Research ArticleMATERIALS SCIENCE

Origami lattices with free-form surface ornaments

See allHide authors and affiliations

Science Advances  29 Nov 2017:
Vol. 3, no. 11, eaao1595
DOI: 10.1126/sciadv.aao1595
  • Fig. 1 Folding kinematics.

    (Category 1) To unfold category 1 lattices, every floor needs to be sliced at its boundary with the adjacent floor. Within this context, a floor is a row of the lattice structure. The unfolded floors (A1, A2,…) are connected in series. Here, a cubic lattice is illustrated as an example of category 1 lattices. Dark and light green denote the same type of folding pattern. (Category 2) The lattices belonging to this category need to be sliced at the middle of their floors as well as the boundary of the floors. The unfolded state of these lattices is made of a backbone that comprises every other half-floor (A1, A2,…) and the remaining half-floors (B1, B2,…) that branch out of the backbone. Therefore, green and pink colors denote folding patterns that face each other after folding. Alternative arrangements of the half-floors are possible, as shown in the two alternative variants. Here, a truncated octahedron lattice is depicted as an example of this category of foldable lattices. (Category 3) The unfolding of category 3 lattices is similar to that of category 2 lattices (a similar notation and color code are used), except that the positioning of the half-floors is not orthogonal anymore. A rhombic dodecahedron lattice is shown as an example of the foldable lattices from this category.

  • Fig. 2 (Self-)folding of origami lattices.

    (A) The folding sequences for a category 3 lattice (rhombic dodecahedron). Folding sequences of all other sample lattices of Fig. 1 can be seen in videos S1 to S3. (B) The time sequence of sequential self-folding in a three-story thick panel lattice. 3D-printed panels were hinged together using metal pins and a number of elastic rubber bands, and thus, the stored potential energy was used as a parameter for programming sequential self-folding. (C) The design of the self-folding lattice including the initial flat configuration and the final folded state. The hinges are designed to provide a confined space that locks the different floors after self-folding, thereby ensuring the integrity of the lattice and providing load-bearing capacity.

  • Fig. 3 Conventional and auxetic metallic origami lattices.

    (A) An aluminum cubic lattice structure comprising three unit cells in each direction. (B) Multilayer assembly of a reentrant lattice structure (a variant of truncated octahedron). (C and D) Compression stress-strain results for cubic and reentrant structures. (E) The evolution of the average Poisson’s ratio with compressive strain, εyy, in the auxetic lattice. The evolution in the shape of the unit cells belonging to the ensemble that was used for calculating the Poisson’s ratio is depicted as well.

  • Fig. 4 Free-form ornamentation of origami lattices.

    (A) EBID was used to deposit gasified platinum-based precursor on top of a polished flat origami truncated octahedron cut from a 200-μm pure titanium foil. Multiple 2D and hierarchical 3D patterns have been produced with feature sizes in the range of a few tens of nanometers. The surface ornaments were imaged using scanning electron microscopy (SEM). The dimensions of the ornaments were measured with atomic force microscopy (AFM; details in the Supplementary Materials). (B) A flat pure titanium foil was patterned using an ultrashort pulse laser. Three spots in the unfolded sheet were patterned using three different types of pattern design. The final configuration of folded lattice shows the arrangement of the three patterned spots. The profiles of the patterns were measured using 3D optical microscopy (details in the Supplementary Materials).

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/3/11/eaao1595/DC1

    section S1. Design and folding sequence

    section S2. Self-folding lattices

    section S3. Folded mechanical metamaterials

    section S4. Free-form surface ornamentation

    fig. S1. Illustration of thick panel cubic lattice origami (category 1).

    fig. S2. The serial connection of three half-floors in a truncated octahedron lattice (category 2).

    fig. S3. A category 3 lattice made from the rhombic dodecahedron unit cell.

    fig. S4. Arrangement of joints in hinged panels.

    fig. S5. Fully folded cubic and reentrant lattices.

    fig. S6. The initial configuration of the ensemble determined from the recorded images using the developed MATLAB code.

    fig. S7. Schematic drawing of the EBID process.

    fig. S8. Position of the titanium sample inside the EBID microscope chamber.

    fig. S9. SEM images of the EBID structures produced on the titanium unit cell.

    fig. S10. Selected AFM images of EBID structures with representative line profiles used to quantify the characteristic dimensions of the EBID structures.

    table S1. EBID process conditions.

    table S2. Characteristic dimensions of the EBID structures, as determined from the AFM, SEM, and stream files.

    video S1. The kinematics of self-folding in cubic lattice origami.

    video S2. The kinematics of self-folding in truncated octahedron lattice origami.

    video S3. Sequential folding of rhombic dodecahedron lattice origami.

    video S4. Sequential folding of cubic lattice prototype.

    References (4454)

  • Supplementary Materials

    This PDF file includes:

    • section S1. Design and folding sequence
    • section S2. Self-folding lattices
    • section S3. Folded mechanical metamaterials
    • section S4. Free-form surface ornamentation
    • fig. S1. Illustration of thick panel cubic lattice origami (category 1).
    • fig. S2. The serial connection of three half-floors in a truncated octahedron lattice (category 2).
    • fig. S3. A category 3 lattice made from the rhombic dodecahedron unit cell.
    • fig. S4. Arrangement of joints in hinged panels.
    • fig. S5. Fully folded cubic and reentrant lattices.
    • fig. S6. The initial configuration of the ensemble determined from the recorded images using the developed MATLAB code.
    • fig. S7. Schematic drawing of the EBID process.
    • fig. S8. Position of the titanium sample inside the EBID microscope chamber.
    • fig. S9. SEM images of the EBID structures produced on the titanium unit cell.
    • fig. S10. Selected AFM images of EBID structures with representative line profiles used to quantify the characteristic dimensions of the EBID structures.
    • table S1. EBID process conditions.
    • table S2. Characteristic dimensions of the EBID structures, as determined from the AFM, SEM, and stream files.
    • References (44–54)

    Download PDF

    Other Supplementary Material for this manuscript includes the following:S

    • video S1 (.mp4 format). The kinematics of self-folding in cubic lattice origami.
    • video S2 (.mp4 format). The kinematics of self-folding in truncated octahedron lattice origami.
    • video S3 (.mp4 format). Sequential folding of rhombic dodecahedron lattice origami.
    • video S4 (.mp4 format). Sequential folding of cubic lattice prototype.

    Files in this Data Supplement:

Navigate This Article