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Probability-Based Analyses of the Snap-Through in Cage-Shaped Mesostructures Under Out-of-Plane Compressions

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Abstract

Three-dimensional (3D) mesostructures with distinct compressive deformation behaviors and tunable mechanical responses have gained increasing interest in recent years. 3D cage-shaped mesostructures are representative framework structures widely exploited in 3D flexible electronics, owing to their unique cellular geometry and unusual mechanical responses. The snap-through behavior of cage-shaped mesostructures could potentially result in the performance degradation of electronics, while it could also be harnessed to design reconfigurable electronics. Due to the complicated deformation modes and random characteristics in experiments, the snap-through behavior of cage-shaped mesostructures remains largely unexplored, especially in terms of probability-based analyses. In this work, we present a systematic study on the configuration evolution and snap-through of 3D cage-shaped mesostructures under out-of-plane compressions. Experimental and computational studies show the existence of two distinct deformation modes associated with the snap-through, which is controlled by the energy barrier based on the energetic analyses. Phase diagrams of the deformation modes decode how key geometric parameters and assembly strain affect the snap-through. Compressive experiments based on periodic arrays (10 × 10) of mesostructures provided a large amount of deformation data, allowing for statistical analyses of the snap-through behavior. These results provide new insights and useful guidelines for the design of 3D reconfigurable devices and multistable metamaterials based on 3D cage-shaped mesostructures.

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Data Availability Statement

All data generated or analyzed used to support the findings of this study are included within the article.

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Acknowledgements

Y.Z. acknowledges support from the National Natural Science Foundation of China (grant nos. 12225206, 12050004 and 11921002), the Tsinghua National Laboratory for Information Science and Technology, the Henry Fok Education Foundation (Grant no. 171003), and a grant from the Institute for Guo Qiang, Tsinghua University (Grant no. 2019GQG1012).

Funding

National Natural Science Foundation of China, 12225206, Yihui Zhang, 12050004, Yihui Zhang, 11921002, Yihui Zhang, the Tsinghua National Laboratory for Information Science and Technology, the Henry Fok Education Foundation, 171003, Yihui Zhang, the Institute for Guo Qiang, Tsinghua University, 2019GQG1012, Yihui Zhang.

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  1. Qing Liu and Zhangming Shen have contributed equally to this work.

Authors and Affiliations

  1. Applied Mechanics Laboratory, Department of Engineering Mechanics, Tsinghua University, Beijing, 100084, China

    Qing Liu, Zhangming Shen, Zhi Liu, Yumeng Shuai, Zengyao Lv, Tianqi Jin, Xu Cheng & Yihui Zhang

  2. Laboratory of Flexible Electronics Technology, Tsinghua University, Beijing, 100084, China

    Qing Liu, Zhangming Shen, Zhi Liu, Yumeng Shuai, Zengyao Lv, Tianqi Jin, Xu Cheng & Yihui Zhang

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  1. Qing Liu
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  2. Zhangming Shen
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  3. Zhi Liu
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Contributions

YZ and XC designed the research; QL led the fabrication work and the experimental characterization with assistance from ZS, XC, ZL, YS, ZL and TJ; ZS led the structural designs, theoretical modeling and FEA predictions with assistance from XC; YZ, XC, QL, and ZS wrote the text and designed the figures; YZ supervised the research. All authors commented on the paper.

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Correspondence to Xu Cheng or Yihui Zhang.

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Liu, Q., Shen, Z., Liu, Z. et al. Probability-Based Analyses of the Snap-Through in Cage-Shaped Mesostructures Under Out-of-Plane Compressions. Acta Mech. Solida Sin. 36, 569–581 (2023). https://doi.org/10.1007/s10338-023-00399-8

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