Research ArticleMATERIALS SCIENCE

Soft mechanical metamaterials with unusual swelling behavior and tunable stress-strain curves

See allHide authors and affiliations

Science Advances  08 Jun 2018:
Vol. 4, no. 6, eaar8535
DOI: 10.1126/sciadv.aar8535
  • Fig. 1 Design concepts of soft mechanical metamaterials with large negative swelling ratios and tunable stress-strain curves.

    (A) Schematic illustration of soft network composite design, with inset denoting a representative unit cell. (B) Cross-sectional view and exploded view of sandwiched horseshoe microstructure consisting of supporting layer (RGD8530; in blue), active layer (SUP705; in red), and encapsulation layer (TangoBlackPlus; in green). The two images at the bottom illustrate a cartoon of the designed microstructure and corresponding image of a 3D-printed sample. (C) Experimental (top) and computational (bottom) results on the evolving configurations of a representative network material during the hydration and dehydration processes. The design parameters are the arc angle θ = 0°, width ratio W2/W1 = 2.5, normalized width W1/r = 0, and length ratio s/rθ = 0.67. (D) Swelling-induced strain components as a function of processing time for the network material in (C). (E) Measured stress-strain curves of the network materials in (C) at different stages of hydration and dehydration. Square and triangular symbols denote the results during hydration and dehydration, respectively. (F) Calculated stress-strain curves of the network materials at different stages of hydration, in comparison to experimental results. (G) Experimental (top) and computational (bottom) results on the deformation sequences of a hydrated (~45 min) network material under a uniaxial stretching. Scale bars, 5 mm (B) and 40 mm (C and G).

  • Fig. 2 Large isotropic swelling and dependence on the microstructure geometries.

    (A) Results of experiments (square symbols), FEA (solid lines), and theoretical model (hollow circles) on swelling-induced strains versus the dimensionless swelling ratio Embedded Image of the hydrogel, for network materials with fixed s/(rθ) = σ0.67 and W2/W1 = 2.5, and six different arc angles (θ). The sudden plateau in the cases of θ = 90° and 180° results from self-contact of microstructures during the shrinkage. (B and C) FEA results on the distribution of swelling-induced strains at Embedded Image over a wide range of length ratios [s/(rθ)] and width ratios (W2/W1) for two representative arc angles (θ = −220° and 0°). (D) Optical images and FEA results of the configurations at the initial, intermediate, and final states of hydration for the network material with θ = −220° as in (A). (E and F) Similar results for two different network materials (with θ = −90° and 0°) in (A). Thickness (that is, the dimension along the out-of-plane direction) is fixed at 3.18 mm in these analyses. Scale bars, 20 mm.

  • Fig. 3 Strategic heterogeneous designs for large anisotropic swellings.

    (A) Swelling path illustrated in the space of strain components (εx-swelling and εy-swelling) for network materials designed in the current work, as compared to traditional soft materials [elastomers (55), polymers (56), and hydrogels (31)] and a metamaterial design reported previously (45). (B) Measured and computed swelling-induced strain components (εx-swelling and εy-swelling) for a design that shrinks only along the x direction and stays almost undeformed along the y direction during hydration. Images on the bottom represent configurations at the initial and final states of hydration. (C) Similar results for a design that shrinks along both the x and y directions during hydration, but at different rates. (D and E) Similar results for two designs that shrink along the x direction and expand along the y direction during hydration. Solid lines and square symbols denote FEA and experiment results, respectively. Scale bars, 20 mm.

  • Fig. 4 Tunable stress-strain curves.

    (A) Schematic illustration of a network design with isotropic swelling (left) and uniaxial stress-strain curves along the x and y directions (middle and right) for the material at different stages of hydration (Embedded Image = 0.0, 0.5, 0.7, and 1.0). (B and C) Optical images that show deformation sequences of a hydrated (Embedded Image = 1.0) network material under uniaxial stretching along the x and y directions. (D and E) Schematic illustration of two network designs with anisotropic swelling and uniaxial stress-strain curves along the x and y directions for the material at different stages of hydration [Embedded Image = 0.0, 0.2, 0.4, and 0.6 in (D) and Embedded Image = 0.0, 0.4, 0.6, and 0.8 in (E)]. In (A), (D), and (E), solid lines and square symbols denote FEA and experiment results, respectively. Scale bars, 40 mm (B and C) and 20 mm (all of the other images).

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/4/6/eaar8535/DC1

    Methods: Mechanics model of the swelling-induced deformations

    fig. S1. Illustration of the sandwich configuration and two different placements of the hydrogel layer relative to the supporting layer.

    fig. S2. Deformations of a straight sandwich structure during the hydration and dehydration processes.

    fig. S3. Distribution of the maximum principal strain for a representative unit cell of the network material at the different stages of hydration and dehydration processes, corresponding to the different states shown in Fig. 1C.

    fig. S4. Distribution of the maximum principal strain for the network structure at the different stages of uniaxial stretching, corresponding to the different states shown in Fig. 1G.

    fig. S5. Illustration of the mechanics model of the swelling-induced deformations and results on the swelling-induced strains.

    fig. S6. Deformations of the network materials during hydration.

    fig. S7. Effect of the filling ratio on the swelling-induced strains of the network materials with straight microstructures (that is, arc angle θ = 0°).

    fig. S8. Soft network materials with anisotropic positive swelling ratios.

    fig. S9. FEA and experiment results on the swelling-induced deformations for the four designs in Fig. 3 (B to E).

    fig. S10. FEA and experiment results on the swelling-induced deformations for the two designs in fig. S8.

    fig. S11. Experimental (left) and computational (right) results on the deformation sequences of a hydrated (~45 min) network material under a uniaxial stretching along the y direction, as in Fig. 4C.

    fig. S12. Tunable elastic modulus and critical strain of the soft network materials.

    fig. S13. Measured mechanical properties of the constituent materials.

    fig. S14. Measured configurations of a representative network sample (that is, the initial state of Fig. 1G) after it was taken from the water and put in the air environment under a natural convection condition for 0, 30, and 60 min.

    fig. S15. Computed swelling-induced strain (εx-swelling or εy-swelling) versus the dimensionless swelling ratio of the hydrogel.

    fig. S16. Experimental demonstration of the network materials with two different scaling factors, with the sample in Fig. 2F to serve as a reference.

  • Supplementary Materials

    This PDF file includes:

    • Methods: Mechanics model of the swelling-induced deformations
    • fig. S1. Illustration of the sandwich configuration and two different placements of the hydrogel layer relative to the supporting layer.
    • fig. S2. Deformations of a straight sandwich structure during the hydration and dehydration processes.
    • fig. S3. Distribution of the maximum principal strain for a representative unit cell of the network material at the different stages of hydration and dehydration processes, corresponding to the different states shown in Fig. 1C.
    • fig. S4. Distribution of the maximum principal strain for the network structure at the different stages of uniaxial stretching, corresponding to the different states shown in Fig. 1G.
    • fig. S5. Illustration of the mechanics model of the swelling-induced deformations and results on the swelling-induced strains.
    • fig. S6. Deformations of the network materials during hydration.
    • fig. S7. Effect of the filling ratio on the swelling-induced strains of the network materials with straight microstructures (that is, arc angle θ = 0°).
    • fig. S8. Soft network materials with anisotropic positive swelling ratios.
    • fig. S9. FEA and experiment results on the swelling-induced deformations for the four designs in Fig. 3 (B to E).
    • fig. S10. FEA and experiment results on the swelling-induced deformations for the two designs in fig. S8.
    • fig. S11. Experimental (left) and computational (right) results on the deformation sequences of a hydrated (~45 min) network material under a uniaxial stretching along the y direction, as in Fig. 4C.
    • fig. S12. Tunable elastic modulus and critical strain of the soft network materials.
    • fig. S13. Measured mechanical properties of the constituent materials.
    • fig. S14. Measured configurations of a representative network sample (that is, the initial state of Fig. 1G) after it was taken from the water and put in the air environment under a natural convection condition for 0, 30, and 60 min.
    • fig. S15. Computed swelling-induced strain (εx-swelling or εy-swelling) versus the dimensionless swelling ratio of the hydrogel.
    • fig. S16. Experimental demonstration of the network materials with two different scaling factors, with the sample in Fig. 2F to serve as a reference.

    Download PDF

    Files in this Data Supplement: