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Origami-based impact mitigation via rarefaction solitary wave creation

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Science Advances  24 May 2019:
Vol. 5, no. 5, eaau2835
DOI: 10.1126/sciadv.aau2835
  • Fig. 1 Geometry of the TCO prototypes.

    (A) Folding motion of the TCO is shown in sequence. (B) The flat sheet with crease patterns (upper left) is composed of mountain crease lines (red), valley crease lines (blue), and the adhesive area (shaded area). The photograph shows corresponding laser-cut paper sheets (lower right). (C) Actual prototype of the origami-based metamaterial and its unit cell (lower right inset). (D) The origami-based metamaterial generates the rarefaction solitary wave despite the application of compressive impact. The system is composed of the TCO unit cells (lower right). To connect the neighboring unit cells, we use the interfacial polygonal cross-section with markers at vertices (lower left). Photo credit: H.Y. and Y.M., University of Washington.

  • Fig. 2 Folding motions of the TCO with strain-softening behavior.

    (A) The axial displacement (u) is defined with respect to the initial height (h0) of the TCO. (B) Top-down view shows the rotational angle (ϕ) defined with respect to the initial angle (θ0). (C) Axial force (F normalized by the spring constant Ka and h0) versus displacement. The dashed red curve with the colored area represents the experimental value with the SD. The solid blue curve denotes the 2DOF linear spring model. The inset shows the variations of the stiffness as a function of the TCO displacement.

  • Fig. 3 Experimental setup and DIC analysis results.

    (A) The shaker is attached to the leftmost unit cell through the sleeve bearing (upper left inset). The folding motion of each unit cell is captured by six action cameras (lower inset). For DIC analysis, the fluorescent green markers are used. (B) Snapshots of the experiment at t = 0, 0.06, 0.11, and 0.14 s. Images from the camera are shown in the left column, where the red (blue) arrows represent the compressive (tensile) velocity vector of the polygon in the axial direction. 3D reconstruction of the TCO chain (right column). The deformation is scaled 2.5 times larger than the original deformation for visual clarity. The gray arrows indicate the propagation of the rarefaction solitary wave. Photo credit: H.Y. and Y.M., University of Washington.

  • Fig. 4 Wave form analysis.

    (A) Space-time evolution of the experimentally measured strain wave propagation in the origami-based system. The black arrow indicates the rarefaction solitary wave, and the green one shows the direction of the propagation. (B) Numerical simulation results show a qualitative agreement with the experimental data. The black arrow indicates the leading compressive wave in front of the rarefaction wave. (C) Amplitude change of the rarefaction solitary wave. The experimental data are fitted by the KdV solution (black curve) to obtain the damping coefficient for numerical and analytical analysis. The error bar represents the SD calculated from five measurements. Simulation results are shown in blue dots, which are fitted to the blue dashed curve. (D) The amplitude of the leading compression is analyzed. The dashed curves are obtained from the exponential fit to the experimental and numerical data. The inset shows the exponential decay of the compressive strain. The shapes of the rarefaction solitary wave (E) at t = 0.10 s and (F) t = 0.15 s are shown.

  • Fig. 5 Wave speed analysis.

    (A) Space-time contour plot of the strain wave for the numerical simulation conducted on the longer chain composed of 50 TCO unit cells. Magnified view of the overtaking moment is shown in the right inset. (B) Trajectory of the rarefaction solitary wave (denoted by the blue markers) and the maximum compressive strain wave (red markers) shows the overtaking behavior of the rarefaction solitary wave. The green line indicates the analytical prediction from the KdV equation. (C) Wave speed of the rarefaction solitary wave is higher than the speed of sound of the medium, which means supersonic behavior.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/5/5/eaau2835/DC1

    Supplementary Text

    Fig. S1. Fabrication of the TCO unit cell.

    Fig. S2. Compression test on the TCO unit cell.

    Fig. S3. Fatigue property of the TCO single unit cell.

    Fig. S4. DIC technique to measure the axial displacement and the rotational angle of each polygon.

    Fig. S5. Surface plot of the elastic potential energy.

    Fig. S6. Effect of damping factor ν.

    Fig. S7. Comparison between the numerical simulations on the TCO chain with/without damping effect.

    Fig. S8. Comparison between the numerical simulations on the nonlinear/linearized TCO chain.

    Fig. S9. Numerical simulation with the application of the initial impact velocity to the first unit.

    Table S1. Numerical constants used in the numerical simulation and analytics.

    Movie S1. Fabrication of the TCO unit cell.

    Movie S2. Experimental demonstration of the rarefaction solitary wave.

    Movie S3. 3D reconstruction of the TCO chain from the experimental result.

  • Supplementary Materials

    The PDF file includes:

    • Supplementary Text
    • Fig. S1. Fabrication of the TCO unit cell.
    • Fig. S2. Compression test on the TCO unit cell.
    • Fig. S3. Fatigue property of the TCO single unit cell.
    • Fig. S4. DIC technique to measure the axial displacement and the rotational angle of each polygon.
    • Fig. S5. Surface plot of the elastic potential energy.
    • Fig. S6. Effect of damping factor ν.
    • Fig. S7. Comparison between the numerical simulations on the TCO chain with/without damping effect.
    • Fig. S8. Comparison between the numerical simulations on the nonlinear/linearized TCO chain.
    • Fig. S9. Numerical simulation with the application of the initial impact velocity to the first unit.
    • Table S1. Numerical constants used in the numerical simulation and analytics.

    Download PDF

    Other Supplementary Material for this manuscript includes the following:

    • Movie S1 (.mp4 format). Fabrication of the TCO unit cell.
    • Movie S2 (.mp4 format). Experimental demonstration of the rarefaction solitary wave.
    • Movie S3 (.mp4 format). 3D reconstruction of the TCO chain from the experimental result.

    Files in this Data Supplement:

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