45. S. Chen, B. Zhuo, and X. Guo, Large area one-step facile processing of microstructured elastomeric dielectric film for high sensitivity and durable sensing over wide pressure range, ACS Appl. Mater. Interfaces 8, 20364 (2016).

    Article  Google Scholar 

  46. T. Zhao, L. Yuan, T. Li, L. Chen, X. Li, and J. Zhang, Pollen-shaped hierarchical structure for pressure sensors with high sensitivity in an ultrabroad linear response range, ACS Appl. Mater. Interfaces 12, 55362 (2020).

    Article  Google Scholar 

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant No. 12272020), and Beijing Natural Science Foundation (Grant No. JQ21001).

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  1. These authors contributed equally to this work.

Authors and Affiliations

  1. Institute of Solid Mechanics, Beihang University, Beijing, 100191, China

    Weipeng Song  (宋维鹏), Tianyu Wang  (王天瑜) & Li-Hua Shao  (邵丽华)

  2. Beijing Mechanical Equipment Institute, Beijing, 100854, China

    Weipeng Song  (宋维鹏)

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  1. Weipeng Song  (宋维鹏)
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  2. Tianyu Wang  (王天瑜)
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  3. Li-Hua Shao  (邵丽华)
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Contributions

Methodology, Investigation, Writing–original draft. Tianyu Wang: Validation, Investigation, Writing–review & editing, Visualization. Li-Hua Shao: Conceptualization, Methodology, Writing–review & editing, Supervision, Project administration, Funding acquisition.

Corresponding author

Correspondence to Li-Hua Shao  (邵丽华).

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Song, W., Wang, T. & Shao, LH. Analytical model for large deformation and capacitance of rhomboidal pressure sensors and experimental verification. Acta Mech. Sin. 39, 122497 (2023). https://doi.org/10.1007/s10409-023-22497-x

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