Soft multistable magnetic-responsive metamaterials

Abstract

The wireless actuation of magnetic soft architectures can enable complex functionalities important in biomedicine and soft robotics. However, transforming and maintaining a device's desired geometry without a sustained energy input remains challenging, especially where environmental stresses can be unpredictable. Here, we create a soft multistable magnetic-responsive metamaterial with programmable energy barriers enabled by a bistable geometry made entirely from soft material. The multistability and magnetic programming enable the soft metamaterials to reversibly transform between stable states, even under mechanical and thermal stresses that far exceed physiological conditions. In addition, the metamaterials can sustain compressive loads more than 10 times their mass, achieve shape reconfiguration in remote and confined spaces, and wirelessly deliver fluids against pressure, suggesting a broad range of future biomedical and soft robot applications.

Fig. 1.. Soft, multi-stable metamaterials.

(A) A soft multistable metamaterial unit cell is designed to be stable in the initial configuration (denoted as “[0]” state) and the transformed configuration (denoted as “[1]” state) and is composed of tilted beams (crosshatched) and supporting segments (solid). In (A) and (B), state [1] is lighter in color. (B) The multistable metamaterial can be created entirely from soft material by adding trapezoidal supporting segments (T.S., red) and reinforced beams (R.B., blue) to a base unit cell geometry (base, gray). (C) Four images during loading in compression of a metamaterial that has one row of four unit cells (1 × 4, row × column) with the T.S. + R.B. unit cell geometry (images for 1 × 4 metamaterials with the other unit cell geometries are shown in fig. S2). In the images, the metamaterial transitions between the open state [0] and the closed state [1] when a vertical load is applied. Scale bar, 10 mm. (D) Experimental force-displacement curves in compression (solid) and tension (dashed) for the four different 1 × 4 metamaterial designs, each composed entirely of one type of unit cell. The lines indicate the mean and shaded regions around the data show one SD for 16 experiments (two models with eight tests each) for each geometry. (E and F) Reversible transformation between stable states is enabled by creating the soft metamaterial from a ferromagnetic composite soft material. In (E), images show a four-row cylindrical metamaterial that geometrically transforms with a permanent magnet (on). The transformed configurations are maintained even when the magnet is removed (off) due to the multistable geometry. Dimensions are 30.2-mm outer diameter and 54.8-mm height in expanded state [0000]. The schematic in (F) shows the programmed magnetic microparticles within the soft material that enable remote and reversible transformation between stable states by a nonuniform field.

Fig. 2.. Programming stability with beam geometry of the unit cell.

(A) Schematic shows a single unit cell of the 2D 1 × 4 model used in the FE simulations. (B and C) Energy barriers in compression (B) and tension (C) due to changes in t/L, θ, and R. In plots with varying R, θ = 60°. Likewise, in plots with varying θ, R = 0.6. (D) Experimental energy barriers in tension for a 2 × 8 cylindrical metamaterial, where the stability is programmed by changing R in each row. Bars indicate the mean values, and error bars show one SD across five tests. (E) Ability to program the energy barriers enables magnetic field–induced transformation of sequential rows of the 2 × 8 cylinder. Dimensions: 30.2-mm outer diameter and 29.1-mm height in fully expanded state [00]. (F and G) High-speed images show the rapid contraction (F) and expansion (G) of a 4 × 8 cylindrical metamaterial with selectively programmed energy barriers (where R = 0.6, 0.4, 0.25, and 0 from bottom to top row) to enable complete expansion. Dimensions: 30.2-mm outer diameter and 54.8-mm height in fully expanded state [0000].

Fig. 3.. Metamaterial performance and potential applications.

(A) Programmed energy barriers enable a 2 × 8 cylindrical metamaterial to maintain the open configuration without an external magnetic field even under load from 13.7 times its mass. (B) The programmable energy barriers and remote actuation are leveraged to deploy a metamaterial with integrated LEDs between multiple stable configurations in a confined space. In images 2, 3, and 4 in the series, the metamaterial and LED assembly are confined within a surface with only the top exposed to demonstrate shape reconfiguration in confined spaces. (C) Magnetic programming and nonuniform field actuation enable selective transformation of metamaterials, as demonstrated by a tilting stage. (D) Multistability and selective triggering enable the remote actuation of 1 × 3 metamaterials that form a valve and peristaltic pump that remain stable when the magnetic field is removed even against the fluid pressure from pumping. In the bottom left inset, the red fluid is pumped to the yellow reservoir. In the bottom right inset, the valve is opened, and the blue fluid is then pumped to the yellow reservoir.

Fig. 4.. Metamaterial stability across temperature range and mechanical pressure.

(A and B) Infrared imaging demonstrates the ability to transform and maintain stable states even in (A) cold (−20°C) and (B) hot (100°C) conditions. (C to F) 4 × 8 cylindrical metamaterial with differing energy barriers in each row can resist the pressure exerted by an air current at 6.6 m/s (C), a water vortex at 150 rpm (D), a vertical water jet at 97 ml/s (E), and a 45° water jet at 84 ml/s (F).

Fig. 5.. Metamaterial recovery after mechanical, chemical, and thermal stressors.

The 2 × 8 cylindrical metamaterials are able to recover their multistability and transformation abilities even after extensive stretching to 175% (A to C), a rapid blunt impact with a force of 87 kN (D to F), a week-long exposure to acid (simulated gastric fluid) (G to I), and fire exposure for 15 s (J to L). In (B), (E), and (H), the metamaterial is able to transform between stable states with an external magnetic field after each stress, respectively. In (K), the transformation capability after the thermal stressor was fully restored after reprogramming the magnetic microparticles. In (C), (F), (I), and (L), experimental data show the metamaterial energy barriers of each case, respectively, where the bars represent the mean and error bars show one SD across five tests.