Research ArticleMATERIALS ENGINEERING

Morphogenesis and mechanostabilization of complex natural and 3D printed shapes

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Science Advances  15 May 2015:
Vol. 1, no. 4, e1400052
DOI: 10.1126/sciadv.1400052
  • Fig. 1 The natural shells.

    (A and B) Digital images of (A) shell-1 and (B) shell-2 taken in their natural form at different projections. On the basis of the actual dimension, computer-generated shapes are created and 3D printed.

  • Fig. 2 Behavior of shell-1.

    (A to C) Stress distribution in (A) hemispherical shape, (B) shape without grooves, and (C) shape with grooves simulated using FEM. Insets show the finite element mesh. Edges are constrained. Color bars indicate von Mises stress (video S1 shows the variation). A vertical section across a line (1–2) is shown with stress distribution. (D) Maximum and minimum stresses in the three shapes obtained from simulation. (E) Maximum and minimum stresses obtained with varying thickness in the simulation. (F to H) Stress distribution obtained from simulation with the three shapes kept on aluminum substrate. Insets show the stress distribution on the bottom surface of the substrate, with color bar showing von Mises stress (video S1 shows the variation).

  • Fig. 3 Behavior of shell-2.

    (A to C) Stress distribution in (A) solid conical shape, (B) hollow conical shape, and (C) natural shape using FEM. Inset shows the finite element mesh. Color bars indicate von Mises stress (video S1 shows the variation). (D) Maximum and minimum stresses observed in the three shapes obtained from simulation. (E) Maximum and minimum stress obtained with varying thickness in the simulation.

  • Fig. 4 Role of shape under loading.

    (A) A flat segment of large-diameter simple shape. (B) Approximated shape of a periodic segment of the circumferential edge of shell-1. (C) Relative change in the maximum bending stress analytically estimated for the approximated segment versus relative change in the material volume for increasing complexity in the shape of shell-1. (D and E) Free-body diagrams of a simplified segment of simple shape of a shell of constant radius (D) and simplified diagram of shell-2 (E). (F) Relative change in the maximum bending stress versus relative difference in the Euler angle obtained analytically. (G) Free-body diagram showing internal forces in tangential direction acting on various helicoidal segments sliced along the major axis of shell-2. (H) Ratio of load transferred on segment end and the applied transverse load (|F|/|P|) in shell-2 with varying Euler angles. r indicates the radius of curvature of the segments.

  • Fig. 5 Experiment and simulation.

    (A and B) Load versus strain plot for natural and 3D printed shell-1. (C and D) Load versus strain plot for natural and 3D printed shell-2. Digital image of the experimental setup of uniaxial compression testing (inset). (E) Stress distribution in shell-1. (F and G) Digital images of natural and 3D printed shells. (H) Stress distribution in shell-2. (I and J) Digital images of natural and 3D printed shell-2.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/1/4/e1400052/DC1

    Fig. S1. (A) SEM images of shell-1 at different magnifications and of different regions. The selected areas are shown in the micrograph. (B) Images of subsurface at different locations after breaking it. (C) Back surface of shell-1.

    Fig. S2. Micrograph of shell-2 at different magnifications and of different regions. The selected areas are shown in the micrograph. A representative composition spectra showing Ca, C, and O in the sample.

    Fig. S3. A representative XRD plot of the natural shell. The samples are collected from different locations.

    Fig. S4. Vickers hardness map of shell-1 and shell-2 showing hardness variation at different locations.

    Fig. S5. The naturally occurring condition of shell-1 and its nomenclature used in the current work.

    Video S1. Stress distribution of the shapes under pressure.

  • Supplementary Materials

    This PDF file includes:

    • Fig. S1. (A) SEM images of shell-1 at different magnifications and of different regions. The selected areas are shown in the micrograph. (B) Images of subsurface at different locations after breaking it. (C) Back surface of shell-1.
    • Fig. S2. Micrograph of shell-2 at different magnifications and of different regions. The selected areas are shown in the micrograph. A representative composition spectra showing Ca, C, and O in the sample.
    • Fig. S3. A representative XRD plot of the natural shell. The samples are collected from different locations.
    • Fig. S4. Vickers hardness map of shell-1 and shell-2 showing hardness variation at different locations.
    • Fig. S5. The naturally occurring condition of shell-1 and its nomenclature used in the current work.

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    Other Supplementary Material for this manuscript includes the following:

    • Video S1 (.avi format). Stress distribution of the shapes under pressure.

    Files in this Data Supplement:

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