Dome-Patterned Metamaterial Sheets

Abstract

The properties of conventional materials result from the arrangement of and the interaction between atoms at the nanoscale. Metamaterials have shifted this paradigm by offering property control through structural design at the mesoscale, thus broadening the design space beyond the limits of traditional materials. A family of mechanical metamaterials consisting of soft sheets featuring a patterned array of reconfigurable bistable domes is reported here. The domes in this metamaterial architecture can be reversibly inverted at the local scale to generate programmable multistable shapes and tunable mechanical responses at the global scale. By 3D printing a robotic gripper with energy-storing skin and a structure that can memorize and compute spatially-distributed mechanical signals, it is shown that these metamaterials are an attractive platform for novel mechanologic concepts and open new design opportunities for structures used in robotics, architecture, and biomedical applications.

Keywords: hierarchical multistability; mechanical metamaterials; mechanologic; soft robotics.

Figure 1

Design of dome‐patterned metamaterial sheets featuring complex shapes, memory effects, programmable mechanical response, and muscle‐free actuation. a) Schematics of an individual dome in two possible stable states: the base state as manufactured (blue) and an inverted, pre‐stressed state (red). The elastic modulus of the sheet material, sheet thickness, dome height, and dome radius are indicated by E, t, h, and r, respectively. b) Combining individual domes into large‐area patterns yields metamaterial sheets with global multistable shapes and mechanical response that can be programmed through material selection and local geometry. c) Global properties can be tuned in unintuitive ways by local state reconfiguration. d) Material computation can be encoded by profiting from the history‐dependence of the dome inversion pattern to reach a particular global shape, three of which are shown. This radically expands the response space, making these sheets ideal candidates for computing and logic through deformation. e) Functional devices can be created by constraining the wide number of possible configurations into selected geometries and patterns. This is schematically illustrated by a soft robotic actuator that changes its global equilibrium shape through air‐driven inversion of local domes.

Figure 2

Shape changes and hierarchical multistability of dome‐patterned strips and sheets. a) FE simulation of a dome‐patterned strip, illustrating the global curvature K generated upon inversion of selected domes. b) Superimposed photographs of a 3D printed dome‐patterned strip with an increasing number of inverted domes. c) The effect of the dome height and strip thickness on the simulated global curvature of strips after inversion of all domes. d) The number and associated photographs of experimentally observed multistable states as a function of the number of inverted domes in a 3 × 3 array. e) Global curvature of patterned sheets featuring a 3 × 3 array of domes of different heights, h. f) Simulated energy landscape of a hierarchically multistable 3 × 3 sheet. The manipulation of local elements activates additional stable shapes on the global level. Energy units are nondimensionalized as the ratio of energy to the lowest global stable state energy with inverted domes, which is the twisted state in this case.

Figure 3

Complex multistable shapes, programmable mechanical response, and muscle‐free actuation enabled by dome‐patterned metamaterials. a) Examples of complex multistable shapes that can be generated using 8 × 8 sheets with specific patterns of inverted domes with normalized Gaussian curvatures of 0, 1, and −1, associated with (i) cylinders, (ii) doubly curved stars, and (iii) saddles, respectively. b) FE analysis of individual domes in a 3 × 3 sheet illustrating the stresses developed upon inversion. c,d) Force‐displacement relations for dome‐patterned sheets subjected to bending (left) and stretching (right). Sheets with an alternating arrangement of inverted domes are compared with a reference sample without dome inversion. The alternating arrangement of inverted domes was used because the induced up‐ and down‐curvatures equalize each other, preventing changes in the global shape of the sheet. e) Pneumatic robotic gripper displaying a dome‐patterned outer skin. f) Snapshots of the gripper at different applied pressures illustrate the reversible inversion of domes and how this can be exploited to exert a grabbing force on an object, even in the absence of pressurization.

Figure 4

Memory and morphology of dome‐patterned metamaterials. a–c) The correlation between the final shape and the inversion pattern and history allows for storing mechanical information and conducting in‐memory logic operations based on the deformations imposed on our sheets. (a) Zero stress state. (b) Different inversion patterns leading to single global shapes independently of the followed order (Movie S4, Supporting Information). (c) Three different inversion histories reaching the same final inverted dome pattern but distinct global shapes: twist‐left (Figure 4c.i, Figure S7b, and Movie S5, Supporting Information), twist‐right (Figure 4c.ii, Figure S7c, and Movie S6, Supporting Information) and cylindrical (Figure 4c.iii, Figure S7d, and Movie S7, Supporting Information). d) Simulations depicting morphologic operations using two connected metasheets (Figure 4d): (d.i) input field leading to twisting shapes for the two metasheets (Movie S8, Supporting Information), (d.ii) input field leading to bending shapes (Movie S9, Supporting Information), and (d.iii) input fields leading to a twisting‐bending shape (Movie S10, Supporting Information). The history and pattern of inverted domes induce rotation of the central, dashed yellow line when the lowest strain energy global state is reached, interpreted as Output 1 (Figure S8f, Supporting Information). No rotation indicates that a coexisting, higher strain energy state is reached, interpreted as Output 0 (dashed red line Figure S8f, Supporting Information). e) Experimental global shapes matching Output 1 (e.i) and Output 0 (e.ii‐iii). f) The spatiotemporal mechanical input pattern (white arrows), collective deformation, and state of center line (output node O1) can be utilized to establish a state transition table (Figure S9, Supporting Information) to provide a direct decision (signal E) in response to spatially distributed environmental inputs, A(C) and B(D), causing deformation of the two connected metasheets. An abstract logic diagram is shown in (f.ii): input patterns on metasheets (CG1 and CG2) lead to bending or twisting shapes of the metasheets (bending, Figure S8b, Supporting Information, and twisting, Figure S8c, Supporting Information), the compatibility of which yields an integral signal represented by Output E.