Advertisement

Abstract

Electronic devices with engineered three-dimensional (3D) architectures are indispensable for frictional-force sensing, wide-field optical imaging, and flow velocity measurement. Recent advances in mechanically guided assembly established deterministic routes to 3D structures in high-performance materials, through controlled rolling/folding/buckling deformations. The resulting 3D structures are, however, mostly formed on planar substrates and cannot be transferred directly onto another curved substrate. Here, we introduce an ordered assembly strategy to allow transformation of 2D thin films into sophisticated 3D structures on diverse curved surfaces. The strategy leverages predefined mechanical loadings that deform curved elastomer substrates into flat/cylindrical configurations, followed by an additional uniaxial/biaxial prestretch to drive buckling-guided assembly. Release of predefined loadings results in an ordered assembly that can be accurately captured by mechanics modeling, as illustrated by dozens of complex 3D structures assembled on curved substrates. Demonstrated applications include tunable dipole antennas, flow sensors inside a tube, and integrated electronic systems capable of conformal integration with the heart.

INTRODUCTION

Biological systems, including both plants (e.g., stems, flowers, and seeds) and animals (e.g., hearts, alveolus pulmonis, brains, blood vessels, and tracheas), mostly have complex three-dimensional (3D) curved surfaces, some with dynamic, time-varying features. Developments of manufacturing approaches/technologies to allow conformal integration of electronic systems with these 3D surfaces are of utmost importance for high-fidelity information interactions with these biological systems (1, 2). The resulting 3D conformal electronic systems have widespread applications in health monitoring (36), human-machine interfaces (7, 8), curved displays (9, 10), therapeutic devices (1116), artificial tissues/organs (1723), and fundamental biomedical research (2429). A variety of manufacturing approaches/technologies were developed in this context, including, for example, transfer printing (3033), 3D printing and direct writing (3441), origami/kirigami (4252), holographic lithography (53), and pneumatically controlled assembly (5457). While 3D printing technologies (e.g., multimaterials 3D printing) can create conducting and insulating components in almost any 3D shapes, these technologies still cannot manufacture high-quality inorganic electronic materials (such as silicon and gallium arsenide) that are essential to high-performance devices. Printing of suspended micrometer-scale 3D structures directly on complex curved surfaces also remains challenging. Transfer printing technologies based on conformal additive stamps have enabled fabrication of various electronic devices with curved 3D shapes, such as silicon pellets (33, 58), photodetector arrays (55, 59, 60), electrically small antennas (34, 54), and shape-adaptive optoelectronic imagers (22, 30, 61, 62). However, these approaches are not able to transfer 3D electronic components/devices onto curved 3D surfaces. While electronic devices with precisely controlled 3D shapes are crucial for the frictional-force sensing (63), flow velocity measurement (64), and optical imaging with a wide-angle field of view (18, 22), development of approaches to allow manufacturing of complex 3D electronic devices on arbitrary 3D curved surfaces remains challenging and rarely explored. Although recently established approaches based on mechanically guided 3D assembly provided access to electronic devices with diverse 3D topologies (6568), the resulting 3D devices are, however, mostly formed on a planar substrate and cannot be transferred directly onto another curved substrate.
In this work, we present a set of unique assembly strategies and design concepts to allow transformation of 2D thin films into complex 3D structures on almost arbitrary 3D curved substrates, including those with regular surfaces (e.g., hemisphere, cylinder, helicoid, spiral, and hyperboloid) and biomimetic surfaces (e.g., twining vines, human face, brain-like surface, aorta, and heart-like surface). The proposed assembly strategies leverage predefined mechanical loadings to deform curved elastomer substrates into flat or cylindrical configurations that allow integration of 2D thin films (i.e., 2D precursors) with selectively defined bonding sites. The release of predefined loadings in the substrate results in an ordered assembly process, including the transformation of 2D precursors into 3D structures at an intermediate (either flat or cylindrical) configuration of the substrate, and the spatial arrangement of 3D structures on the target curved configuration of the substrate. Quantitative mechanics modeling based on nonlinear finite element analyses (FEA) captures accurately the entire process of the ordered assembly, providing a powerful tool for the rational design of these assembly strategies. On the basis of combined theoretical and experimental studies, we showcased the assembly of diverse 3D structures (in semiconductors, metals, polymers, oxides, and graphene) on curved substrates with a dozen of different 3D topologies, across a wide range of length scales (with the curvature radius down to 500 μm). The resulting structures could be shaped with unique 3D topologies inaccessible previously, such as hierarchical 3D topologies (e.g., hierarchical hemispheres, hierarchical cylinders, and hierarchical helices) and 3D structures inside spherical/cylindrical shells. Excellent compatibility with the well-established planar microfabrication techniques suggests a broad range of application opportunities. Examples demonstrated here include a dipole antenna whose resonant frequency is continuously tunable in a wide range, a highly stretchable integrated electronic system that can be conformally wrapped onto the apex of the heart, and a piezoresistive 3D flow sensor assembled on the inner surface of a tube, with potentials for long-term monitoring of blood flows in veins/arteries.

RESULTS

Conceptual illustration of the ordered assembly strategy

Figure 1A provides a schematic illustration of the proposed ordered assembly strategy for the formation of complex 3D structures on curved surfaces (human face in this example). Here, a thin elastomer (1 mm in thickness; Ecoflex, Smooth-On) with a human face shape serves as the assembly substrate, which was fabricated by casting and curing liquid precursors in a 3D-printed polymeric mold (see fig. S1 for details). An equal biaxial prestretch (~20%) allows the human-face substrate to be flattened. An additional level of biaxial prestretch (from ~20 to 40%) stores elastic strain energy in the substrate that can be used for the buckling-guided assembly of the 2D precursor structures, similar to the process reported previously (65, 68). In this example, a decorative mask in a bilayer of Ag (5 μm) and polyethylene terephthalate (PET; 75 μm) serves as the 2D precursor structure, which is bonded with the biaxially prestretched substrate at strategically defined locations (in yellow). By releasing the prestretch from 40 to 20%, the substrate remains an approximately flat configuration, and the compressive forces applied to the precursor structure trigger the buckling process that lifts the 2D precursor up into 3D configuration, that is, the first-order assembly. Further release of the prestretch (to zero) recovers the substrate to the original 3D shape, and the associated spatial movements of the bonding sites map the mask structure into the final 3D configuration on the human face substrate, that is, the second-order assembly. Replacing the mask design with a ribbon network enables the assembly of beard-like structure on the human face substrate (fig. S2). Full 3D FEA (see Materials and Methods for details) capture well both the spatial deformations of thin-film structure and elastomer substrate during the entire process of the ordered assembly. Good agreements of final 3D configurations of the assembly between FEA predictions and optical images indicate that FEA can be used as a reliable tool of the structural design.
Fig. 1. Conceptual illustration of the ordered assembly strategy of complex 3D structures on curved surfaces.
(A) Illustration of the ordered assembly strategy with the formation of a 3D decorative mask on a human face. The two images on the right correspond to the FEA prediction and optical image of 3D structures in a bilayer of Ag (5 μm) and PET (75 μm). (B) Top panel illustrates a helicoid substrate and FEA results of the helicoidal substrate that can be flattened by torsional and tensile loadings. Bottom panel presents the ordered assembly process of 3D leaf-like structures [Al (2.5 μm)/PET (30 μm)] on helicoidal substrates with FEA predictions and an optical image. (C) Conceptual illustration of the assembly of 3D structures on the inner surface of a cylindrical tube, where the substrate is cropped obliquely, flattened by bending deformations, and then prestretched, before the integration with the 2D precursor. Bottom panel presents the ordered assembly process of a hierarchical 3D helical structures [Al (2.5 μm)/PET (30 μm)] inside cylindrical tubes with FEA predictions and an optical image. (D) Illustration of the assembly process of 3D structures on a substrate with the Möbius-band shape, along with FEA predictions and optical image of ant-like structures [Al (2.5 μm)/PET (30 μm)] assembled on the substrate. Scale bars, 20 mm in (A), 10 mm in (B) and (D), and 5 mm in (C). Photo credit: Z.X. and T.J., Tsinghua University.
In principle, the ordered assembly strategy proposed here applies to curved substrates with any developable surfaces, as these surfaces can be flattened simply by bending deformations, after which 2D precursor structures can be integrated with the flattened substrate to implement the 2D-to-3D assembly through controlled compressive buckling. The strategy also applies to curved substrates with nondevelopable surfaces that can be approximately flattened by mechanical loadings, such as the human face substrate (Fig. 1A). To flatten curved substrates with more complex 3D topologies, the uniaxial or biaxial prestretch is sometimes insufficient, and in these cases, combined tensile/bending/torsional loadings could be exploited. Figure 1B and movie S1 illustrate the assembly strategy on a helicoid elastomer substrate that can be flattened by torsional loadings (720°), rather than tensile loadings. In this example, an additional level of uniaxial prestretch (20%) is applied after the substrate is flattened. After integration with the 2D precursor structures, release of the prestretch enables the first-order assembly of the leaf-like 3D structures on both sides of the flattened substrate. Further release of the torsion allows transformation of the substrate into the helicoid surface, resulting in the spatial rearrangement of two leaf-like 3D structures during the second-order assembly. These two leaf-like structures become very close to each other in the final state of two-order assembly, although they are initially located at two different sides of the flattened substrate. The as-assembled structures on the helicoid substrate are very deformable and can undergo larges levels of bending or twisting deformations (fig. S3). Figure S4 showcases other examples of 3D structures assembled on the helicoid substrate, including those with both ribbon- and membrane-shaped geometries.
Assembly of 3D structures on the inner surface of a cylindrical shell is very challenging, because it is very difficult to transfer predefined 2D precursors directly onto the inner surface, especially for cylindrical shells with small radii (e.g., <1 cm). Here, we extend the ordered assembly strategy to solve this challenge, by introducing oblique cropping to the cylindrical substrate, such that the substrate can be flattened by bending deformations. Figure 1C presents a schematic illustration of this process, where the cropping angle is 30°, and the two ends experience a relative rotation of 1800° to reach a flat configuration. An additional level of uniaxial prestretch (20%) is applied to the flattened substrate to drive the first-order assembly of the 2D precursor structure. The second-order assembly allows formation of the 3D structure on the inner surface of the cylindrical substrate (Fig. 1C, right bottom). The final 3D configuration features a hierarchical 3D helical topology, in which the small helices (pitch ~4 mm) form through the compressive buckling of serpentine precursor structures (during first-order assembly), and the large helices (pitch ~20 mm) arise from the oblique rolling of the cropped substrate (during second-order assembly). This type of hierarchical 3D configuration is unachievable previously. Two additional 3D structures formed on the inner surfaces of the cylindrical substrate are in fig. S5.
This assembly strategy also works for the substrate with Möbius-band shape, an interesting nonorientable surface with only one side and only one boundary curve. Here, an initial cropping is also required such that the curved substrate can be flattened by combined bending, torsional and tensile loadings (Fig. 1D). The bottom panel shows three ant-like structures assembled on the Möbius-band substrate, noting that the cropped sections are glued together after the ordered assembly. While the three “ants” are initially placed on two different sides of the cut substrate, they are transformed onto the same curved surface after the assembly. For all of the 3D structures in Fig. 1, FEA predictions always agree well with corresponding optical images in experiments. These results also show that the ordered assembly strategy allows 3D assembly on a very broad range of curved surfaces. It is noteworthy that the 3D assembly on curved substrates differs qualitatively from that on planar substrates, because the ordered assembly strategy involves distinct design considerations, such as the magnitude and form of predefined mechanical loadings required to flatten the curved substrate, as discussed in Fig. 1.

Assembly of complex 3D structures on curved surfaces that can be flattened

This section highlights the fundamental principles and design methods for the ordered assembly of 3D structures on curved surfaces that can be deformed into approximately flat configurations by predefined mechanical loadings. For a prescribed curved substrate, the design factors of the ordered assembly include (i) distribution of bonding sites on the curved substrate, (ii) magnitude and form of predefined mechanical loadings required to flatten the substrate, (iii) additional level of uniaxial/biaxial prestretch applied to the flattened substrate, (iv) layout of 2D precursors and location of bonding sites, and (v) dimensions of 2D precursor materials and their mechanical properties. While the last three factors are similar to those in conventional buckling-guided 3D assembly strategy based on planar substrates (65, 68), the first two factors correspond to new design considerations because of the mechanical constraint of curved substrates. Hence, we mainly focus on discussions of the additional two factors in this study and unravel the crucial role of surface curvature on the final 3D configuration of the assembled structures.
Figure 2A presents an example of developable curved substrate with a horseshoe shape to illustrate the effect of design factors on the ordered 3D assembly. Quantitative mechanics modeling captures the evolving profile of the curved substrate, as the uniaxial applied strain (εappl) increases (fig. S6A). Note that εappl = (LL0) / L0 denotes the engineering strain applied to the curved surface, where L and L0 are the end-to-end distance of the curved substrate profile along the x axis direction, in the deformed and undeformed configurations, respectively. The curved substrate can be assumed as “flattened,” when its relative height (h/L) is sufficiently small (e.g., <0.05 in this study), where h is the dimension of the deformed substrate along the z axis direction. Accordingly, the critical applied strain (εcritical) required to flatten the substrate can be determined as εcritical = (Larc-lengthL0)/L0 (i.e., 45% for the horseshoe substrate), where Larc-length is the arc length of the substrate profile in the undeformed configuration. Figure 2B illustrates the ordered assembly process of three 3D structures on the horseshoe substrate, where a uniaxial prestretch of εpre = 90% is used, noting that (εpre – εcritical = 45%) is applied to the flattened substrate during the prestretch. Here, the layouts of 2D precursors are exactly the same for the three designs, while the distributions of bonding sites on the horseshoe substrate are different. The resulting ribbon structures exhibit distinct 3D shapes, suggesting the important role that the distribution of bonding sites plays on the final 3D configuration of assembled structure. Figure S6 (B and C) presents 3D ribbon structures assembled on a fractal horseshoe substrate with a relative high critical strain (75%), where certain regions of assembled structures are in contact with the substrate, due to the highly wavy surface topology.
Fig. 2. Assembly of complex 3D structures on curved surfaces that can be flattened.
(A) Schematic illustration of curved substrates with the horseshoe shapes, which can be flattened by uniaxial stretching. (B) Optical images that illustrate the assembly process of 3D ribbon structures on the horseshoe substrates. (C) FEA and experiment results on the generatrix profile of a hemispherical elastomer substrate under different levels of biaxial stretching. R0 denotes the radius of the initial hemisphere. (D) FEA predictions of the maximum principal strain contours in the hemispherical substrate under different levels of biaxial stretching (0, 30, 50, and 100%). (E) Comparison of straight ribbons with different length (Lribbon) assembled on the hemispherical substrate by FEA predictions. (F) 2D geometries, FEA predictions, and experimental images of various 3D structures [Cu (100 nm)/PI (8 μm) in (i) and (ii), and Al (2.5 μm)/PET (30 μm) in (iii) to (vi)] assembled on the convex and concave surfaces of hemispherical substrates. (G to J) Inverse design for a hemi-ellipsoidal surface assembled on the hemispherical substrate. (K to N) Inverse design of small hemispheres with the same height (hi) assembled at different spatial locations on the hemispherical substrate. (O and P) Optical images of a network of helical microscale structures and a tiny 3D rhomboid ribbon microscale structure assembled on a brain-like surface. Scale bars, 10 mm in (B), (F) [(iii) to (vi)], (I), and (M) and (O) (ii); 3 mm in (F) [(i) and (ii)], and (P) (left); and 500 μm in (P) (right). Photo credit: Z.X. and T.J., Tsinghua University.
As a very representative nondevelopable surface, the hemisphere serves as an ideal shape to illustrate the effect of surface curvature on the assembled 3D configuration and the route to 3D shape customization. Hemispherical elastomer substrates with a range of different radii (R0 = 5 and 15 mm) and thicknesses (t = 0.3, 1, and 2 mm) were fabricated with casting and curing. A thinner substrate (with a smaller normalized thickness, t/R0) requires a lower biaxial strain to flatten the substrate (fig. S7). Figure 2C shows the variation of generatrix profile during the biaxial prestretch, for a typical hemispherical substrate (with t/R0 = 2/15). Here, the relative height reduces to 0.05 when the biaxial applied strain reaches εcritical ≈ 50%. The strain distribution in Fig. 2D exhibits a clear gradient along the radial direction at different levels of biaxial strain (30, 50, or 100%), representing a key difference from that of planar substrates. Another key difference arises from the spatial curvature of the substrate surface, which induces spatially varying rotations of bonding sites during the second-order assembly (fig. S8). It is noteworthy that both the convex and the concave surfaces of the hemispherical substrate can be exploited to assemble 3D structures, but the resulting geometries are highly different. In comparison to the assembly on the convex surface, the assembly on the concave surface enables formation of arch-shaped structures with larger heights, because of the spatial rotations of bonding sites along different orientations during the second-order assembly (Fig. 2E and fig. S9). The effect of substrate curvature on the final configuration of 3D structure becomes more evident, with increasing lateral dimension (e.g., ribbon length Lribbon) of the assembled structure relative to the curvature radius (R0) of the substrate (Fig. 2E). In the condition of Lribbon/R0 = 1/3, the two arch-shaped structures on the convex and concave surfaces of the hemispherical substrate have almost the same geometric configuration.
With a clear understanding of the nonuniform strain distribution and the curvature effect, precisely controlled 3D architectures can be assembled on the hemispherical substrate. Figure 2F, figs. S10 and S11, and movie S2 provide a dozen examples of 3D ribbon and membrane structures, assembled on either the convex or the concave surface. The first two microscale structures in Fig. 2F are assembled on a relatively small hemispherical substrate (R = 5 mm and t = 1 mm), where strategic folding deformations (highlighted by yellow color) are generated by reducing the thickness (3 μm for creases and 9 μm for other regions) of the 2D precursor. The second example exploits a mesh design with parallelogram units, such that a cellular 3D cage [Cu (100 nm)/polyimide (PI; 8 μm)] is formed on top of the hemispherical substrate. The third and fourth examples of Fig. 2F represent a spatial array of 3D tent structures and four kirigami-inspired membrane structures with raised tables along different orientations, respectively. Aside from the convex surface of the hemispherical substrate, 3D structures can also be assembled on its concave surface (last two designs of Fig. 2F and fig. S10B). In particular, packing two thin hemispherical substrates together enables the creation of 3D structures inside a sphere, which is inaccessible previously. The last example in Fig. 2F highlights a couple of honeybee-like structures inside a very thin spherical substrate (R = 15 mm and t = 300 μm).
The shape customization of 3D structures assembled on curved substrates is more challenging than that based on planar substrates, because of the spatial rotations of bonding sites and nonuniform strain distribution. However, the rational design approaches established for the assembly on planar substrates (6971) can be theoretically extended to deal with the inverse design of 3D assembly on curved substrates, considering that both strategies are implemented through mechanical deformations. For the inverse design of 3D surfaces, we extend the discretization-based method based on the topology optimization (70) to take into account the curvature effect of the 3D substrate. Figure 2 (G to J) and fig. S12 provide results of the inverse design for a hemi-ellipsoidal surface (with an aspect ratio of a:b:c = 2:1:1, where a corresponds to the semimajor axis, and b and c correspond to the semiminor axes of an ellipse) assembled on the hemispherical substrate. Considering the axis-symmetric geometry, the hemi-ellipsoidal surface is discretized into eight identical ribbon components (fig. S12, A and B). Figure S12D presents the optimization history of the inverse design for the hemi-ellipsoidal target surface based on the adaptive genetic algorithm. Figure 2 (G to J) presents the comparison between the target hemi-ellipsoidal surface and optimized surface assembled on the hemispherical substrate, along with the experimental image. The assembled 3D surface structure agrees well with the design target, as evidenced by the accordance of the generatrix profile (fig. S12E). For the inverse design of ribbon-type 3D structures, we can extend the optimization-based method reported in (71) to account for the curvature effect of the substrate. Figures S13 and S14 provide results of the inverse design for two ribbon structures (a curvy 3D ribbon structure and a 3D ribbon framework) assembled on the hemispherical substrate.
Figure 2 (K and L) presents a design inspired by the compound eye of the fly, with a hierarchical 3D topology, which contains an array of 16 small hemispheres on a large hemisphere. Each small hemisphere consists of 10 identical ribbons [Al (2.5 μm)/PET (30 μm)] with strategic width distributions along the length direction (59, 69). Here, a design target focuses on achieving the same height of small hemispheres assembled at different spatial locations. Considering the axial symmetry, the small hemispheres can be grouped into three categories (i.e., inner, middle, and outer). The first-order assembly leads to the formation of 16 small hemispheres (radius, ~2 to 3 mm) on the flattened substrate, and the second-order assembly maps those small hemispheres onto the surface of the large hemisphere (radius, ~15 mm; Fig. 2M). By tailoring the dimensions of 2D precursor structures for the three different categories, the normalized heights (hi/R0, i = 1, 2, and 3) of assembled small hemispheres are almost the same (~0.18), despite evident height changes during the second-order assembly (Fig. 2N). In comparison, a considerable variation of the normalized height (from 0.16 to 0.23) can be observed by using uniformly distributed 2D precursor designs (fig. S15). The hierarchical hemispherical structures have potential applications in tunable optoelectronic devices.
Excluding the hemispherical substrate, the ordered assembly strategy is also applicable to curved substrates with other complex nondevelopable surfaces. Figure 2 (O and P) and figs. S16 and S17 present two examples, with a brain-like surface and a hierarchical hemispherical surface, respectively. In comparison to the hemispherical substrate, a higher level of biaxial prestretch (100%) is required to flatten the brain-like substrate. The two-order assembly allows formation of a helical ribbon network that covers a considerable portion of the brain-like substrate (Fig. 2O). Tiny 3D microscale structures with lateral dimensions close to the feature size of the “sulcus” can also be assembled, with an example appearing in Fig. 2P. Here, evident bending/twisting deformations are involved during the 3D assembly, because of the complex sulcus topology.

Assembly of complex 3D structures on cylindrical or cylinder-like surfaces

This section focuses on the assembly on curved substrates with another class of basic 3D geometries, i.e., cylindrical or cylinder-like surfaces. In addition to the planar configuration, cylindrical configurations represent another type of basic geometries that can serve directly as the platform of buckling-guided 3D assembly. Here, we introduce two types of assembly strategies based on compressive and tensile buckling, respectively, for cylindrical substrates (Fig. 3, A and B). In both cases, an accurate alignment of the 2D precursor with the cylindrical surface is required during the process of transfer printing. Figure 3A illustrates the strategy that uses the release of radial prestretch (25%) in an aorta-like substrate to drive the compressive buckling of precursor structures [Al (2.5 μm)/PET (30 μm)]. Both helical and double helical structures are assembled along the axial direction of each “artery.” The second strategy, inspired by the concept of tensile buckling (72), makes use of the circumferential shrinkage during the axial stretching to drive the mechanical assembly of precursor structures. Figure 3B presents a set of straight ribbons with different lengths (Lribbon = πR0/6, πR0/2, πR0, and 3πR0/2), each attached along the circumferential direction of the cylindrical substrate. Applying 100% axial tension to the substrate gives rise to a set of curved ribbon structures with distinct profiles (Fig. 3B, middle). Here, the curvature effect also comes into play through spatial rotations of bonding pads that conform to the curved surface. The resulting ribbon structure evolves gradually from an arch shape to an elliptical shape, with the ribbon length increasing from πR0/6 to 3πR0/2. For a thin cylindrical elastomer substrate under axial stretching, the two normal strain components along the axial and circumferential directions satisfy a simple relation, according to the results of mechanics modeling (fig. S18). Understanding of these deformation characteristics could facilitate the selection of the applied strain (or prestretch) in the aforementioned strategies.
Fig. 3. Assembly of complex 3D structures on cylindrical or cylinder-like surfaces.
(A) Schematic of the aorta model used as the curved substrate, and the assembly process of helical and double-helical structures on this substrate by compressive buckling. The optical image on the rightmost corresponds to 3D structures in a bilayer of Al (2.5 μm)/PET (30 μm). (B) Assembly process of straight ribbons with different length on a cylindrical substrate by tensile buckling. θ0 denotes the central angle corresponding to a straight ribbon wrapping on the substrate along the circumferential direction. The rightmost chart presents the dimensionless maximum out-of-plane heights (Umax/R0) of different straight ribbons versus the uniaxial strain applied to the cylindrical substrate. (C) 2D geometries, FEA predictions, and experimental images of various 3D structures [(i) Cu (100 nm)/PI (8 μm); (ii to iv and vi) Al (2.5 μm)/PET (30 μm); (v) Cu (100 nm)/SU-8 (8 μm)] assembled on cylindrical substrates. Scale bars, 2 mm in (i), 10 mm in (ii) to (iv) and (vi), and 1 mm in (v). (D) 2D precursor, FEA predictions, and experimental images of kirigami-inspired scale-like 3D structures formed by tensile buckling. (E) FEA predictions and experimental images illustrate the ordered assembly process of an array of kirigami-inspired scale structures on an Archimedean spiral fiber. (F to H) Inverse design of helical structures with the same heights (h) and pitches (p) assembled at different spatial regions on the spiral fiber. Scale bars, 10 mm in (A), (D), (E), and (G). Photo credit: Z.X. and T.J., Tsinghua University.
Figure 3C and movie S3 present a set of 3D structures assembled on the cylindrical substrate. The first four examples in Fig. 3C correspond to designs based on the strategy of tensile buckling, while the last two are assembled through compressive buckling. Here, the curvature effect plays a notable role, especially when the 2D precursor structure covers a complete circle, as illustrated by the first four designs of Fig. 3C, where there are three, five, nine, and nine periodical unit cells (from left to right) along the circumferential direction. The resulting structures are in a closed form along the circumferential direction, representing a topological distinction from those assembled on planar substrates. In particular, the fourth structure exhibits a hierarchical cylindrical configuration, with nine small semicircle structures (radius, ~3 mm) that form a large circle (radius, ~15 mm). It is noteworthy that FEA serve as a reliable tool in the structural designs of these examples, as evidenced by excellent agreements of predicted 3D configurations with experimental results. Figure 3D and fig. S19 highlight an array of scale-like structures with customized 3D shapes, which is formed by tensile buckling (50%). Inspired by the kirigami design (73, 74), the representative unit cell in the initial 2D state consists of two arc triangles with strategic cuts, such that the spatial movements of the bonding sites result in a rotational pop-up of triangular structures. The entire 2D precursor design is composed of a rectangular region with 6 × 25 array that fully covers the tube, and a triangular region with 6 U cells along the axial direction that exhibits a gradient to mimic the head region of a pangolin.
The above strategy also allows assembly of 3D structures on cylinder-like surfaces, such as the Y-branch tube (figs. S20 and S21) and the hyperboloid surface (fig. S22), where the strain gradient can be programmed to form nonuniformly distributed 3D structures. In combination with the ordered assembly strategy developed in this work, 3D structures can be formed on more complex cylinder-like surfaces, such as helical or spiral fibers. Figure 3E presents an Archimedean spiral fiber (12 mm in diameter) that can be predeformed into a straight fiber through bending deformations and then prestretched (40%) to store elastic energy for triggering the compressive buckling of the precursor structure. Release of the prestretch enables the first-order assembly of the kirigami-inspired scale structure on a straight substrate, and further release of the bending allows the second-order assembly of the scale structure on the spiral substrate. These hierarchical 3D structures that resemble the scale of the snake are also inaccessible previously. An accurate shape control of assembled 3D structure on this spiral fiber is also very challenging, because of the spatially nonuniform strain distribution in the substrate. Figure 3F provides an example of the inverse design targeted on realizing two helical structures with same heights and pitches but at two different locations (inner and outer sides) of the substrate. For a given 2D precursor design on the inner side, the geometry of the 2D precursor design and the length of the bonding pad on the outer side can be optimized with aid of FEA, noting that the end-to-end distance of the serpentine precursor is kept the same at the two locations. The results in Fig. 3 (G and H) show that the two helical structures assembled on the inner and outer sides of the spiral substrate indeed have almost the same heights and pitches.

Demonstrations of 3D electronic devices on curved surfaces

The ordered assembly strategy developed in this work exhibits an excellent compatibility with the well-developed planar fabrication techniques available in semiconductor industries, thereby conferring a versatile applicability to the assembly of 3D structures in a diversity of materials, across a broad range of length scales. Figure 4A and fig. S23 provide a range of complex 3D structures assembled on cylindrical, hemispherical, and helical substrates, where five different materials [including silicon (Si), indium tin oxide (ITO), copper, laser-induced graphene (LIG), and aluminum, all based on a polymer] were used. The width and thickness of the ribbon in these structures span a wide range of length scales, from 20 μm to 3 mm (width), and from 5 to 32.5 μm (thickness), respectively. In particular, the smallest structure (Fig. 4A, leftmost panel) is made of Si and PI and was assembled on a very slim cylindrical substrate (2 mm in diameter). The dynamic process of the ordered assembly for the ribbon network fully covering a hemispherical substrate (Fig. 4A, middle panel) is illustrated in movie S4.
Fig. 4. Applicability of the assembly strategy to diverse high-performance materials and electronic devices.
(A) Optical images of various curved substrates and assembled 3D structures with a diversity of materials and length scales [(i) Si (50 nm)/PI (3 μm); (ii) indium tin oxide (ITO; 50 nm)/SU-8 (5 μm); (iii) Cu (100 nm)/PI (8 μm); (iv) laser-induced graphene (LIG) (10 μm) and PI (25 μm); (v) Al (2.5 μm)/PET (30 μm)]. Scale bars, 100 μm, 200 μm, 5 mm, 5 mm, and 10 mm (from left to right). (B to D) A highly tunable frequency-reconfigurable dipole antenna. (B) Illustration of a highly tunable dipole antenna assembled on the concave surface of a hemispherical substrate, along with FEA and experimental images of the dipole antenna [Cu (6 μm)/PI (25 μm)]. (C) Results of electromagnetic simulations and experimental measurements for the return loss (S11) as a function of the frequency for the dipole antenna under different levels of applied strains. (D) Results of electromagnetic simulations for continuous tunability resonant frequency shift as a function of applied strains. Scale bars, 5 mm. Photo credit: Z.X., T.J., and S.X., Tsinghua University.
Moreover, the proposed strategy allows assembly of planar microelectronic devices into desired 3D configurations on curved 3D substrates. Figure 4B illustrates the design and formation of a highly tunable dipole antenna [Cu (6 μm)/PI (25 μm)] on the concave surface of a hemispherical substrate (2 mm in thickness), where a biaxial prestretch (200%) is used. The optical image of the fabricated antenna is in good agreement with the deformed configuration obtained from FEA (Fig. 4B, bottom). The as-assembled antenna is highly deformable and can be transformed into an arch-shaped antenna (and even planar ribbon antenna) on a flat substrate by biaxially stretching the substrate by 50% (and 200%). Such a marked shape change enables a highly tunable resonant frequency of the dipole antenna through simple mechanical deformations. Electromagnetic simulations and measurements yield spectrum responses of the reflection coefficient (S11) for the as-assembled antenna at three different levels (0, 50, and 200%) of biaxial stretching, over a frequency range of 0 to 6 GHz (Fig. 4C). The S11 curve clearly shifts leftward by increasing the biaxial stretching. In particular, the resonant frequency that corresponds to the minimum S11 decreases from 4.35 to 2.31 GHz according to the measurement (from 4.28 to 2.28 GHz, according to simulations), representing around twofold reduction. This indicates that the resonant frequency can be adjusted continuously in the range of 2.31 and 4.35 GHz, by applying an appropriate level of biaxial stretching (Fig. 4D). This level of continuous tunability highly exceeds those (up to ~1.6 times) reported previously for flexible antennas (75). During the process of mechanical stretching, the radiation patterns of the dipole antenna change slightly, according to the results of gain surfaces/maps (fig. S24).
Because the assembly strategy allows construction of 3D structures on a variety of complex curved substrates, it suggests a broad spectrum of biomedical application opportunities that require intimate conformal integration of electronic devices with curved surfaces of human organs. Note that 2D stretchable electronics, when integrated with ultrathin substrates, can also be conformally attached to 3D surfaces. However, to conform to nondevelopable curved surfaces (e.g., hemisphere and apex of the heart), large stretching deformations could be induced in 2D stretchable electronics, which also result in constrained deformations in the target objects (e.g., fingertip and heart). In comparison, the curved substrate in this study can be customized precisely to better conform to the target 3D surface in the as-assembled configuration, without inducing additional mechanical deformations. Figure 5A and fig. S25 present a schematic illustration of a 3D piezoresistive flow sensor assembled on the inner surface of a tube (10 mm in diameter), which can be potentially implanted in veins/arteries for long-term monitoring. Here, the tube is cropped, bent, and biaxially prestretched (15%), before the integration with the 2D precursor structure. The flow sensor consists of a copper layer (300 nm) that serves both as sensing components and as interconnects, two PI layers (1 and 30 μm) that encase the copper layer as a physical protection, and a thicker layer (tape, ~200 μm) that bears the flow pressure and transfers the forces to the strain sensors. Figure 5 (B and C) provides an optical image of the fabricated 3D flow sensor sitting on the inner surface of an elastomer tube (10 mm in diameter and 1 mm in thickness), and the cross-sectional view of the flow sensor based on FEA calculations. At increased levels of flow velocity, the strain induced in the copper layer increases, and the resulting change of the resistance is measured to determine the magnitude of flow velocity. Figure 5D and fig. S25B highlight the relationship between the relative resistance change of the 3D flow sensor and the flow velocity, where an excellent linear dependence can be observed for flow velocities under 0.11 m/s. As a comparison, the 2D precursor of the flow sensor adhered to the inner surface of the tube can hardly sense the variation of the flow velocity, because of the flat configuration that is parallel with the flow direction. It is also noteworthy that the 3D flow sensors are flexible and relatively small (height ~2 mm) and, therefore, do not have a considerable influence on the flow velocity (fig. S25C). Further studies could follow by optimizing the strain sensor design to improve the performance (e.g., sensitivity and velocity range) of the 3D flow sensor.
Fig. 5. Demonstration of 3D electronic devices that can be conformally attached onto curved surfaces of human organs.
(A to D) 3D piezoresistive flow sensor. (A) Illustration of the assembly process of a 3D piezoresistive flow sensor on the inner surface of a cylindrical tube. (B) Optical image of the fabricated device [PI (1 μm)/Cu (250 nm)/PI (25 μm)]. (C) Schematic illustration of the measurement of flow velocity. (D) Measured relative resistance changes at different flow velocities based on the 3D piezoresistive flow sensor and its 2D counterpart. (E to G) 3D integrated electronic system. (E) Schematic and optical image of a 2D integrated electronic system consisting of two commercial green LEDs, eight temperature sensors, and a humidity sensor. (F) Optical image of the assembled 3D integrated electronic system conformally wrapped onto the apex of a heart model. (G) Temperature mapping and the magnitude of relative humidity measured by the 3D device system at two different ambient conditions. Scale bars, 5 mm in (B) and 10 mm in (E) and (F). Photo credit: Z.X., T.J., and S.X., Tsinghua University.
Figure 5 (E to G) demonstrates another integrated electronic device [with commercial light-emitting diodes (LEDs) and temperature/humidity sensors] on a curved substrate that resembles the apex of the heart. The 2D precursor comprises a functional layer (with two green LEDs, eight temperature sensors, and a humidity sensor), an interconnection layer (Cu, 6 μm in thickness), and a supporting layer (PI, 25 μm in thickness), as shown in Fig. 5E. Figure 5F and fig. S26 depict the ordered assembly process of the entire device. In the final state of assembly, the ribbon network shows a two-floor configuration, where the two LEDs are located at the peaks of second-floor arc ribbons, and the eight temperature sensors are at the top regions of first-floor arc ribbons. The humidity sensor is placed at the top region of a cage-like structure. Note that the 3D configuration of the entire device predicted by FEA agrees remarkably well with the experimental image, even for such a complex system. The sensor array with sophisticated 3D spatial arrangement can potentially measure accurate spatial distributions of temperature and humidity away from the substrate surface, which is not possible using conformal devices. Figure 5G and fig. S27B show temperature distributions and relative humidity measured by the 3D device at two different states, suggesting the capability of monitoring temperature/humidity variations at different spatial locations around the heart. Note that the LEDs in the integrated device system can be used in the light-based diagnosis, for example, to locally activate a photosensitizing agent to produce reactive oxygen species for cell killing (7679). In addition, the device offers a high level of stretchability and an excellent mechanical reliability. During the cyclic biaxial stretching (with an amplitude of 60% and a frequency of 0.042 Hz) for 150 times, the temperature outputs of the device remain very stable (fig. S27, C and D).

DISCUSSION

In summary, the ordered assembly strategy and design methods reported here provide immediate access to complex 3D structures on a variety of curved surfaces, ranging from regular surfaces (such as hemisphere, cylinder, helicoid, spiral, and hyperboloid) to biomimetic surfaces (such as twining vines, human face, brain-like surface, aorta, and heart-like surface). Quantitative mechanics modeling allows precise prediction of the ordered assembly process, establishing a powerful tool for the rational design of various assembly-related parameters (e.g., 2D precursor layout, distribution of bonding sites, magnitude and form of predefined mechanical loadings, and dimensions of 2D precursor materials). Combination of the surface topology of curved substrate and the pop-up geometry of 3D structures allows formation of unique 3D configurations, including hierarchical 3D topologies (e.g., hierarchical hemispheres, cylinders, and helices) and 3D structures inside spherical/cylindrical shells, which are qualitatively distinct from those reported previously. Demonstrations in this work include the frequency-reconfigurable dipole antenna on a hemisphere, highly stretchable 3D integrated electronic system capable of conformal integration with the apex of the heart, and piezoresistive 3D flow sensor on the inner surface of a tube. Further studies could follow by developing multimodal 3D friction/pressure/strain sensors on heart/liver-like surfaces for health monitoring, tunable 3D optoelectronic devices on hemispheres or hierarchical hemispheres, and tissue scaffolds that match curved surfaces of target organs.

MATERIALS AND METHODS

Finite element analysis

Three-dimensional FEA based on the commercial software Abaqus were performed to calculate the deformations of curved substrates and 2D precursor structures during the two-stage assembly. Four-node 2D shell elements (S4R) with bilayer/trilayer laminates and eight-node 3D solid elements (C3D8R) were adopted to model the 2D precursor structure and the silicone substrate. Refined mesh sizes ensured the computational accuracy. Results of the linear buckling simulation determined the initial imperfections implemented in the postbuckling analyses. The hard frictionless contact model allowed simulation of the mechanical interaction between 2D precursors and the substrate. Displacement components were prescribed to the boundaries of the substrate, consistent with that in experiments. The silicone substrate was modeled by an isotropic hyperelastic model based on the Mooney-Rivlin law, where the effective elastic modulus and Poisson’s ratio were given by EEcoflex-20 = 16 kPa and νEcoflex-20 = 0.49 for Ecoflex-20 substrate (Smooth-on, USA); EPDMS = 810 kPa and νPDMS = 0.49 for polydimethylsiloxane (PDMS) substrate (10:1, Sylgard 184, DOW, USA); and Erubber-like = 160 kPa and νrubber-like = 0.49 for 3D printed rubber-like substrate (Agilus30, Stratasys, USA). The 2D precursor materials were modeled by an isotropic linear elastic model, and their elastic modulus (E) and Poisson’s ratio (ν) are ECu = 119 GPa and νCu = 0.34 for copper (Cu); EPI = 2.5 GPa and νPI = 0.34 for PI; ESU-8 = 4.02 GPa and νSU-8 = 0.22 for SU-8; EAl = 70 GPa and νAl = 0.42 for aluminum (Al); EAg = 83 GPa and νAg = 0.37 for silver (Ag); and EPET = 2.8 GPa and νPET = 0.37 for PET.

Fabrication of curved elastomer substrates

Fabrication of curved elastomer substrates (with the human-face, heart-like, hemispherical, brain-like, and hierarchical hemispherical shapes) began with manufacturing the casting mold of the target curved surface through machining or 3D printing, as shown in fig. S1. Spraying a light and even coating of release agent (Ease Release 200, Smooth-On, USA) on the surface of molds, followed by pouring silica gel (Ecoflex 00-20A/B, Smooth-on, USA; or PDMS, Sylgard 184, DOW, USA) mixed by (1A:1B or 10:1) into the molds and curing for over 4 hours in a vacuum oven for degassing at room temperature, yielded solid elastomers with prescribed 3D shapes. Demolding the elastomer substrates from the molds generated curved substrates in a freestanding form. For complex curved substrates (with the aorta-like, helical, horseshoe shape, fractal horseshoe shape, helicoid, Möbius band, and spiral fiber shapes) that are difficult to manufacture through molding, the curved elastomer substrates were fabricated by PolyJet 3D printing technique (J750 Digital Anatomy, Stratasys, USA) with rubber-like material (Agilus30, Stratasys, USA).

Fabrication of 3D microscale structures in photodefinable epoxy (SU-8) with metal or oxide nanomembrane

Fabrication of 3D microscale structures in SU-8 began with spin coating an ultrathin sacrificial layer of Omnicoat (~17 nm in thickness; MicroChem, USA) on a silicon wafer, followed by spin coating a layer of SU-8 (~8 μm in the thickness; SU-8 2000 series, MicroChem, USA), and patterning SU-8 layer into desired 2D geometries by lithography. Electron beam evaporation (or sputtering) allowed deposition of metal (or ITO) nanomembranes on the SU-8 layer, which was then patterned by photolithography and wet etching. Layers of Ti (10 nm)/SiO2 (100 nm) deposited by electron beam evaporation, followed by photolithography patterning and wet etching, defined the bonding sites of SiO2 on the top layer. Etching the exposed Omnicoat by oxygen plasma and partially undercutting, followed by immersion in N-methyl pyrrolidone (NMP), removed the Omnicoat completely and released the 2D precursor structure from the silicon wafer. Retrieving the 2D precursor structure by a PDMS stamp and transferring it onto a water-soluble tape [polyvinyl alcohol (PVA); Aquasol Co., USA] allowed integration of the 2D precursor structure with the target elastomer substrate (flattened or cylindrical substrate). Alignment marks designed around the 2D precursor facilitated the alignment with the stretched elastomer substrate (fig. S28) under a microscope. Exposing the elastomer substrate and the 2D precursor structure (on the PVA tape) to ultraviolet-induced ozone yielded hydroxyl termination. Laminating the tape onto the target elastomer substrate with the bonding sites side down, followed by baking in an oven at 70°C for 10 min, yielded strong chemical covalent bonds between the elastomer substrate and the bonding sites of 2D precursor structure. Washing by hot water removed the PVA tape. For 3D assembly on the cylinder-like substrates, slowly stretching the substrate (based on the tensile buckling strategy) or slowly releasing the predefined loading completed the assembly process. For 3D assembly on other substrates, slowly releasing the predefined loading completed the assembly process. A schematic illustration of the fabrication process appears in fig. S29.

Fabrication of 3D microscale structures in PI with metal or semiconductor nanomembrane by photolithography

Fabrication of 3D microscale structures in PI began with spin coating a thin sacrificial layer of poly(methyl methacrylate) (∼200 nm in thickness; 950 PMMA A4, MicroChem, USA), followed by spin coating a layer of PI (∼3 to 8 μm in thickness; paa1002, Furunte) on a silicon wafer. Electron beam evaporation allowed deposition of a thin layer of copper (∼100 nm in thickness) or Si (50 nm)/Ni (50 nm). Photolithography and wet etching defined desired patterns for the metal (Cu or Ni) layer, and inductively coupled plasma (ICP) etching defined patterns for the PI layer or bilayer of Si/PI. For 2D precursor structures in PI/Si/Ni, the Ni layer was removed by wet etching. Immersion in acetone to dissolve the underlying PMMA layer yielded released 2D precursor structures that were then retrieved by a PDMS stamp and transferred to a water-soluble tape (PVA; Aquasol Co., USA). The remaining process of the 3D assembly followed similar procedures of 3D microscale structures in SU-8 described above. A schematic illustration of the fabrication process appears in fig. S30.

Fabrication of 3D structures at submillimeter scale

Fabrication of 3D structures in PET with metal thin film began with laminating a commercial thin film [Al (2.5 μm)/PET (30 μm) or Ag (5 μm)/PET (75 μm)] onto a thermal release tape, followed by automatic laser cutting (Universal VLS2.30, USA) or mechanical cutting (Silhouette CAMEO, USA) into desired 2D precursors. Baking the thermal release tape on a hotplate at 90°C for 2 min allowed integration of the retrieved 2D precursor structures onto a PVA tap. Dispensing a commercial adhesive (Super Glue, Gorilla Glue Company, USA) at the predefined bonding sites of 2D precursors, followed by aligning and laminating 2D precursor structures (with adhesive side down) onto the surface of target elastomer substrate and curing for ~2 min at room temperature, formed strong adhesion at the bonding sites. The PVA tape was then dissolved and washed by hot water. The process of 3D assembly followed similar procedures of 3D structures in SU-8 as described above. Fabrication of 3D structures in PI with LIG began with laminating a commercial PI thin film (30 μm) onto a thermal release tape, followed by ablating the PI thin film with a CO2 laser cutting machine (Universal VLS2.30, USA) in the scanning mode, generated cellular graphene on the top surface of the PI thin films. The remaining process of 3D assembly followed similar procedures described above.

Fabrication and measurements of integrated electronic devices

Preparation of 2D precursors began with a commercial flexible printed circuit board (FPCB) [a bilayer of copper (6 μm)/PI (25 μm)], laminated on a glass slide coated with PDMS (10:1; Sylgard 184) with PI side down. Laser cutting (Universal VLS2.30, USA) allowed patterning of the FPCB layer into the desired layouts. Photolithography and wet etching patterned the copper layer into designed geometries of interconnects and electrodes. The two commercial green LEDs, eight temperature sensors, and a humidity sensor were then welded with the predesigned electrodes. Transferring the 2D integrated electronic device onto the surface of biaxially prestretched substrate, followed by dispensing a commercial adhesive (Super Glue, Gorilla Glue Company, USA) at predefined bonding sites and curing for ~2 min at room temperature, formed strong adhesion at the bonding sites. Slowly releasing the biaxial prestretch completed the assembly of 3D integrated electronic devices.

Fabrication and measurement of a 3D flow velocity sensor

Preparation of 2D precursor of flow velocity sensor began with spin coating a thin sacrificial layer of PMMA (~200 nm), followed by spin coating a layer of PI (∼20 μm) on a silicon wafer and curing. Depositing a thin layer of copper (~300 nm in thickness) by electron beam evaporation, followed by the photolithography and wet etching, yielded a copper layer with desired patterns. Spin coating an ultrathin layer of PI (~1 μm in thickness) served as an encapsulation layer. Deposition of a layer of titanium (~50 nm) by electron beam evaporation, followed by photolithography with alignment and wet etching by hydrofluoric acid (HF; 5%) solution, realized the pattern of the titanium layer as hard mask. ICP etching the bilayer of PI (upper and bottom) and removing the hard mask by immersion in HF solution realized the entire shape of 2D precursor. ICP etching the upper PI layer through the shadow mask (PET, 50 μm in thickness) defined the exposed two electrodes for electrical measurement, and then the exposed two electrodes were welded with conducting wires, which allowed connection to an electrical instrument for testing. After removing the PMMA by immersion in acetone, the 2D precursor structures were retrieved by a PVA tape. Assembly of 3D flow velocity sensor began with cropping an elastomer tube (10 mm in diameter and 1 mm in thickness; PDMS) along a generatrix that served as the assembly platform. The cropped elastomer tube was then flattened and biaxially prestretched by 15%. The remaining process of 3D assembly followed similar procedures for 3D structures at submillimeter scale described above. Gluing the tube along the incision completed the fabrication of the 3D flow velocity sensor on the inner surface of the tube. The fabricated 3D flow velocity sensor was tested in a water pipe, where the water flow was generated by a peristaltic pump with an adjustable flow velocity. The elastomer tube integrated with the 3D flow velocity sensor was connected to the water pipe, followed by connecting the device to the electrical test instrument (34465A, Keysight). The resistance values of the device were collected under different levels of flow velocities.

Fabrication, electromagnetic simulations, and measurements of a 3D tunable dipole antenna

Fabrication of a 3D tunable dipole antenna began with laminating a commercial FPCB [a bilayer of copper (6 μm)/PI (25 μm)] on a thermal release tape with PI side down, followed by programmable laser cutting (Universal VLS2.30) of the FPCB into the desired pattern. Baking the thermal release tape on a hotplate at 90°C for 2 min allowed integration of the retrieved 2D precursors onto a PVA tape. A hemispherical elastomer substrate served as the assembly platform. Dispensing a commercial adhesive (Super Glue, Gorilla Glue Company, USA) at the predefined bonding sites of 2D precursor structures, followed by aligning and laminating 2D precursors (with adhesive side down) onto the surface of biaxially prestretched (200%) elastomer substrate and curing for ~2 min at room temperature, formed strong adhesion at the bonding sites. Slowly releasing the biaxial prestretch completed the 3D assembly process. For the tunable dipole antennas, a slidable connector and an SMA adapter whose connecting surface stayed at the bottom surface of the substrate were then welded with the predesigned electrode. Electromagnetic simulations were conducted by the commercial software ANSYS HFSS to obtain the coefficient (S11) and radiation pattern of the tunable antenna. Refined mesh sizes were exploited to ensure computational accuracy. The 3D configuration of the antenna model obtained from the mechanics simulations was imported into the electromagnetic simulation. All the metal conducting layers and polymeric supporting layers used layer impedance boundary with prescribed thicknesses. The relative permittivity (εr), relative permeability (μr), and conductivity (σ) are εr_Cu = 1, μr_Cu = 0.999991, and σCu = 5.8 × 107 S/m; εr_PI = 3.5, μr_PI = 1, and σPI = 0 S/m; and εr_Substrate = 2.55, μr_Substrate = 1, and σSubstrate = 2.5 × 10−14 S/m. The antenna was measured using a network analyzer (E5071B, Agilent). The resonant frequencies of the antenna in different deformed states were read directly from the instrument after connecting the antenna to the instrument with a coaxial cable.

Acknowledgments

We would like to thank X. Feng from Tsinghua University for offering access to microfabrication facilities in the laboratory.
Funding: Y.Z. acknowledges support from the National Natural Science Foundation of China (grant nos. 12050004 and 11921002), the Tsinghua National Laboratory for Information Science and Technology, the Henry Fok Education Foundation, and a grant from the Institute for Guo Qiang, Tsinghua University (grant no. 2019GQG1012). Z.X. acknowledges support from the National Natural Science Foundation of China (grant no. 61904095) and National Postdoctoral Program for Innovative Talents (grant no. BX20180157). H.S. acknowledges support from the National Natural Science Foundation of China (grant no. 11902178).
Author contributions: Y.Z. designed and supervised the research; Z.X. led the fabrication work, with assistance from T.J., S.X., F.Z., X.C., and W.P.; T.J., Z.X., and Y.Z. led the structural designs and mechanics modeling, with assistance from S.X., Q.H., Z.J., and Z.S.; Z.X., T.J., S.X., and Y.Z. led the device design and characterization, with assistance from K.B., Z.J., H.S., and Y.S.; and Y.Z. and Z.X. wrote the manuscript and designed the figures. All authors commented on the paper.
Competing interests: The authors declare that they have no competing interests.
Data and materials availability: All data needed to evaluate the conclusions in the paper are present in the paper and/or the Supplementary Materials.

Supplementary Materials

This PDF file includes:

Figs. S1 to S30

Other Supplementary Material for this manuscript includes the following:

Movies S1 to S4

REFERENCES AND NOTES

1
Y. Park, T. S. Chung, G. Lee, J. A. Rogers, Materials chemistry of neural interface technologies and recent advances in three-dimensional systems. Chem. Rev. 122, 5277–5316 (2021).
2
D.-H. Kim, N. Lu, R. Ma, Y.-S. Kim, R.-H. Kim, S. Wang, J. Wu, S. M. Won, H. Tao, A. Islam, K. J. Yu, T.-i. Kim, R. Chowdhury, M. Ying, L. Xu, M. Li, H.-J. Chung, H. Keum, M. McCormick, P. Liu, Y.-W. Zhang, F. G. Omenetto, Y. Huang, T. Coleman, J. A. Rogers, Epidermal electronics. Science 333, 838–843 (2011).
3
S. H. Byun, J. Y. Sim, K. C. Agno, J. W. Jeong, Materials and manufacturing strategies for mechanically transformative electronics. Mater. Today Adv. 7, 100089 (2020).
4
Y. Yu, H. Y. Y. Nyein, W. Gao, A. Javey, Flexible electronics: Flexible electrochemical bioelectronics: The rise of in situ bioanalysis (Adv. Mater. 15/2020). Adv. Mater. 32, 2070115 (2020).
5
Y. Lee, V. K. Bandari, Z. Li, M. Medina-Sánchez, M. F. Maitz, D. Karnaushenko, M. V. Tsurkan, D. D. Karnaushenko, O. G. Schmidt, Nano-biosupercapacitors enable autarkic sensor operation in blood. Nat. Commun. 12, 4967 (2021).
6
S.-H. Byun, C. S. Kim, K.-C. Agno, S. Lee, Z. Li, B. J. Cho, J.-W. Jeong, Design strategy for transformative electronic system toward rapid, bidirectional stiffness tuning using graphene and flexible thermoelectric device interfaces. Adv. Mater. 33, 2007239 (2021).
7
Y. Yu, J. Nassar, C. Xu, J. Min, Y. Yang, A. Dai, R. Doshi, A. Huang, Y. Song, R. Gehlhar, A. D. Ames, W. Gao, Biofuel-powered soft electronic skin with multiplexed and wireless sensing for human-machine interfaces. Sci. Robot. 5, eaaz7946 (2020).
8
W. Zhou, S. Yao, H. Wang, Q. Du, Y. Ma, Y. Zhu, Gas-permeable, ultrathin, stretchable epidermal electronics with porous electrodes. ACS Nano 14, 5798–5805 (2020).
9
H. O. Jacobs, A. R. Tao, A. Schwartz, D. H. Gracias, G. M. Whitesides, Fabrication of a cylindrical display by patterned assembly. Science 296, 323–325 (2002).
10
M. K. Choi, J. Yang, T. Hyeon, D. H. Kim, Flexible quantum dot light-emitting diodes for next-generation displays. npj Flex. Electron. 2, 10 (2018).
11
S.-H. Byun, J. Y. Sim, Z. Zhou, J. Lee, R. Qazi, M. C. Walicki, K. E. Parker, M. P. Haney, S. H. Choi, A. Shon, G. B. Gereau, J. Bilbily, S. Li, Y. Liu, W.-H. Yeo, J. G. McCall, J. Xiao, J.-W. Jeong, Mechanically transformative electronics, sensors, and implantable devices. Sci. Adv. 5, eaay0418 (2019).
12
K. Sim, F. Ershad, Y. C. Zhang, P. Y. Yang, H. Shim, Z. Y. Rao, Y. T. Lu, A. Thukral, A. Elgalad, Y. T. Xi, B. Z. Tian, D. A. Taylor, C. J. Yu, An epicardial bioelectronic patch made from soft rubbery materials and capable of spatiotemporal mapping of electrophysiological activity. Nat. Electron. 3, 775–784 (2020).
13
D. H. Kim, N. S. Lu, R. Ghaffari, Y. S. Kim, S. P. Lee, L. Z. Xu, J. A. Wu, R. H. Kim, J. Z. Song, Z. J. Liu, J. Viventi, B. de Graff, B. Elolampi, M. Mansour, M. J. Slepian, S. Hwang, J. D. Moss, S. M. Won, Y. G. Huang, B. Litt, J. A. Rogers, Materials for multifunctional balloon catheters with capabilities in cardiac electrophysiological mapping and ablation therapy. Nat. Mater. 10, 316–323 (2011).
14
D.-H. Kim, R. Ghaffari, N. Lu, S. Wang, S. P. Lee, H. Keum, R. D’Angelo, L. Klinker, Y. Su, C. Lu, Y.-S. Kim, A. Ameen, Y. Li, Y. Zhang, B. de Graff, Y.-Y. Hsu, Z. Liu, J. Ruskin, L. Xu, C. Lu, F. G. Omenetto, Y. Huang, M. Mansour, M. J. Slepian, J. A. Rogers, Electronic sensor and actuator webs for large-area complex geometry cardiac mapping and therapy. Proc. Natl. Acad. Sci. U.S.A. 109, 19910–19915 (2012).
15
L. Z. Xu, S. R. Gutbrod, A. P. Bonifas, Y. W. Su, M. S. Sulkin, N. S. Lu, H. J. Chung, K. I. Jang, Z. J. Liu, M. Ying, C. Lu, R. C. Webb, J. S. Kim, J. I. Laughner, H. Y. Cheng, Y. H. Liu, A. Ameen, J. W. Jeong, G. T. Kim, Y. G. Huang, I. R. Efimov, J. A. Rogers, 3D multifunctional integumentary membranes for spatiotemporal cardiac measurements and stimulation across the entire epicardium. Nat. Commun. 5, 3329 (2014).
16
A. Ghosh, L. Li, L. Xu, R. P. Dash, N. Gupta, J. Lam, Q. Jin, V. Akshintala, G. Pahapale, W. Liu, A. Sarkar, R. Rais, D. H. Gracias, F. M. Selaru, Gastrointestinal-resident, shape-changing microdevices extend drug release in vivo. Sci. Adv. 6, eabb4133 (2020).
17
C. Choi, M. K. Choi, S. Y. Liu, M. S. Kim, O. K. Park, C. Im, J. Kim, X. L. Qin, G. J. Lee, K. W. Cho, M. Kim, E. Joh, J. Lee, D. Son, S. H. Kwon, N. L. Jeon, Y. M. Song, N. S. Lu, D. H. Kim, Human eye-inspired soft optoelectronic device using high-density MoS2-graphene curved image sensor array. Nat. Commun. 8, 1–11 (2017).
18
Y. M. Song, Y. Xie, V. Malyarchuk, J. Xiao, I. Jung, K. J. Choi, Z. Liu, H. Park, C. Lu, R. H. Kim, R. Li, K. B. Crozier, Y. Huang, J. A. Rogers, Digital cameras with designs inspired by the arthropod eye. Nature 497, 95–99 (2013).
19
H. C. Ko, M. P. Stoykovich, J. Song, V. Malyarchuk, W. M. Choi, C. J. Yu, J. B. Geddes III, J. Xiao, S. Wang, Y. Huang, J. A. Rogers, A hemispherical electronic eye camera based on compressible silicon optoelectronics. Nature 454, 748–753 (2008).
20
S. Wu, Q. J. Ze, J. Z. Dai, N. Udipi, G. H. Paulino, R. K. Zhao, Stretchable origami robotic arm with omnidirectional bending and twisting. Proc. Natl. Acad. Sci. U.S.A. 118, e2110023118 (2021).
21
J. Kim, M. Lee, H. J. Shim, R. Ghaffari, H. R. Cho, D. Son, Y. H. Jung, M. Soh, C. Choi, S. Jung, K. Chu, D. Jeon, S. T. Lee, J. H. Kim, S. H. Choi, T. Hyeon, D. H. Kim, Stretchable silicon nanoribbon electronics for skin prosthesis. Nat. Commun. 5, 5747 (2014).
22
M. S. Kim, G. J. Lee, C. Choi, M. S. Kim, M. Lee, S. Y. Liu, K. W. Cho, H. M. Kim, H. Cho, M. K. Choi, N. S. Lu, Y. M. Song, D. H. Kim, An aquatic-vision-inspired camera based on a monocentric lens and a silicon nanorod photodiode array. Nat. Electron. 3, 546–553 (2020).
23
H. Yang, M. Ji, M. Yang, M. Shi, Y. Pan, Y. Zhou, H. J. Qi, Z. Suo, J. Tang, Fabricating hydrogels to mimic biological tissues of complex shapes and high fatigue resistance. Matter 4, 1935–1946 (2021).
24
Y. Park, C. K. Franz, H. Ryu, H. W. Luan, K. Y. Cotton, J. U. Kim, T. S. Chung, S. W. Zhao, A. Vazquez-Guardado, D. S. Yang, K. Li, R. Avila, J. K. Phillips, M. J. Quezada, H. Jang, S. S. Kwak, S. M. Won, K. Kwon, H. Jeong, A. J. Bandodkar, M. D. Han, H. B. Zhao, G. R. Osher, H. L. Wang, K. Lee, Y. H. Zhang, Y. G. Huang, J. D. Finan, J. A. Rogers, Three-dimensional, multifunctional neural interfaces for cortical spheroids and engineered assembloids. Sci. Adv. 7, eabf9153 (2021).
25
Y. X. Liu, J. X. Li, S. Song, J. Kang, Y. Tsao, S. C. Chen, V. Mottini, K. McConnell, W. H. Xu, Y. Q. Zheng, J. B. H. Tok, P. M. George, Z. N. Bao, Morphing electronics enable neuromodulation in growing tissue. Nat. Biotechnol. 38, 1031–1036 (2020).
26
A. I. Egunov, Z. H. Dou, D. D. Karnaushenko, F. Hebenstreit, N. Kretschmann, K. Akgun, T. Ziemssen, D. Karnaushenko, M. Medina-Sanchez, O. G. Schmidt, Impedimetric microfluidic sensor-in-a-tube for label-free immune cell analysis. Small 17, e2002549 (2021).
27
Z. Li, Y. Liu, O. Hossain, R. Paul, S. Yao, S. Wu, J. B. Ristaino, Y. Zhu, Q. Wei, Real-time monitoring of plant stresses via chemiresistive profiling of leaf volatiles by a wearable sensor. Matter 4, 2553–2570 (2021).
28
A. Burton, S. N. Obaid, A. Vázquez-Guardado, M. B. Schmit, T. Stuart, L. Cai, Z. Chen, I. Kandela, C. R. Haney, E. A. Waters, H. Cai, J. A. Rogers, L. Lu, P. Gutruf, Wireless, battery-free subdermally implantable photometry systems for chronic recording of neural dynamics. Proc. Natl. Acad. Sci. U.S.A. 117, 2835–2845 (2020).
29
W. Xu, Z. Qin, C.-T. Chen, H. R. Kwag, Q. Ma, A. Sarkar, M. J. Buehler, D. H. Gracias, Ultrathin thermoresponsive self-folding 3D graphene. Sci. Adv. 3, e1701084 (2017).
30
K. Sim, S. Chen, Z. Li, Z. Rao, J. Liu, Y. Lu, S. Jang, F. Ershad, J. Chen, J. Xiao, C. Yu, Three-dimensional curvy electronics created using conformal additive stamp printing. Nat. Electron. 2, 471–479 (2019).
31
H. Park, H. Cho, J. Kim, J. W. Bang, S. Seo, Y. Rahmawan, D. Y. Lee, K. Y. Suh, Multiscale transfer printing into recessed microwells and on curved surfaces via hierarchical perfluoropolyether stamps. Small 10, 52–59 (2014).
32
C. Pfeiffer, X. Xu, S. R. Forrest, A. Grbic, Direct transfer patterning of electrically small antennas onto three-dimensionally contoured substrates. Adv. Mater. 24, 1166–1170 (2012).
33
C. Wang, C. Linghu, S. Nie, C. Li, Q. Lei, X. Tao, Y. Zeng, Y. Du, S. Zhang, K. Yu, H. Jin, W. Chen, J. Song, Programmable and scalable transfer printing with high reliability and efficiency for flexible inorganic electronics. Sci. Adv. 6, eabb2393 (2020).
34
J. J. Adams, E. B. Duoss, T. F. Malkowski, M. J. Motala, B. Y. Ahn, R. G. Nuzzo, J. T. Bernhard, J. A. Lewis, Conformal printing of electrically small antennas on three-dimensional surfaces. Adv. Mater. 23, 1335–1340 (2011).
35
H. S. An, Y. G. Park, K. Kim, Y. S. Nam, M. H. Song, J. U. Park, High-resolution 3D printing of freeform, transparent displays in ambient air. Adv. Sci. 6, 1901603 (2019).
36
Y. L. Kong, I. A. Tamargo, H. Kim, B. N. Johnson, M. K. Gupta, T. W. Koh, H. A. Chin, D. A. Steingart, B. P. Rand, M. C. McAlpine, 3D printed quantum dot light-emitting diodes. Nano Lett. 14, 7017–7023 (2014).
37
Z. Zhao, J. Wu, X. Mu, H. Chen, H. J. Qi, D. Fang, Origami by frontal photopolymerization. Sci. Adv. 3, e1602326 (2017).
38
B. Dai, L. Zhang, C. Zhao, H. Bachman, R. Becker, J. Mai, Z. Jiao, W. Li, L. Zheng, X. Wan, T. J. Huang, S. Zhuang, D. Zhang, Biomimetic apposition compound eye fabricated using microfluidic-assisted 3D printing. Nat. Commun. 12, 6458 (2021).
39
S. H. Park, R. T. Su, J. Jeong, S. Z. Guo, K. Y. Qiu, D. Joung, F. B. Meng, M. C. McAlpine, 3D printed polymer photodetectors. Adv. Mater. 30, e1803980 (2018).
40
T. van Manen, S. Janbaz, A. A. Zadpoor, Programming 2D/3D shape-shifting with hobbyist 3D printers. Mater. Horizons 4, 1064–1069 (2017).
41
H. Aharoni, Y. Xia, X. Zhang, R. D. Kamien, S. Yang, Universal inverse design of surfaces with thin nematic elastomer sheets. Proc. Natl. Acad. Sci. U.S.A. 115, 7206–7211 (2018).
42
K. Zhang, Y. H. Jung, S. Mikael, J. H. Seo, M. Kim, H. Y. Mi, H. Zhou, Z. Y. Xia, W. D. Zhou, S. Q. Gong, Z. Q. Ma, Origami silicon optoelectronics for hemispherical electronic eye systems. Nat. Commun. 8, 1782 (2017).
43
X. Y. Guo, H. Li, B. Y. Ahn, E. B. Duoss, K. J. Hsia, J. A. Lewis, R. G. Nuzzo, Two- and three-dimensional folding of thin film single-crystalline silicon for photovoltaic power applications. Proc. Natl. Acad. Sci. U.S.A. 106, 20149–20154 (2009).
44
K. Liu, T. Tachi, G. H. Paulino, Invariant and smooth limit of discrete geometry folded from bistable origami leading to multistable metasurfaces. Nat. Commun. 10, 4238 (2019).
45
P. O. Mouthuy, M. Coulombier, T. Pardoen, J. P. Raskin, A. M. Jonas, Overcurvature describes the buckling and folding of rings from curved origami to foldable tents. Nat. Commun. 3, 1290 (2012).
46
Z. R. Zhai, Y. Wang, K. Lin, L. L. Wu, H. Q. Jiang, In situ stiffness manipulation using elegant curved origami. Sci. Adv. 6, eabe2000 (2020).
47
Y. K. Lee, Z. H. Xi, Y. J. Lee, Y. H. Kim, Y. Hao, H. Choi, M. G. Lee, Y. C. Joo, C. Kim, J. M. Lien, I. S. Choi, Computational wrapping: A universal method to wrap 3D-curved surfaces with nonstretchable materials for conformal devices. Sci. Adv. 6, eaax6212 (2020).
48
V. Neu, I. Soldatov, R. Schäfer, D. D. Karnaushenko, A. Mirhajivarzaneh, D. Karnaushenko, O. G. Schmidt, Creating ferroic micropatterns through geometrical transformation. Nano Lett. 21, 9889–9895 (2021).
49
J. Cui, F. R. Poblete, Y. Zhu, Origami/kirigami-guided morphing of composite sheets. Adv. Funct. Mater. 28, 1802768 (2018).
50
H. D. McClintock, N. Doshi, A. Iniguez-Rabago, J. C. Weaver, N. T. Jafferis, K. Jayaram, R. J. Wood, J. T. B. Overvelde, A fabrication strategy for reconfigurable millimeter-scale metamaterials. Adv. Funct. Mater. 31, 2103428 (2021).
51
Y. Li, J. Yin, Metamorphosis of three-dimensional kirigami-inspired reconfigurable and reprogrammable architected matter. Mater. Today Phys. 21, 100511 (2021).
52
Y. Tang, Y. Li, Y. Hong, S. Yang, J. Yin, Programmable active kirigami metasheets with more freedom of actuation. Proc. Natl. Acad. Sci. U.S.A. 116, 26407–26413 (2019).
53
W. G. Lu, R. Xiao, J. Liu, L. Wang, H. Z. Zhong, Y. T. Wang, Large-area rainbow holographic diffraction gratings on a curved surface using transferred photopolymer films. Opt. Lett. 43, 675–678 (2018).
54
M. Jobs, K. Hjort, A. Rydberg, Z. G. Wu, A tunable spherical cap microfluidic electrically small antenna. Small 9, 3230–3234 (2013).
55
A. K. Katiyar, K. Y. Thai, W. S. Yun, J. Lee, J. H. Ahn, Breaking the absorption limit of Si toward SWIR wavelength range via strain engineering. Sci. Adv. 6, eabb0576 (2020).
56
Q. Zhang, X. Kuang, S. Weng, L. Yue, D. J. Roach, D. Fang, H. J. Qi, Shape-memory balloon structures by pneumatic multi-material 4D printing. Adv. Funct. Mater. 31, 2010872 (2021).
57
Y. Hong, Y. Chi, S. Wu, Y. Li, Y. Zhu, J. Yin, Boundary curvature guided programmable shape-morphing kirigami sheets. Nat. Commun. 13, 530 (2022).
58
K. Sim, S. Chen, Y. Li, M. Kammoun, Y. Peng, M. Xu, Y. Gao, J. Song, Y. Zhang, H. Ardebili, C. Yu, High fidelity tape transfer printing based on chemically induced adhesive strength modulation. Sci. Rep. 5, 16133 (2015).
59
W. Lee, Y. Liu, Y. Lee, B. K. Sharma, S. M. Shinde, S. D. Kim, K. Nan, Z. Yan, M. D. Han, Y. G. Huang, Y. H. Zhang, J. H. Ahn, J. A. Rogers, Two-dimensional materials in functional three-dimensional architectures with applications in photodetection and imaging. Nat. Commun. 9, 1417 (2018).
60
K. Sim, Z. Rao, Y. Li, D. Yang, C. Yu, Curvy surface conformal ultra-thin transfer printed Si optoelectronic penetrating microprobe arrays. npj Flex. Electron. 2, 2 (2018).
61
H. W. Liu, Y. G. Huang, H. Jiang, Artificial eye for scotopic vision with bioinspired all-optical photosensitivity enhancer. Proc. Natl. Acad. Sci. U.S.A. 113, 3982–3985 (2016).
62
D. J. Fan, B. Lee, C. Coburn, S. R. Forrest, From 2D to 3D: Strain- and elongation-free topological transformations of optoelectronic circuits. Proc. Natl. Acad. Sci. U.S.A. 116, 3968–3973 (2019).
63
C. F. Hu, W. S. Su, W. L. Fang, Development of patterned carbon nanotubes on a 3D polymer substrate for the flexible tactile sensor application. J. Micromech. Microeng. 21, 115012 (2011).
64
Z. Y. Liu, D. P. Qi, W. R. Leow, J. C. Yu, M. Xiloyannnis, L. Cappello, Y. Q. Liu, B. W. Zhu, Y. Jiang, G. Chen, L. Masia, B. Liedberg, X. D. Chen, 3D-structured stretchable strain sensors for out-of-plane force detection. Adv. Mater. 30, 1707285 (2018).
65
S. Xu, Z. Yan, K. I. Jang, W. Huang, H. R. Fu, J. Kim, Z. Wei, M. Flavin, J. McCracken, R. Wang, A. Badea, Y. Liu, D. Q. Xiao, G. Y. Zhou, J. Lee, H. U. Chung, H. Y. Cheng, W. Ren, A. Banks, X. L. Li, U. Paik, R. G. Nuzzo, Y. G. Huang, Y. H. Zhang, J. A. Rogers, Assembly of micro/nanomaterials into complex, three-dimensional architectures by compressive buckling. Science 347, 154–159 (2015).
66
Y. H. Zhang, Z. Yan, K. W. Nan, D. Q. Xiao, Y. H. Liu, H. W. Luan, H. R. Fu, X. Z. Wang, Q. L. Yang, J. C. Wang, W. Ren, H. Z. Si, F. Liu, L. H. Yang, H. J. Li, J. T. Wang, X. L. Guo, H. Y. Luo, L. Wang, Y. G. Huang, J. A. Rogers, A mechanically driven form of kirigami as a route to 3D mesostructures in micro/nanomembranes. Proc. Natl. Acad. Sci. U.S.A. 112, 11757–11764 (2015).
67
H. Fu, K. Nan, W. Bai, W. Huang, K. Bai, L. Lu, C. Zhou, Y. Liu, F. Liu, J. Wang, M. Han, Z. Yan, H. Luan, Y. Zhang, Y. Zhang, J. Zhao, X. Cheng, M. Li, J. W. Lee, Y. Liu, D. Fang, X. Li, Y. Huang, Y. Zhang, J. A. Rogers, Morphable 3D mesostructures and microelectronic devices by multistable buckling mechanics. Nat. Mater. 17, 268–276 (2018).
68
Y. H. Zhang, F. Zhang, Z. Yan, Q. Ma, X. L. Li, Y. G. Huang, J. A. Rogers, Printing, folding and assembly methods for forming 3D mesostructures in advanced materials. Nat. Rev. Mater. 2, 17019 (2017).
69
Z. C. Fan, Y. Y. Yang, F. Zhang, Z. Xu, H. B. Zhao, T. Y. Wang, H. L. Song, Y. G. Huang, J. A. Rogers, Y. H. Zhang, Inverse design strategies for 3D surfaces formed by mechanically guided assembly. Adv. Mater. 32, 1908424 (2020).
70
Z. Xu, Z. Fan, W. Pang, Y. Zi, Y. Zhang, Inverse design strategies for buckling-guided assembly of 3D surfaces based on topology optimization. Extreme Mech. Lett. 51, 101582 (2022).
71
Z. Xu, Z. Fan, H. Fu, Y. Liu, Y. Zi, Y. Huang, Y. Zhang, Optimization-based approach for the inverse design of ribbon-shaped three-dimensional structures assembled through compressive buckling. Phys. Rev. Applied 11, 054053 (2019).
72
X. G. Guo, X. J. Wang, D. P. Ou, J. L. Ye, W. B. Pang, Y. G. Huang, J. A. Rogers, Y. H. Zhang, Controlled mechanical assembly of complex 3D mesostructures and strain sensors by tensile buckling. npj Flex. Electron. 2, 1–7 (2018).
73
A. Rafsanjani, L. S. Jin, B. L. Deng, K. Bertoldi, Propagation of pop ups in kirigami shells. Proc. Natl. Acad. Sci. U.S.A. 116, 8200–8205 (2019).
74
S. Babaee, Y. C. Shi, S. Abbasalizadeh, S. Tamang, K. Hess, J. E. Collins, K. Ishida, A. Lopes, M. Williams, M. Albaghdadi, A. M. Hayward, G. Traverso, Kirigami-inspired stents for sustained local delivery of therapeutics. Nat. Mater. 20, 1085–1092 (2021).
75
S. Soltani, A. J. R. Hillier, S. J. Holder, J. C. Batchelor, Antenna-based popup vapor sensor guided by controlled compressive buckling. IEEE Sens. J. 20, 2304–2312 (2020).
76
K. Yamagishi, I. Kirino, I. Takahashi, H. Amano, S. Takeoka, Y. Morimoto, T. Fujie, Tissue-adhesive wirelessly powered optoelectronic device for metronomic photodynamic cancer therapy. Nat. Biomed. Eng. 3, 27–36 (2019).
77
Y. Lee, D.-H. Kim, Wireless metronomic photodynamic therapy. Nat. Biomed. Eng. 3, 5–6 (2019).
78
A. Bansal, F. Y. Yang, T. Xi, Y. Zhang, J. S. Ho, In vivo wireless photonic photodynamic therapy. Proc. Natl. Acad. Sci. U.S.A. 115, 1469–1474 (2018).
79
H. Lee, Y. Lee, C. Song, H. R. Cho, R. Ghaffari, T. K. Choi, K. H. Kim, Y. B. Lee, D. Ling, H. Lee, S. J. Yu, S. H. Choi, T. Hyeon, D.-H. Kim, An endoscope with integrated transparent bioelectronics and theranostic nanoparticles for colon cancer treatment. Nat. Commun. 6, 10059 (2015).

Information & Authors

Information

Published In

View large Science Advances cover image
Science Advances
Volume 8 | Issue 32
August 2022

Submission history

Received: 11 January 2022
Accepted: 27 June 2022

Permissions

See the Reprints and Permissions page for information about permissions for this article.

Acknowledgments

We would like to thank X. Feng from Tsinghua University for offering access to microfabrication facilities in the laboratory.
Funding: Y.Z. acknowledges support from the National Natural Science Foundation of China (grant nos. 12050004 and 11921002), the Tsinghua National Laboratory for Information Science and Technology, the Henry Fok Education Foundation, and a grant from the Institute for Guo Qiang, Tsinghua University (grant no. 2019GQG1012). Z.X. acknowledges support from the National Natural Science Foundation of China (grant no. 61904095) and National Postdoctoral Program for Innovative Talents (grant no. BX20180157). H.S. acknowledges support from the National Natural Science Foundation of China (grant no. 11902178).
Author contributions: Y.Z. designed and supervised the research; Z.X. led the fabrication work, with assistance from T.J., S.X., F.Z., X.C., and W.P.; T.J., Z.X., and Y.Z. led the structural designs and mechanics modeling, with assistance from S.X., Q.H., Z.J., and Z.S.; Z.X., T.J., S.X., and Y.Z. led the device design and characterization, with assistance from K.B., Z.J., H.S., and Y.S.; and Y.Z. and Z.X. wrote the manuscript and designed the figures. All authors commented on the paper.
Competing interests: The authors declare that they have no competing interests.
Data and materials availability: All data needed to evaluate the conclusions in the paper are present in the paper and/or the Supplementary Materials.

Authors

Affiliations

Applied Mechanics Laboratory, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, P.R. China.
Center for Flexible Electronics Technology, Tsinghua University, Beijing 100084, P.R. China.
Roles: Conceptualization, Data curation, Formal analysis, Funding acquisition, Investigation, Methodology, Project administration, Resources, Software, Validation, Visualization, Writing - original draft, and Writing - review & editing.
Present address: Institute of Solid Mechanics, Beihang University (BUAA), Beijing 100191, P.R. China.
Applied Mechanics Laboratory, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, P.R. China.
Center for Flexible Electronics Technology, Tsinghua University, Beijing 100084, P.R. China.
Roles: Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Software, Visualization, and Writing - original draft.
Applied Mechanics Laboratory, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, P.R. China.
Center for Flexible Electronics Technology, Tsinghua University, Beijing 100084, P.R. China.
Roles: Data curation, Formal analysis, Investigation, Software, Validation, and Visualization.
Applied Mechanics Laboratory, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, P.R. China.
Center for Flexible Electronics Technology, Tsinghua University, Beijing 100084, P.R. China.
Roles: Formal analysis and Investigation.
Applied Mechanics Laboratory, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, P.R. China.
Roles: Formal analysis, Investigation, and Software.
Present address: Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA.
Applied Mechanics Laboratory, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, P.R. China.
Center for Flexible Electronics Technology, Tsinghua University, Beijing 100084, P.R. China.
Roles: Investigation and Validation.
Applied Mechanics Laboratory, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, P.R. China.
Center for Flexible Electronics Technology, Tsinghua University, Beijing 100084, P.R. China.
Roles: Investigation and Validation.
Ziyao Ji
Applied Mechanics Laboratory, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, P.R. China.
Center for Flexible Electronics Technology, Tsinghua University, Beijing 100084, P.R. China.
Roles: Investigation, Validation, and Visualization.
Applied Mechanics Laboratory, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, P.R. China.
Center for Flexible Electronics Technology, Tsinghua University, Beijing 100084, P.R. China.
Roles: Investigation and Validation.
Applied Mechanics Laboratory, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, P.R. China.
Center for Flexible Electronics Technology, Tsinghua University, Beijing 100084, P.R. China.
Roles: Investigation and Validation.
Applied Mechanics Laboratory, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, P.R. China.
Center for Flexible Electronics Technology, Tsinghua University, Beijing 100084, P.R. China.
Roles: Funding acquisition, Investigation, Validation, and Visualization.
Applied Mechanics Laboratory, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, P.R. China.
Center for Flexible Electronics Technology, Tsinghua University, Beijing 100084, P.R. China.
Roles: Investigation, Validation, and Visualization.
Applied Mechanics Laboratory, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, P.R. China.
Center for Flexible Electronics Technology, Tsinghua University, Beijing 100084, P.R. China.
Roles: Conceptualization, Data curation, Funding acquisition, Investigation, Methodology, Project administration, Supervision, Validation, Writing - original draft, and Writing - review & editing.

Funding Information

Institute for Guo Qiang Tsinghua University: 2019GQG1012

Notes

*
Corresponding author. Email: [email protected]
These authors contributed equally to this work.

Metrics & Citations

Metrics

Article Usage
Altmetrics

Citations

Export citation

Select the format you want to export the citation of this publication.

View Options

View options

PDF format

Download this article as a PDF file

Download PDF

Check Access

Log in to view the full text

AAAS ID LOGIN

AAAS login provides access to Science for AAAS Members, and access to other journals in the Science family to users who have purchased individual subscriptions.

Log in via OpenAthens.
Log in via Shibboleth.

More options

Purchase access to this article

Download and print this article within 24 hours for your personal scholarly, research, and educational use.

Media

Figures

Multimedia

Tables

Share

Share

Share article link

Share on social media

(0)eLetters

eLetters is an online forum for ongoing peer review. Submission of eLetters are open to all. eLetters are not edited, proofread, or indexed. Please read our Terms of Service before submitting your own eLetter.

Log In to Submit a Response

No eLetters have been published for this article yet.