Materials challenges in conformable and foldable devices

Mechanical instabilities in soft materials, precipitated by dewetting,^{Reference Herminghaus, Jacobs, Mecke, Bischof, Fery, Ibn-Elhaj and Schlagowski1} swelling,^{Reference Tanaka, Sun, Hirokawa, Katayama, Kucera, Hirose and Amiya2} crumpling,^{Reference Lobkovsky, Gentges, Li, Morse and Witten3,Reference Trujillo, Kim and Hayward4} wrinkling,^{Reference Cerda, Ravi-Chandar and Mahadevan5} buckling,^{Reference Roman and Pocheau6} and collapsing,^{Reference Zhang, Lo, Taylor and Yang7,Reference Chandra and Yang8} are often gateways to large deformation and shape change in response to relatively small external perturbations. Exploiting this provides new opportunities to design reconfigurable materials with dramatically adjustable physical properties. Recently, spontaneous pattern transformation in periodic porous membranes has been demonstrated, triggered by swelling, drying, polymerization, and mechanical compression together with shape memory effects over multiple length scales.^{Reference Mullin, Deschanel, Bertoldi and Boyce9–Reference Wu, Cho, Choi, Ge, Li, Han, Lubensky and Yang19} The resulting photonic^{Reference Zhu, Wu, Dong, Chen and Yang15} and phononic^{Reference Jang, Koh, Bertoldi, Boyce and Thomas20,Reference Shan, Kang, Wang, Qu, Shian, Chen and Bertoldi21} bandgap properties, along with varying auxetic response (i.e., negative Poisson ratio),^{Reference Wu, Cho, Choi, Ge, Li, Han, Lubensky and Yang19,Reference Bertoldi, Reis, Willshaw and Mullin22,Reference Gatt, Caruana-Gauci, Attard, Casha, Wolak, Dudek, Mizzi and Grima23} are significantly altered due to the change of lattice symmetry, pore size, pore shape, or the volume filling fraction. Mechanical instabilities, however, if uncontrolled, can lead to sudden structural changes and unwanted features, such as defects, antiphase boundaries, and fracture.

At the same time, there is growing interest in flexible and wearable electronics,^{Reference Sekitani and Someya24–Reference Kim, Lu, Ma, Kim, Kim, Wang, Wu, Won, Tao, Islam, Yu, Kim, Chowdhury, Ying, Xu, Li, Chung, Keum, McCormick, Liu, Zhang, Omenetto, Huang, Coleman and Rogers26} energy-storage devices (e.g., batteries^{Reference Xu, Zhang, Cho, Lee, Huang, Jia, Fan, Su, Su, Zhang, Cheng, Lu, Yu, Chuang, Kim, Song, Shigeta, Kang, Dagdeviren, Petrov, Braun, Huang, Paik and Rogers27} and supercapacitors),^{Reference Weng, Su, Wang, Li, Du and Cheng28–Reference Ge, Yang, Fan, Zhang, Xiao, Gogotsi and Yang31} optics,^{Reference Song, Xie, Malyarchuk, Xiao, Jung, Choi, Liu, Park, Lu, Kim, Li, Crozier, Huang and Rogers32,Reference Xu, Yu, Wang, Malyarchuk, Xie and Rogers33} artificial muscles,^{Reference Baughman34,Reference Jager, Smela and Inganas35} actuators,^{Reference Keplinger, Sun, Foo, Rothemund, Whitesides and Suo36} tunable color displays,^{Reference Li, Shim, Deng, Overvelde, Zhu, Bertoldi and Yang14} and smart windows,^{Reference Lee, Zhang, Cho, Cui, Van der Spiegel, Engheta and Yang37,Reference Ge, Lee, Yang, Cho, Li, Gianola and Yang38} which often involve large area or volume changes (with strain up to 1000%). For example, wearable devices must stretch to wrap around an object (e.g., wrist) or fold into a compact package for later deployment. Therefore, the devices should be lightweight, flexible, and, more importantly, conformable to a non-flat object and bendable to a large curvature without losing mechanical or electrical performance.

Conformability is especially important for biomedical devices that detect the temperature of the skin or motion of the heart, lung, or brain.^{Reference Webb, Bonifas, Behnaz, Zhang, Yu, Cheng, Shi, Bian, Liu, Kim, Yeo, Park, Song, Li, Huang, Gorbach and Rogers39,Reference Dagdeviren, Yang, Su, Tran, Joe, Anderson, Xia, Doraiswamy, Dehdashti, Feng, Lu, Poston, Khalpey, Ghaffari, Huang, Slepian and Rogers40} The ability to withstand repeated large deformations in these devices presents a major challenge in materials science and engineering, since most devices are made of hard materials or are hybrids consisting of hard and soft materials. While hard materials offer durability, fast response time, and overall device performance superior to soft materials, they tend to fail when the applied strain is greater than 3%. The critical strain of fracture is defined as:^{Reference Suo25}

(1)$${\varepsilon _c} \approx \sqrt {\Gamma /(Ea)}$$,

where Γ is the fracture energy, E is the Young’s modulus, and a is the flaw size, on the order of the film thickness. For a typical hard material, Γ = 10 J m^–2, E = 100 GPa (e.g., SiO₂ or Si), and a = 1 µm, it yields ε_c ∼ 1%.^{Reference Suo25} In comparison, a compliant silicone sample (E = 2 MPa) can stretch up to ∼200% strain without fracture.

In the last decade, there has been significant progress in the use of low-cost, flexible materials, such as polymers,^{Reference Sekitani and Someya24,Reference Kim, Lu, Ma, Kim, Kim, Wang, Wu, Won, Tao, Islam, Yu, Kim, Chowdhury, Ying, Xu, Li, Chung, Keum, McCormick, Liu, Zhang, Omenetto, Huang, Coleman and Rogers26} paper,^{Reference Weng, Su, Wang, Li, Du and Cheng28,Reference Zheng, Hu, Wu, Xie and Cui29,Reference Ge, Yang, Honglawan, Li and Yang41} fabrics,^{Reference Jost, Dion and Gogotsi42} and cellulose nanofibers^{Reference Moon, Martini, Nairn, Simonsen and Youngblood43,Reference Zhu, Fang, Preston, Li and Hu44} as templates or scaffolds for depositing metals or using carbon-based conductive ink (e.g., carbon nanotubes and graphene) as electrodes. The interfacial contact between the hard and soft materials, however, is vulnerable to delamination or crack formation at large strains. Moreover, wrinkles will form on a compliant substrate upon release of the strain.^{Reference Yang, Khare and Lin45}

Khang et al.^{Reference Khang, Jiang, Huang and Rogers46} created electronic devices from wavy thin strips of semiconductors by taking advantage of the wrinkling effect. This effect describes the smooth surface undulations which result from uneven expansion of a surface consisting of materials with different mechanical properties (e.g., silicone versus semiconductors). Coupled with ultrathin film thickness (100–200 nm) (e.g., Si, GaAs, AlAs), they demonstrated extremely high stretchability (up to ∼100%), compressibility (up to ∼25%), and bendability (curvature radius down to ∼5 mm)—not possible in single crystalline, micron-sized semiconductors. Further, by introducing a self-similar, serpentine design of electrical interconnects, stretchability of 90% was achieved for systems with surface filling ratios of 50% active devices.^{Reference Zhang, Fu, Su, Xu, Cheng, Fan, Hwang, Rogers and Huang47} Nevertheless, most conformability demonstrated in the literature is on a compliant, planar surface. When draping a soft substrate such as cloth onto a simple object such as a sphere, it is not possible to conformably wrap the entire sphere without formation of wrinkles and creases. The immediate question is how to render rigid devices super-flexible so that they can wrap around a sphere without bending and stretching. Can such devices wrap around any shape? How do we amplify the expandable strain without changing the material’s intrinsic properties?

Besides electronics, folding a two-dimensional (2D) sheet into a complex three-dimensional (3D) shape is important for space-saving and shape transformation in packaging, furniture assembly, electronics, energy storage,^{Reference Ge, Yang, Fan, Zhang, Xiao, Gogotsi and Yang31,Reference Song, Ma, Tang, Cheng, Wang, Krishnaraju, Panat, Chan, Yu and Jiang48} biomedical devices,^{Reference Gracias49} solar cells,^{Reference Guo, Li, Yeop Ahn, Duoss, Hsia, Lewis and Nuzzo50} and robotics,^{Reference Hawkes, An, Benbernou, Tanaka, Kim, Demaine, Rus and Wood51,Reference Felton, Tolley, Demaine, Rus and Wood52} as well as in art and architecture. How can flat surfaces be transformed into any desired 3D structure without disruptive or catastrophic deformation? Origami has been exploited in a wide range of materials (e.g., hydrogels, shape-memory alloys, silicone, shrinkable polymers, shape-memory polymers, and liquid crystal elastomers), coupled with micropatterning and different stimuli (e.g., swelling/shrinking, heating, capillarity, and light),^{Reference Hawkes, An, Benbernou, Tanaka, Kim, Demaine, Rus and Wood51–Reference Qi, Conner, Qi and Martin60} or patterned cuts of ultrathin films of hard materials (e.g., Si) that can be compressed into 3D structures.^{Reference Xu, Yan, Jang, Huang, Fu, Kim, Wei, Flavin, McCracken, Wang, Badea, Liu, Xiao, Zhou, Lee, Chung, Cheng, Ren, Banks, Li, Paik, Nuzzo, Huang, Zhang and Rogers61} These techniques require buckling and wrinkling of the sheet, from which curved folds are obtained.

Origami in paper art, however, is about the folding of a nonstretchable 2D surface into 3D with zero Gaussian curvature everywhere.^{Reference Borrelli, Jabrane, Lazarus and Thibert62} Sharp folds require both bending and stretching of the materials. It has been demonstrated that sharp folds can be formed when swelling a micropatterned polymer trilayer.^{Reference Na, Evans, Bae, Chiappelli, Santangelo, Lang, Hull and Hayward56} Fabrication of a trilayer sheet, however, is non-trivial; it requires precise alignment of micropatterns in different layers and selective swelling of one or two layers to direct the folding direction. As mentioned earlier, most device components are rigid. How can one create perfectly sharp folds without shearing and stretching the sheet?

“The art of structure is how and where to put holes,” said structural engineer and architect, Le Ricolais.^{Reference Abruzzo and Solomon63} Following his lead, we propose that the key to addressing these challenges lies in intentional cuts. The expansion of a cut can be considered as the reverse process of compacting a pore. The cut can be prescribed as a simple line (straight or curved), a square, a hexagon, a circle, or an array of these units. Owing to this diversity, cuts can serve many different purposes.

In the case of line cuts, upon stretching, individual units connected by the remaining material act as hinges that rotate to open the cuts: By engineering the line cut geometry and cut length, we can minimize local stress concentration at the cut regions.^{Reference Tang, Lin, Han, Qiu, Yang and Yin64} By cutting out unnecessary parts, we can reduce the weight and material waste, and simplify the folding steps. This combination of cutting and folding is referred to as kirigami, a cousin of origami. Importantly, cut-out in kirigami allows control of the local formation of an intrinsic (Gaussian) curvature, which is, at best, cumbersome in origami when folding from a flat sheet. This allows the efficient formation of more complex 3D structures without stretching or shearing the 2D sheet.

In this article, we report recent progress in the design of super-conformable and foldable structures by employing fractal cutting and lattice-based kirigami elements. We highlight the algorithmic design of cut geometries in a periodic 2D lattice that can be buckled into a variety of desired 2D and 3D shapes (i.e., pluripotency) without deformation of the rigid units or surfaces.

Engineering fractal cuts for super-conformable materials

We have proposed a new approach dubbed “fractal cut patterning” to the design of 2D structures.^{Reference Cho, Shin, Costa, Kim, Kunin, Li, Lee, Yang, Han, Choi and Srolovitz65} We can transform a nonstretchable sheet into a highly stretchable and super-conformable material with a wide range of desired shapes and patterns by introducing a set of simple cuts in a multilevel hierarchy with different motifs. A detailed description of the method follows.

Basic principle: Rotating units

The essence of the design is to introduce cuts into a flexible base, dividing the material into rotating units prescribed by the cutting pattern, as exemplified in Figure 1a. The units (e.g., squares or triangles) between cuts are effectively rigid (i.e., no deformation), and the connections between these units behave as nearly free rotational hinges by bending as in Figure 1b. It follows that the deformation of the structure by biaxial or uniaxial stretching occurs primarily through rotation of the units, rather than by significant deformation of the units themselves. Hereafter, we describe our concept with the case of square-cut patterns for simplicity without losing its generality.

Figure 1.

(a) Basic deformation principles behind the patterns of the cuts. Cuts divide the material into rotating units. Upon equal biaxial stretching, each unit rotates clockwise (white arrows) or counterclockwise (yellow arrows), (b) by bending a finite hinge (width, w; height, h) so that the original structure expands. A square rotating unit of length L is shown. (c) Finite element calculations of silicone rubber sheets with multilevel hierarchical cuts are given.^{Reference Cho, Shin, Costa, Kim, Kunin, Li, Lee, Yang, Han, Choi and Srolovitz65}

Fractal cut pattern: Hierarchy and motif alternation

Two classes of cut patterns are used: “hierarchical” and “motif alternation.” The hierarchical pattern concept is illustrated by finite element (FE) simulation results in Figure 1c for a simple pattern of cuts producing square units. Such square units can be subdivided into smaller squares by repeating the cut pattern within the original square. While the subdivision can, in principle, go on ad infinitum creating a true fractal cut pattern, the focus is on patterns of finite hierarchy degree or level (i.e., the number of times the same cut pattern is reproduced on the units left by the preceding cuts). Increasing the hierarchy level leads to increasingly complex structures and enhanced expandability upon stretching. Along with expandability, pore shape, apparent density, and elastic stiffness (assuming the hinges have some resistance to rotation) all vary with the hierarchy level. The variables that determine the final structure of the stretched sheet are the rotation angles between rotating units, the number of which increases as the hierarchy level increases.

In addition to hierarchy, another design parameter is the cut motif. As shown in Figure 2, the level 1 structure can be cut into two different ways, either the α-motif (red) or β-motif (blue). The cut motif is kept constant, as indicated by the red lines in Figure 1c (the α-motif). This same motif applied homogeneously leads to the same unit rotation pattern across the entire structure, as indicated by the white and yellow arrows in Figure 1a. Although the degrees of freedom increase with the level of hierarchy, with each level the incremental rotational angle decreases, limiting the expandability and, at some point, providing diminishing marginal response. By using alternating cut motifs, we can improve upon this: another motif, β, could be formed by rotating the α-motif by 90°, as shown in blue at the bottom of Figure 2. We denote the strain at each level i in an N-level structure as ε_N(x ₁x ₂. . . x _N), where x _i denotes the motif (e.g., x _i refers to the α- or β-motif). The square units in the β-motifs rotate in opposite directions relative to those in the α-motifs. Thus, the combination of α- and β-motifs between levels produces alternating rotation directions of the units, allowing larger rotation angles and strains at higher levels.

Figure 2.

The two cut motifs, α (red) and β (blue) in a hierarchical structure and diverse combinations of the hierarchy (or number of levels) and motifs (a–d).^{Reference Cho, Shin, Costa, Kim, Kunin, Li, Lee, Yang, Han, Choi and Srolovitz65}

For example, the maximum lateral strain in the level 4 structure that consists of a single-cut motif is ε₄(αααα) = ε₄(ββββ) = 108% (see Figure 2a and Figure 3a), while for the alternating motif it is ε₄(βαβα) = 130% (see Figure 2b and Figure 3b). In addition, the total number of ways to cut the sheet increases with an additional motif. At the first level, where the α- or β-motif can be applied, there were only two permutations. At the second level, each of the four subsquares had one of two motifs (i.e., 16 possibilities). Therefore, in a level-2 structure, there are 32 permutations. Hence, the concept of motif extends the versatility of the fractal cut structure and even allows for heterogeneous response within the same sheet.

Figure 3.

Macroscopic experimental realization of a fractal cut concept. The shape changes of silicone rubber sheets stretched with patterned cuts in Figure 2a–d are identical to those seen from the finite element calculations. The smallest feature size (hinge width) is 2 mm. (e) Photo of a stretchable electrode embedded with ε₃(ααα) fractal cuts in a silicone rubber sheet coated with a thin conducting film, and conformable wrapping of the structure around a baseball without wrinkles. The green LED light remains lit after wrapping. Scale bar: 40 mm.^{Reference Cho, Shin, Costa, Kim, Kunin, Li, Lee, Yang, Han, Choi and Srolovitz65}

Engineering complex shape and structure via fractal cutting

The concept of the fractal cut pattern provides the basic palette that can be used to draw (i.e., cut a pattern) on a blank canvas or a material sheet (e.g., experimental demonstration using silicone sheets with fractal structures as seen in Figure 3). The diverse combination of hierarchical levels and motifs can further achieve a wide range of desirable programmed shapes. For example, Figure 3c shows the nonuniform expansion of a level 3 structure with an inhomogeneous combination of α- and β-motifs in the fractal cut structure corresponding to Figure 2c. Figure 3d shows the directional expansion resulting from a mixture of different hierarchy levels and motifs corresponding to Figure 2d.

When stretched, the square sheets show final shapes that closely match the simulation prediction. The concept of fractal cutting is not confined to a specific material system, nor to a specific feature size. For example, a poly(dimethylsiloxane) sheet with a reduction of the smallest feature size (at hinges) from 2 mm to 40 μm in a level 4 structure (see Figure 4a–b) shows identical structures as predicted by FE simulation and as those with macroscopic size (see Figure 3). Hence the described approach to forming highly expandable pluripotent materials can be applied to different scales. It should also be noted that while the presented results in this review focus on 2D sheets with square units, the same concept can be applied to other 2D and 3D structures with different base units.

Figure 4.

Poly(dimethylsiloxane) sheets differentiated with microscopic patterned cuts. The smallest feature size (hinge width) is 40 μm. (a) One unit of the homogeneous structure notated as ε₄(αααα). (b) One unit of the ε₄(βαβα) structure. (ε_i represents the maximum possible strain of a struture with i levels of cut motifs α or β). Scale bar: 200 μm.^{Reference Cho, Shin, Costa, Kim, Kunin, Li, Lee, Yang, Han, Choi and Srolovitz65}

Algorithmic lattice kirigami: Toward pluripotent foldable materials

Cuts do not only allow for stretching and large deformation in two dimensions. By choosing the cuts and geometry correctly, it is possible to bind edges together by folding into the third dimension. This is known as kirigami—cutting combined with folding. This added complexity can lead to 3D structures but, in principle, also leads to a bewildering array of possible motifs and folds. Fortuitously, a highly restricted set of cuts and folds can be exploited to construct arbitrary landscapes at a given resolution.^{Reference Castle, Cho, Gong, Jung, Sussman, Yang and Kamien66,Reference Sussman, Cho, Castle, Gong, Jung, Yang and Kamien67}

The key to this construction is the connection between elasticity, topological defects, and intrinsic geometry.^{Reference Seung and Nelson68–Reference Kamien70} We start with a crystalline lattice, the honeycomb, or equivalently, its dual lattice, the triangular lattice. As a 2D system, we can consider both dislocations and disclinations, the former adding an extra row of atoms, the latter creating a large lattice distortion, as shown in Figure 5. The third dimension provides a way to relieve this divergent strain because of the powerful relation between intrinsic curvature, Gaussian curvature, and local coordination of the lattice.

Figure 5.

Flat distorted sheets of a triangular lattice buckling into the third dimension. (Left) A fivefold defect (a “5”) buckles into a positive Gaussian curvature surface to relieve strain (note that the struts are more regular). (Right) A sevenfold defect (a “7”) buckles into a saddle with negative Gaussian curvature. Courtesy of H.S. Seung and D.R. Nelson.

The essence of kirigami is to exploit this connection between local topology and the third dimension to control the location of Gaussian curvature. Unlike origami that can only make changes in the mean curvature, kirigami allows changes in both the mean and Gaussian curvatures. Similarly, to make conical or saddle structures out of flat paper requires hidden flaps, making a heavier, more wasteful structure. Moreover, any origami cone can be ironed-out back to flat, making the structure, at best, metastably rigid.

Our primitive kirigami building block is shown in Figure 6a.^{Reference Castle, Cho, Gong, Jung, Sussman, Yang and Kamien66} Following the definition of a “5,” a point with coordination 5, and a “7,” a point with coordination 7 (as depicted in Figure 5), we build kirigami out of 5–7 pairs. Note first that a lone 5–7 pair, though neutral from the point of view of disclinations, creates a dislocation in the flat crystal with Burgers vector proportional to the separation between the 5 and the 7. Charvolin, Rivier, and Sadoc^{Reference Sadoc, Rivier and Charvolin71} demonstrated how this can be accommodated by a neat step in a 3D structure. In Figure 6a, we can see this explicitly—a yellow pentagon adjacent to a green heptagon (a 5 and 7, respectively) draws the red lines on top of the plateau closer in the valley. The opposing 5–7 pair restores the spacing of the red lines. Attaching these together through a cut in the sheet of paper leads to the climb and glide structures shown in Figure 6. Once cut and folded, these structures have few degrees of freedom and can support their weight (and the weight of others) through the shear modulus of the paper. A bend modulus is not necessary to create rigidity in the 3D structure.

Figure 6.

The essence of kirigami. (a) The climb cut, where two dislocations are separated by a climb. Top: We remove the hatched region and make mountain (M) and valley (V) folds along the indicated lines. The yellow regions have become pentagons, the green regions heptagons. Bottom: Final state with the edges of the cut identified by pasting. (b) The glide cut. We remove the hatched regions and make a cut along the ratchet, then make |M| and |V| folds along the indicated lines, followed by gliding of the triangles along the ratchet to the final form. The ratchet allows for interlocking of the final folded structure without the need for pasting.

Just as with origami, the design of a pattern made by gluing together the units in Figure 6 leads to a unique (or almost unique) final structure. However, we have found another fold motif, the “sixon”^{Reference Sussman, Cho, Castle, Gong, Jung, Yang and Kamien67} (see Figure 7) that can be folded in three different ways, constituting a “degeneracy”: transforming from one state to another (i.e., “popping a triangle from up to down or down to up”) only requires opening and reclosing the three excised hexagons that bound the relevant triangular plateau. Because of this degeneracy, there are enough degrees of freedom to generate arbitrary surfaces with maximum slope. This kirigami is pluripotent.^{Reference Sussman, Cho, Castle, Gong, Jung, Yang and Kamien67} As seen in Figure 8, by choosing a targeted surface, we can project the height onto the triangular lattice and assign a local folding sequence, leading to reconfiguration between one target and another.

Figure 7.

Top, a two-level kirigami fold motif that can be distorted through rigid folding into a three-level structure with “0,” “1,” and “2” (bottom) indicating different elevations. The three-level structure, however, has a threefold degeneracy that can be exploited to generate arbitrary topographies as seen in Figure 8 and in Reference Reference Sussman, Cho, Castle, Gong, Jung, Yang and Kamien67, depending on the local assignment of the fold direction, thus the level of elevation. The blue lines depict the line along which the final fold is made. The three different choices of fold lines are labeled α, β, and γ.

Figure 8.

Demonstration of the pluripotent design capability of the sixon lattice. Starting from the base configuration of a 151 × 151 grid of triangular plateaus, a target surface is first selected (e.g., a monkey saddle or Mt. Katahdin). The height of this target surface is projected onto the grid of triangular patches, and from this a local sequence of fold assignments is made to construct the final kirigami structure.^{Reference Sussman, Cho, Castle, Gong, Jung, Yang and Kamien67}

Summary

We have demonstrated two scale-invariant strategies to create expandable and shape-shifting structures that, in principle, can be applied to any material at different length scales, enabling new applications of off-the-shelf materials in flexible and wearable electronic, photonic, and phononic devices. It also suggests intriguing new ways of manipulating nanomaterials (e.g., nanocomposites)^{Reference Shyu, Damasceno, Dodd, Lamoureux, Xu, Shlian, Shtein, Glotzer and Kotov72} and ultrathin films of emerging materials (such as graphene and molybdenum disulfide) for new switchable transistors, biosensors, and topological insulators. By prescribing cuts with different motifs, identifying edges in the right geometry, and programming the folding directions, we show that a single flat sheet can be transformed into a variety of targeted 2D and 3D structures.

The cutting and folding strategies presented here offer a pluripotent platform for new technologies. For example, the fractal cut structures can be used as scaffolds to integrate conventional hard devices without sacrificing device performance during large expansion and collapsing, and are super-conformable to objects of different shapes. They can be exploited as highly tunable antenna and wireless communication filters. They can also be extended to 3D (e.g., for a foldable and deployable solar panel in space or for miniaturized optics that are capable of 360° sensing and imaging).

Evermore rich structural reconfigurations can be obtained from more complex cut patterns. This also raises questions of how to program the shape change with increased complexity, and what are the algorithms to guide cuts and identify edges. Can we embed spatial and temporal cues in materials, for example, via patterning, elasticity gradients, or the use of smart materials that can be responsive to environmental conditions (e.g., heat and light) spontaneously, and reversibly? Clearly, this field is wide open. We hope this article will inspire multidisciplinary collaborations between materials scientists and engineers, mechanical engineers, physicists, mathematicians, computer scientists, device engineers, and biomedical engineers to solve many of these issues.