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Quasi-Static Energy Absorption of Miura-Ori Metamaterials

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Abstract

Analytical modeling is conducted to examine the quasistatic response of Miura-ori-based metamaterials under compression in two principal directions. For the \(x_{3}\) direction (out-of-plane) compression, the analytical results agree well with experiments and finite-element (FE) simulations. For compression in the \(x_{1}\) direction (in-plane), the analytical model can predict the initial force. Additionally, the strain-hardening effect of the cell wall material of Miura-ori metamaterial is also taken into consideration, and verified by the FE simulations. The ratio of the two forces corresponding to compression in the two respective directions is also obtained, offering a convenient way of assessing material properties. The energy absorption efficiency in different directions is compared. This study demonstrates that the performance of origami metamaterials can be tuned merely by changing the geometric parameters of the origami unit. The work should also provide theoretical guidance for designing metamaterials at small-scale unit cells.

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Acknowledgements

The authors thank the Australian Research Council for financial support through Discovery Grants (DP180102661) and the National Natural Science Foundation of China (Grant No. 11872125).

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Authors and Affiliations

  1. School of Engineering, Swinburne University of Technology, Hawthorn, VIC, 3122, Australia

    Wei Qiang, Jianjun Zhang & Guoxing Lu

  2. Institute of Mechanics, Bulgarian Academy of Sciences, Acad. G. Bonchev St., Block 4, 1113, Sofia, Bulgaria

    Dora Karagiozova

  3. Department of Civil & Infrastructure Engineering, RMIT University, Melbourne VIC, 3000, Australia

    Phuong Tran

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  1. Wei Qiang
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  2. Jianjun Zhang
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  3. Dora Karagiozova
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  5. Guoxing Lu
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Correspondence to Guoxing Lu.

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Appendices

Appendix

Force-displacement curve in elastic stage

To evaluate the elastic response of Miura-ori materials under compression, it is assumed that the elastic deformation of cell walls is localized in a limited zone with bending along creases; the arc length of this region is nt (t is the wall thickness and n is usually within the range of 2~5). When the dihedral angle \(\theta\) reaches a certain value \(\theta_{el}\), the bending moment is assumed to be equal to the fully plastic bending moment. \(\theta_{el}\) can be obtained as 34:

$$ \theta_{el} = { }\theta_{0} + 3n\sigma_{Y} /E $$
(20)

The radius R of this zone and its relationship with bending moment can be approximately expressed as:

$$ R = \frac{nt}{{\theta_{el} - \theta_{0} }} $$
(21)
$$ M_{el} = \frac{EI}{R} $$
(22)

where I is the second moment of inertia of the cross-section. Therefore, the elastic response can be determined.

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Qiang, W., Zhang, J., Karagiozova, D. et al. Quasi-Static Energy Absorption of Miura-Ori Metamaterials. JOM 73, 4177–4187 (2021). https://doi.org/10.1007/s11837-021-04939-w

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  • DOI: https://doi.org/10.1007/s11837-021-04939-w

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