![reliability. The structural engineering can bridge the gap between the
large deformation and inorganic materials, by which low-modulus
mechanics of high-modulus materials can be achieved to accommodate
extreme mechanical deformations. While applied research in this area
has been abundant in recent years, review from the standpoint of
fundamental mechanics is needed to advance the field in new
directions. For example, the new opportunities and challenges of
flexible electronics derived from the conceptual breakthroughs of
emerging mechanical metamaterials.
The rest of this chapter is organized as follows. In Sect. 1.2, several
representative application scenarios are demonstrated to show the
significance of flexible electronics. In Sect. 1.3, an overview of historical
developments of structural engineering of flexible electronics is
presented with a focus on the pioneering achievements, from initial
wavy strategies to subsequent self-assembly strategies and then to
flexible mechanical metamaterials. In Sect. 1.4, from the view of
structural opportunities, several common advanced functional
materials are discussed. Finally, in Sect. 1.5, perspectives on the
remaining challenges and open opportunities in the mechanically-
guided structural engineering of flexible electronics are offered.
1.2 Applications of Flexible Electronics
Flexible electronics that can apply on complex curvilinear surfaces have
aroused extensive interest and become one of the greatest concerned,
cutting-edge interdisciplines. They have broad innovative application
prospects like wearable electronics [1], epidermal electronics [2],
robotic skin [3], and aircraft smart skin [4]. The requirements of
flexible electronics differ from application to application, from
bendability and rollability for easier handling of large area
photovoltaics, to conformability onto irregular shapes, and to hybrid of
stretchability, twistability, foldability, and deformability for electronic
skin. This section will present some representative application
scenarios, offering insights into the significance of structural
engineering of flexible electronics.
1.2.1 Wearable Human Healthcare](https://image.slidesharecdn.com/106375-250313203024-f3e401b7/85/Flexible-Electronics-Theory-and-Method-of-Structural-Design-1st-Edition-Yongan-Huang-28-320.jpg)
![Flexible electronics can be built into our clothes and accessories,
attached to our skin, and even implanted in our bodies. The
corresponding branches are wearable electronics [5, 6, 7], epidermal
electronics [2, 8, 9], and implantable electronics [10–13], respectively
(Fig. 1.1). Such bioelectronics have been changing conventional medical
diagnoses by endowing them with combined features of wearability,
comfortability, remote operation, and timely feedback. Specifically, they
can be utilized for continuous, noninvasive, real-time, and comfortable
monitoring of vital biometric signs, which provide important clinically
related information for disease diagnosis, preventive healthcare, and
rehabilitation care [14, 15]. In a word, flexible electronics offer bright
promise for next-generation healthcare and biomedical applications.](https://image.slidesharecdn.com/106375-250313203024-f3e401b7/85/Flexible-Electronics-Theory-and-Method-of-Structural-Design-1st-Edition-Yongan-Huang-29-320.jpg)
![Fig. 1.1 Flexible electronics can be used as wearable electronics [5–7], epidermal
devices [2, 8, 9], and implantable electronics [12, 13]
Various physical and physiological signals can be measured by
wearable electronics, such as electrophysiological signals [16, 17], body
motion [18], and muscle movement [19] (e.g., walking, jogging, and eye
blinking). Such real-time monitoring of muscle activities is useful for
clinical gait analysis and muscle fatigue evaluation, which can improve
exercise performance and even prevent unexpected catastrophic
situations. With epidermal electronics, vital physiological signals, such
as pulse, heart and respiration rate, body temperature, and skin and
breath moisture, can be continuously and long-timely tracked in a
mechanically unfeelable manner [20, 21]. In this way, chronic diseases
like diabetes and glaucoma can be effectively diagnosed and managed
with noninvasive, transcutaneous therapeutic treatment. Moreover,
with the advent of biocompatible and bioresorbable materials,
implantable electronics have been developed for in vivo recording of
internal conditions, such as intracranial pressure [22], biochemical
constituents (e.g., metabolites and electrolytes) [23], and
electrophysiological signals [24] (e.g., electrocardiogram, ECG;
electromyogram, EMG; electroencephalogram, EEG; electrooculogram,
EOG; and electroglottogram, EGG). Direct contact with the dynamic
curvilinear tissues and organs can provide accurate neural and
physiological signals.
One of the most challenges of flexible electronics for human
applications is how to maintain intimate and effective contact with the
complex, time-dynamic surfaces of skin, tissues and organs during
service [25]. For example, organs such as the heart, arteries, and alveoli
undergo periodic areal strains of up to several tens of percent.
Structural engineering and materials engineering are two main
strategies. Structural engineering can circumvent the high threshold of
intrinsically flexible/stretchable materials. Moreover, rational
structural designs can not only enable the stretchability of conventional
stiff, non-stretchable, and even brittle materials, but realize the
programmable deformability of such materials to better adapt the
targeted surfaces.
1.2.2 Robotics and Haptic Interface](https://image.slidesharecdn.com/106375-250313203024-f3e401b7/85/Flexible-Electronics-Theory-and-Method-of-Structural-Design-1st-Edition-Yongan-Huang-30-320.jpg)
![The research of robotics has grown into a popular field in the past few
years (Fig. 1.2a) [26]. Electronic skin (E-skin) is the most intuitive
application of flexible electronics in robotics to enhance perceptibility
and interactivity, which is emerging rapidly with the goal of matching
or even surpassing the performance of human skin (Fig. 1.2b, c) [27,
28]. Moreover, soft robots can integrate E-skin and soft actuators to
achieve integrated control of sensing and driving (Fig. 1.2d, e) [29–32],
and programmability and multifunction [33]. With the increasing
demand, flexible electronics have broad application prospects in the
field of soft robots [34]. Mechanical compliance is a prerequisite for E-
skin to accommodate complex dynamic environments while
maintaining its multiple functionalities. In this regard, structural
engineering of E-skin has been developed for compliant designs,
enabling the integration of imperceptible sensing systems with great
conformability to 3D surfaces.](https://image.slidesharecdn.com/106375-250313203024-f3e401b7/85/Flexible-Electronics-Theory-and-Method-of-Structural-Design-1st-Edition-Yongan-Huang-31-320.jpg)
![Fig. 1.2 Flexible electronics in soft robotics. a Human–machine interaction [26]. b
Electronic skin [28]. c Prosthetic skin [27]. d Self-powered soft robot [31]. e Soft,
autonomous robots [32]. f Programmable, reprocessable multifunctional soft robots
[33]
More importantly, analogy to human skin, E-skin should exhibit
extraordinary sensing abilities for numerous tactile and thermal
stimuli, object recognition, texture discrimination, slip detection,
sensory-motor feedback, etc. The flexible sensors are the key to
realizing this goal. Taking the flexible pressure sensors as examples,
microstructural engineering of the active layers is one of the most](https://image.slidesharecdn.com/106375-250313203024-f3e401b7/85/Flexible-Electronics-Theory-and-Method-of-Structural-Design-1st-Edition-Yongan-Huang-32-320.jpg)
![admirable strategies to enhance the performance of flexible sensors
like sensitivity, linearity, and sensing range. Common microstructural
designs include regular pyramids [29, 35], hemispheres [30], and
pillars [36, 37]. Moreover, bioinspired hierarchical structural arrays
[38], randomly distributed spinosum [39], and bioinspired cone arrays
[40] have been proposed successively. Recently, Bai et al. reported an
iontronic pressure sensor with ultra-broad-range high sensitivity based
on graded intrafillable architecture [41]. Ji et al. synergistically
optimized the sensitivity and linearity of flexible pressure sensors via
double conductive layer and porous microdome array [42]. Not long
ago, Liu et al. introduced Origami designs to broaden the sensing range
of flexible sensors [43]. In the future, continuous breakthroughs of
structural engineering for the applications of flexible electronics in soft
robotics will appear, such as the introduction of emerging mechanical
metamaterials [44, 45], and the structural design of a driving-sensing
integrated strategy suitable for soft robots.
1.2.3 Smart Skin in Aircraft
Recently, the demands of flexible electronics applied in the field of
aeronautics are increasing such as the flexible smart sensing skin [4,
46–49]. The flexible smart sensing skin can realize the in-situ
measurement of aerodynamic parameters without changing the
structure attributes and flow field environment, making it a promising
candidate in wind tunnel test, unmanned driving, morphing aircraft,
and other related fields. Compared with the traditional method of
pressure taps [50], the pressure-sensitive paint [51], and the
conventional smart skin [52], recent significant technical advances in
flexible electronics have overcome many historic drawbacks, e.g.,
avoidance of the inevitable structural damage and significant increase
of weight, real-time and in-situ measurement, and high-density sensing
network. However, unlike the applications in human and robots, the
extreme operating environments of aircrafts impose strict limitations
to the materials. The widely used intrinsically flexible/stretchable
materials, such as PDMS and Ecoflex, are incompetent and unsuitable
for such situations due to insufficient strength, temperature sensitivity
(low glass-transition temperature), high-frequency fitration, and so on.
Therefore, the structural engineering of flexible electronics made of](https://image.slidesharecdn.com/106375-250313203024-f3e401b7/85/Flexible-Electronics-Theory-and-Method-of-Structural-Design-1st-Edition-Yongan-Huang-33-320.jpg)
![conventional stiff, stable, and high-performace materials is natural and
sagacious choice.
Furthermore, the intelligent flexible sensing (iFlexSense) skin is a
key enabling technology for the wind tunnel test and the future “Fly-by-
Feel” control of morphing aircraft (Fig. 1.3). It represents the next-
generation skin of aircraft that can exhibit more powerful sensing
functions. The smart skin can “feel”, “think”, and “react” in real time
based on high-resolution state-sensing, awareness, and self-diagnostic
capabilities, endowing the aircraft with the ability to change shape
according to the fly states and structural health [4]. Undoubtedly, such
advanced functions pose great challenges to the mechanical properties
of the flexible smart sensing skin, especially for the deformability. It
should hold extra features: (i) capability of adaptive deformation with
the infrastructural skin, (ii) low membrane stiffness to allow small
actuation requirement, (iii) effectively sensing air loads while
maintaining initial surface geometry, and (iv) high elasticity and
recovery to allow multiple cycles of deformation [53]. Empirically and
reasonably, the realization of these targets mainly relies on the
structural engineering of flexible electronics. Predictably, future
aircrafts with more controlled systems will lead to the increasing need
for flexible electronics applied on the aircraft surface.
Fig. 1.3 Intelligent flexible sensing (iFlexSense) skin for aircraft [54]
1.3 Structural Strategies](https://image.slidesharecdn.com/106375-250313203024-f3e401b7/85/Flexible-Electronics-Theory-and-Method-of-Structural-Design-1st-Edition-Yongan-Huang-34-320.jpg)
![1.3.1 Wavy Strategy
The wavy strategy was first proposed in the pioneering work of flexible
electronics in 2006, in which flexible devices made of single-crystal
silicon were buckled into microscale, periodic, and wavy shapes [55].
Thin silicon ribbons (20 ~ 320 nm) were firstly fabricated by
lithographic processing and then transferred to the surface of a pre-
strained elastomer substrate (e.g., PDMS). After releasing the pre-
strain, the silicon ribbons were compressed to wavy structures. Wavy
silicon can be reversibly stretched and compressed to large levels of
strain without damage. The strains of the whole system during
deformation are accommodated mainly through changes of the
wavelengths and amplitudes of the wavy structures rather than the
mechanical properties of materials. The wavy silicon ribbons of 100 nm
thickness can be stretched up to 30% that overwhelms the 1% strain
limit of silicon. Such strategy renders the conventional stiff,
nonstretchable, and even brittle materials sufficiently deformable to act
as flexible electronics. It not only allows large-scale stretchability
without degradation in electronic performances, but also realizes good
conformability on complex surfaces. The wavy strategies pave the new
way for the structural engineering of flexible electronics.
Many mechanical models have been established to analyze the
configuration of wavy structures. In the beginning, under the small-
deformation assumption (<5%) and the principle of minimum potential
energy, Khang et al. [55] and Huang et al. [56] developed an energetic
method to describe the buckling behaviors, in which the out-of-plane
displacement is assumed as a sinusoidal profile. Afterward, considering
the practical large deformations (>5%), Jiang et al. [57] and Song et al.
[58] developed a nonlinear finite-deformation model, by which the
wavelength and amplitude of wavy profile can be predicted.
Following this direction, the theoretical framework is gradually and
continuously improved, and more and more situations are considered,
including post-buckling [59], finite-width effect [60], local versus global
buckling [61], thermomechanical analysis [62, 63], adhesion-governed
buckling [64], rigid/soft wavy surfaces [65, 66], 1D/2D wavy surfaces
[67, 68], and moderately large-deflection theory [69]. Relying on the
underlying mechanisms, the wavy designs are widely applied in flexible
electronics. Initially, Khang et al. presented a stretchable single-crystal](https://image.slidesharecdn.com/106375-250313203024-f3e401b7/85/Flexible-Electronics-Theory-and-Method-of-Structural-Design-1st-Edition-Yongan-Huang-35-320.jpg)
![silicon p-n diode on a PDMS substrate at −11%(top), 0% (middle), and
11% (bottom) applied strains [55]. Furthermore, Kim et al.
demonstrated stretchable and foldable silicon integrated circuits based
on 2D wavy designs [70]. Ko et al. realized the wrapping of a silicon
membrane circuit on a golf ball (Fig. 1.4a) [71]. Noteworthily, except for
the full bonding method, the selective bonding method is also widely
used to generate wavy structures on the elastomeric substrates. For
example, Sun et al. constructed metal–semiconductor field-effect
transistors based on buckled wavy GaAs ribbons [72].
Fig. 1.4 Various structure strategies in stretchable electronics: a Wavy [71], b
serpentine [73], c self-similar [74] strategies
1.3.2 Island-Bridge Strategy
Originating from and then beyond the wavy strategies, the island-
bridge strategies were proposed to achieve higher levels of
stretchability. The non-stretchable functional components reside at the
low-strain islands and the stretchable interconnects form the bridges to
accommodate the mechanical stretchability and electrical conductivity.
Due to the much lower stiffness of the bridges than the islands, the
islands and adhered functional devices are mechanically isolated. In
other words, the key point of island-bridge strategies lies in the design
of bridges. By now, there are three representative successful cases,
namely arc-shaped [75, 76], serpentine [77–80], and fractal
interconnects [74, 81–83]. Since the arc-shaped designs are very
similar to the wavy strategies in the previous section, here we mainly
introduce the latter two.](https://image.slidesharecdn.com/106375-250313203024-f3e401b7/85/Flexible-Electronics-Theory-and-Method-of-Structural-Design-1st-Edition-Yongan-Huang-36-320.jpg)
![Arc-shaped interconnects. Under stretching and compression, switch-
on/off of out-of-plane buckling of arc-shaped interconnects can
accommodate the applied strain. Initially, the arc-shaped interconnects
were usually treated as clamped beams or films, and the out-of-plane
buckling displacement was assumed as sinusoidal profiles [75]. After
that, to break the limitation of the sinusoidal assumption for the large
displacements, a finite-deformation theoretical model was developed,
which can offer a more accurate prediction of the amplitude [84]. Wang
et al. presented a systematic analysis for the buckling behaviors and
gave the critical criteria, by which the buckling behaviors are
determined by the relationship between pre-strain and adhesion and
the modes can be subdivided into global buckling, local buckling, and
no buckling [85].
Serpentine interconnects. The serpentine strategy was firstly applied
in the milestone work of epidermal electronics in 2011 [2], in which the
concept of epidermal electronics was defined. With the filamentary
serpentine designs, the system provided elastic, reversible responses to
large-strain deformations with effective moduli (<150 kPa), bending
stiffnesses (<1 nN/m), and areal mass densities (<3.8 mg/cm2
). Those
merits are in orders of magnitude smaller than those possible with
conventional electronics or even with recently explored flexible
devices. Thereafter, the filamentary serpentine interconnects have been
widely explored in flexible electronics. A representative example is the
soft microfluidic assemblies of sensors, circuits, and radios for the skin,
in which strain-isolated device components are connected by a
freestanding serpentine interconnecting network (Fig. 1.4b) [73].
A systematic and comprehensive investigation of mechanical
behaviors in such serpentine interconnects has been performed by
researchers. In earlier research, the serpentine interconnects were
mostly freestanding and the stretchability relies on the folding,
tenuous, and thin designs. Zhang et al. developed analytical models to
reveal the buckling mechanisms in such stretchable serpentine
microstructures, including the buckling and post-buckling behaviors
[80]. A scaling law was established to determine the critical buckling
strain, by which symmetric and anti-symmetric buckling modes were
identified. Soon after, Zhang et al. further proposed a pre-strain](https://image.slidesharecdn.com/106375-250313203024-f3e401b7/85/Flexible-Electronics-Theory-and-Method-of-Structural-Design-1st-Edition-Yongan-Huang-37-320.jpg)
![approach that can significantly improve the stretchability (more than
two times) compared to the situation without pre-strain [86]. The
analytical model can not only effectively predict the wavelength but
also explain the influence of thickness, offering a rational method to
obtain the desired stretchability.
Moreover, in 2016, Su et al. introduced a different route to design
the serpentine interconnects, where tenuous and freestanding
geometries were substituted by thick and bonded layouts to enhance
the mechanical and electrical performance [87]. The in-plane and out-
of-plane buckling modes were replaced by pure in-plane scissor-like
deformations. More specifically, with the increase of thickness, the
deformation mechanisms change from wrinkling (localized, multiwave,
out-of-plane buckling) to buckling (coupled out-of-plane buckling and
twisting) and then to scissoring (pure in-plane bending deformation).
The scissor-like deformations significantly increased stretchability
from 20% for thin, buckling interconnects to ~ 100% for thick,
scissoring interconnects. The findings provide a significant supplement
and open a new direction for the design of serpentine interconnects. In
addition, Yang et al. proposed a “cut-and-paste” process to manufacture
the multiparametric epidermal sensing systems based on the
serpentine designs [88]. Pan et al. discussed the effect of substrate
thickness and concluded that the reduction of the substrate can
improve the stretchability [89].
Fractal interconnects. Aiming to reconcile the mutually exclusive
requirements of large stretchability and high-area coverage, fractal
design concepts were introduced for stretchable electronics. Before
that, Zhang et al. showed the increase of surface filling ratios by
increasing the fractal order from 1 to 4 [81]. As with the other
strategies, fractal interconnects can also be divided into freestanding
and bonding layouts. For the freestanding situation, the deformations
can be further divided into pure in-plane stretching for large thickness-
width ratio (>1) and spatial buckling for small thickness-width ratio
(<1/5). For the former case, Zhang et al. gave recursive formulae to
describe the relationship between fractal orders and flexibility and
stretchability [81]. For the latter case, Xu et al. propounded ordered
unraveling mechanisms to interpret the deformations [82]. In addition](https://image.slidesharecdn.com/106375-250313203024-f3e401b7/85/Flexible-Electronics-Theory-and-Method-of-Structural-Design-1st-Edition-Yongan-Huang-38-320.jpg)
![to the abovementioned serpentine shape, fractal designs can be applied
to many other shapes [83, 90], e.g., zigzag, sinusoidal, and horseshoe.
Su et al. developed an analytic method to directly compute the elastic
energy and the tensile stiffness of fractal interconnects of arbitrary
order n and in arbitrary shape [83]. Furthermore, Dong et al.
investigated the bonding configuration of such interconnects with the
elastomer substrate [91, 92].
By dint of the simultaneous large stretchability and high-area
coverage, fractal interconnects used as bridges between mechanically
isolated islands have shown unique advantages in stretchable lithium-
ion batteries [82], epidermal electronics (Fig. 1.4c) [74], and radio-
frequency antennas [93]. Furthermore, fractal designs can also enhance
conformability on soft, curvilinear surfaces, which are meaningful for
applications in bio-systems. Xu et al. presented a fractal electrode array
distributed over a rabbit heart circumference to deliver cardiac
electrical stimulation and sense cardiac electrical activity [94].
Moreover, fractal electrodes are conformable to more complex
biological surfaces, in which the fractal electrode meshes can be
directly and chronically mounted on the complex surfaces of the auricle
and the mastoid [95]. The case of the auricle proved another advantage
of fractal interconnects, namely directional guided deformability to
match the complex topology of the auricle. Specifically, all-vertical
Peano curves were used to get selective high stretchability along with
the longitudinal coordinates.
1.3.3 Kirigami and Origami Strategy
Recently, the concept of Kirigami mechanical metamaterials (Kiri-MMs)
has been introduced into the design of flexible electronics [54]. The
salient structural traits including negative Poisson’s ratio [44, 96],
ultra-stretchability [97–100], mechanical programmability [101–105],
and transformability from 2 to 3D [106–108] provide a brand-new
research strategy. Specifically, the programmability enables the
possibility to fit arbitrary curvilinear surfaces [105], and the
transformability from 2 to 3D is a perfect solution to the contradiction
between 2D planar processing technology and 3D conformal demands
[106, 109]. Compared with other thin open-mesh serpentine or island-
bridge strategies introduced above, Kirigami structures have a high fill](https://image.slidesharecdn.com/106375-250313203024-f3e401b7/85/Flexible-Electronics-Theory-and-Method-of-Structural-Design-1st-Edition-Yongan-Huang-39-320.jpg)
![factor, which are particularly desirable for high-density sensing or high-
resolution imaging [110]. In the early stage, graphene Kirigami was an
impressive example to demonstrate the salient traits of Kirigami [111],
by which one-atom-thick graphene sheets were transformed into
resilient and morphing structures without sacrificing electrical
performance.
By now, Kirigami-inspired creative applications have become
abundant, including self-powered strain sensor (Fig. 1.5a) [112], soft
crawler (Fig. 1.5b) [113], morphable stent (Fig. 1.5c) [114], shoe grip
(Fig. 1.5d) [115], adaptive imager (Fig. 1.5e) [110], and flexible car shell
[116]. The underlying mechanism of Kirigami structures relies on the
local buckling of hinges under low-energy loads to empower the whole
structural reconfigurability. Rafsanjani and Bertoldi investigated the
mechanisms of the buckling-induced Kirigami and studied how the
behavior evolves when the thickness is progressively decreased [109].
However, all these creative buckling-driven traits are poles apart from
the fully conformal goals of flexible electronics that require coating as
smooth as possible. Current studies mostly directly make use of the
buckling-induced traits, but how to restrain buckling while keeping
extraordinary mechanical properties of Kiri-MMs remains open. As a
note, despite non-stretchable PI used in curvy, shape-adaptive imagers,
the ultrathin thickness (~5 μm) makes the devices sufficiently
compliant [110]. To address this challenge, we show that using soft
material at the hinges of Kiri-MM can restrain this local buckling effect
and improve conformability [117], which will be presented in the
following chapter.](https://image.slidesharecdn.com/106375-250313203024-f3e401b7/85/Flexible-Electronics-Theory-and-Method-of-Structural-Design-1st-Edition-Yongan-Huang-40-320.jpg)
![Fig. 1.5 Kirigami strategy: a self-powered strain sensor [112], b soft crawler [113], c
morphable stent [114], d shoe grip [115], and e adaptive imager [110]
As for the design methods, fractal Kirigami can further enhance the
stretchability. Programmable Kirigami mechanical metamaterials are
becoming popular. Choi et al. propounded a meaningful inverse
Kirigami design method, in which the cutting path was determined by
objective and constrained functions derived from targeted conformal
shapes [105]. Most recently, based on the computer graphics, Jiang et al.
presented an affirmative solution to realize the targeted
programmability of Kirigami sheet between arbitrary shapes, in
particular between a 2D sheet and a 3D curved surface [118]. This so-
called inverse problem for Kirigami cut and fold patterns is solved by
drawing on a differential-geometric interpretation of the morph and
progress in geometric computing. Therefore, it is convinced that
Kirigami will be a powerful strategy to design the flexible electronics.
As the twin concept of Kirigami, Origami is another admired
strategy to build wonderful structures. Because of the ability to hold
creases and bend at will, a 2D sheet can be folded into arbitrary shapes.
The mechanisms of Origami have been widely studied for a very long
time, including mathematics [119], geometry [120], and compliant
mechanisms [121]. Many Origami strategies have been proposed like](https://image.slidesharecdn.com/106375-250313203024-f3e401b7/85/Flexible-Electronics-Theory-and-Method-of-Structural-Design-1st-Edition-Yongan-Huang-41-320.jpg)
![Miura-ori and its variants, Ron Resch’s tessellation, and square twist.
Either way, the kernel always roots in the crease patterns. Mechanically,
the creases act as soft hinges to connect the stiffer facets, and the low-
energy deformation of the creases induces the morphability of the
whole Origami structures (Fig. 1.6a) [122]. Similar to previous “island-
bridge” strategies, the strain-free facets between the creases are
uniquely suited as the integration platform to mount active devices of
flexible electronics. Moreover, as Origami-based mechanisms often
feature multiple discrete folding motions, they enable the realization of
programmable 3D multishapes. In a nutshell, Origami has many ideal
characteristics: monolithic preparation, scale-independent, perfect self-
assembly compatibility, and unlimited design space based on rich
folding patterns, making it very suitable for applications in flexible
electronics.
Fig. 1.6 Origami strategy. a Transformable Origami with multiple degrees of
freedom [122]. b Ori-MMs-based silicon optoelectronics for hemispherical
electronic eye systems. Reproduced with permission [128]. c Ori-MMs-based
conformal electronics made of non-stretchable materials [131]. d Origami-based
electrothermal devices [132]. e Stretchable Origami robotic arm [133]. f Origami-
based wide-range flexible capacitive pressure sensors [43]
Recently, Origami has been explored for applications in many
engineering fields, e.g., compactly deployable solar arrays for space
applications [123], self-folding crawling robots for machine
manufacturing [124], and medical stents for biomedical applications
[125]. Its strut in flexible electronics may start from the Origami](https://image.slidesharecdn.com/106375-250313203024-f3e401b7/85/Flexible-Electronics-Theory-and-Method-of-Structural-Design-1st-Edition-Yongan-Huang-42-320.jpg)
![lithium-ion batteries proposed in 2014 [126]. This Origami battery
exhibited stable and reliable performances under large cycles of
mechanical deformations. By utilizing printable ZnO nanowires and
carbon electrodes, Lin et al. developed a stretchable and deformable
Origami photodetector array based on the Miura-ori strategy [127]. The
Origami photodetector array can provide excellent capabilities of
omnidirectional photodetection. Furthermore, Zhang et al. developed
Origami silicon optoelectronics for dense, scalable, and compact
hemispherical electronic eye systems [128] (Fig. 1.6b), which were
compatible with mature complementary metal–oxide–semiconductor
(CMOS) technologies that enable deployments in extremely high
density. In the same period, Origami was introduced to fabricate a
flexible and foldable thermoelectric nanogenerator [129]. Most
recently, Qi et al. displayed reconfigurable flexible electronics driven by
Origami magnetic membranes [130]. In addition, Origami can be
adopted to realize full wrapping of conformal electronics made of non-
stretchable materials (Fig. 1.6c) [131], to structure electrothermal
devices with controllable multi-degrees-of-freedom shape morphing
(Fig. 1.6d) [132], to enable stretchable robotic arm with
omnidirectional bending and twisting soft robotics (Fig. 1.6e) [133],
and to devise wide-range flexible capacitive pressure sensors (Fig. 1.6f)
[43]. Incidentally, a number of computer-aided tools to Origami such as
TreeMaker and Oripa have been developed. TreeMaker allows new
Origami bases to be designed for special purposes and Oripa tries to
calculate the folded shape from the crease pattern. All these
achievements demonstrate the potential of the Origami to develop
spatial flexible electronics.
1.3.4 Buckling-Driven Assembly Strategy
Buckling-driven assembly strategy is another milestone of structural
engineering of flexible electronics (Fig. 1.7) [134]. It relies on the
control of buckling to realize 2D-to-3D transformation, with the release
of prestrained elastomer substrate to provide initial mechanical drive
and vice versa. It can be reversibly stretched and buckled between 2D
and 3D configurations without degradation of performance even with a
large number of cyclic loadings [106, 135, 136]. The 3D stretchable
multifunctional photodetector is a convincing paradigm for the](https://image.slidesharecdn.com/106375-250313203024-f3e401b7/85/Flexible-Electronics-Theory-and-Method-of-Structural-Design-1st-Edition-Yongan-Huang-43-320.jpg)
![effectiveness of the buckling-driven assembly strategy [137]. The
interconnects of the device exploit a sandwich configuration, with the
graphene encased by two SU-8 layers, and then the SU-8 layers are
buckled into a hemispherical structure, rendering a 3D arrangement of
the MoS2 patches that serve as photodetecting elements. The
advantages include (i) the concurrent tracking of the direction and
intensity of the incident light, (ii) optically transparent system allowing
the detection of incident angles, and (iii) high geometrical extensibility
like an octagonal prism and an octagonal prismoid. Note that these
merits cannot be easily achieved by photodetector arrays in planar
layouts.
Fig. 1.7 Buckling-driven assembly strategy. a Schematic illustration of the assembly
process guided by controlled buckling [134]. b 3D Origami micro/nanostructures
[138]. c 3D Kirigami mesostructures [106]
Except for the compressive buckling, the 3D assembly can be also
realized by tensile buckling that can circumvent the pre-stretching limit
[139]. When the substrate is stretched uniaxially, the nonbonded
regions of the 2D precursor are delaminated from the substrate,
resulting in a 3D transformation through coordinated bending/twisting
deformations and translational/rotational motions. The derivative](https://image.slidesharecdn.com/106375-250313203024-f3e401b7/85/Flexible-Electronics-Theory-and-Method-of-Structural-Design-1st-Edition-Yongan-Huang-44-320.jpg)
Flexible Electronics Theory and Method of Structural Design 1st Edition Yongan Huang
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- 6. YongAn Huang, YeWang Su and Shan Jiang Flexible Electronics Theory and Method of Structural Design
- 7. YongAn Huang State Key Laboratory of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology, Wuhan, China YeWang Su Institute of Mechanics, Chinese Academy of Sciences, Beijing, China Shan Jiang Hangzhou Institute of Technology, Xidian University, Hangzhou, China ISBN 978-981-19-6622-4 e-ISBN 978-981-19-6623-1 https://doi.org/10.1007/978-981-19-6623-1 Jointly published with Science Press, Beijing, China. The print edition is not for sale in China (Mainland). Customers from China (Mainland) please order the print book from: Science Press. © Science Press 2022 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use.
- 8. The publishers, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publishers nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publishers remain neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Singapore Pte Ltd. The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721, Singapore
- 9. Foreword Flexible electronics are electronics that can be stretched, bent, twisted, and deformed into arbitrary shapes. They break through the bottleneck and monopoly of traditional, rigid IC technologies and represent the next-generation electronics. Flexible electronics were introduced about two decades ago and have attracted increasing interest since then, both because of their compelling physical properties and because of their potential applications. The topic of flexible electronics stands at the crossroad of physics (mechanics, photonics, electromechanical coupling, etc.) and engineering (material engineering, structure engineering, electrical engineering, etc.). Their representative applications include epidermal/implantable/wearable electronics for human health monitoring, artificial skin for robotics or human–robot interaction, and smart sensing skin for aircraft. The flexibility has become the trend of modern life. Should the current growth trend in flexible electronics research continue, it is not inconceivable to witness a near explosion in industrial interest, as what happened over half a century ago in the field of IC electronics and more recently in photonics. Structure engineering and material engineering are two main research branches of flexible electronics and mutually reinforcing. Compared to the intrinsically flexible and stretchable materials, structural engineering has proven its unique advantages, e.g., stretchable inorganic electronics. High-performance inorganic materials are ubiquitous in modern electronics, but their natural rigidity and brittle character (e.g., the fracture strain of silicon is only ~ 2%) limit the deformability of the resulting devices. Structural designs can render inorganic electronics into forms that provide large effective levels of deformability, while maintaining the high-performance electrical properties. After the first decade during which the topic remained mainly theoretical with a few proof-of-concept demonstrations appearing in the literature, the latest evolution has been toward applications. The mechanical explanations for various structural designs are now quite well understood, efficient numerical methods have been developed, and sufficient verifying experiments have been conducted. Thus, the topic of structure engineering of flexible electronics has become mature for books.
- 10. This book is the first one about systematic introduction of structural designs of flexible electronics. It covers the state-of-the-art and comprehensive works on theoretical modeling, numerical simulations, and experiments of the authors and also provides a rather exhaustive perspective on the realm of flexible electronics. These achievements are very useful for further development of flexible electronics. I think this book is a timely and good summary for this rising field in which an increasing number of young researchers are putting their efforts. This is an excellent reference book for both academic research and industrial design of flexible electronics. Han Ding Wuhan, China
- 11. Preface Over the past decade, the area of flexible electronics has experienced great developments since it opens up a series of unprecedented applications with broad interests and potentials for impact. The most salient trait of flexible electronics is their deformability during the working process, making them potential candidates for applications in many fields like wearable electronics, epidermal electronics, human– machine interfaces, soft robotics, aircraft smart skin, other biomedical devices, and the related systems. The study of flexible electronics has thus become one of the most active and fast-growing interdisciplines in physics (e.g., solid mechanics, condensed matter physics) and engineering (e.g., electrical engineering, mechanical engineering, structural engineering). By now, one of the main challenges is to reduce the strains in the rigid inorganic electronic materials and metallic interconnects, while accommodating the large applied deformations. The various solutions may be summed up as two strategies: advanced functional materials and flexible micro-/nano- structural designs. Structural designs of devices can ensure the high-performance electrical properties of inorganic electronics under complex deformation, such as stretchability, conformability, and stability. This book provides an overview of the underlying theory and method of structural designs for flexible/stretchable electronics. Based on the mechanical mechanism, this book discusses the main structural deformation behaviors, including the buckling of film/fiber-on-substrate, self-similar design with/without substrate, conformal design on soft/rigid surfaces, stability design under stretching/compression, Kirigami-based conformal design, multiple neutral plane design. Moreover, the related advanced fabrication technologies, devices, and applications are also presented. The review of the developments of flexible electronics is discussed in Chap. 1, focusing on the branch of structural designs. In Chap. 2, the buckling behaviors of typical film-on-substrate systems in flexible electronics are presented. Especially, an analytical mechanical model of the island–bridge structure is established and the accurate solution is obtained. A validated scaling law is found to reveal the dependence of the normalized maximum strain in the island on the
- 12. prestrain of the substrate, which controls the mechanical failure of the island–bridge structure and provides a theoretical basis for fracture- safe design of stretchable electronics. Then, thermomechanical properties are discussed in detail, where the model of the film-on- substrate structure is established based on interface continuity and considered as a function of room, working, and deposit temperatures. In Chap. 3, the buckling behaviors of typical fiber-on-substrate systems in flexible electronics are demonstrated. A mechano- electrospinning (MES) technique is first proposed to fabricate large- area, high-performance stretchable piezoelectric nanowire devices without out-of-surface buckling or wrinkling, by which polyvinylidene difluoride nanofibers can be direct-written onto a pre-strained elastomeric substrate. Then, the inherent competing mechanism between out-of-/in-surface buckling of micro-/nanowires on elastomeric substrates is first uncovered. Theoretical analysis and numerical simulations are presented to discover the critical factors that govern the competition between the two buckling modes. In Chap. 4, fractal-inspired geometric designs in electrical interconnects are analyzed in theory to simultaneously achieve large stretchability and high aerial coverage for stretchable electronics. A universal mechanical theory based on the energy density is developed for the self-similar interconnects with a representative element of arbitrary shape to calculate the stiffness and to estimate the stretchability. The key parameters governing the tensile stiffness are identified. After that, the fractal-inspired space-filling structures of electronic materials (including monocrystalline silicon) are demonstrated for electrophysiological sensors, precision monitors and actuators, and radio frequency antennas. In Chap. 5, the bonding configuration of self-similar serpentine interconnects on the elastomer substrate is considered. The stretchability of the order-2 self-similar interconnects bonded onto the PDMS substrate is studied through analytical modeling, finite element simulations, and experiments. The scaling law is built to predict the stretchability of the structure. Then, the application of self-similar interconnects in surface electrodes is introduced to design surface electrodes with high mechanical adaptability (stretchability and
- 13. conformability with skin) and high electrical sensitivity/stability which are usually a pair of paradoxes. In Chap. 6, the conformal behaviors of flexible electronics on rigid substrates are studied. A mechanical analysis framework based on the energy method is established for understanding the conformability of flexible electronics on target surfaces. On this basis, the specific derivation process for two representative practical cases of rigid substrates are displayed, including 1D conformability of membranes on rigid wavy substrates and 2D conformability of island–bridge structures on non-developable rigid surfaces. Effects of key factors containing geometric parameters of electrodes, areal coverage of electrodes, and external loads are disinterred. In Chap. 7, the conformal behaviors of flexible electronics on soft substrates are investigated. An interfacial mechanical model describing epidermal electronics and skin system is put forward. Similarly, the contact behaviors of three representative soft cases are reviewed, including (i) 1D conformability on soft substrate, (ii) 2D conformability on wavy soft substrate, and (iii) 2D conformability on complex soft substrate. Furthermore, local failure analysis of island during conformal process is given a special discussion for the 2D conformability on complex soft substrate. The conformability of epidermal electronics is validated by experiments with different substrate thickness, areal coverage, and external loadings. In Chap. 8, a significant in-plane design strategy for highly stretchable electronics is propounded, in which thick bar geometries are used to replace conventional thin ribbon layouts to yield scissor- like deformations instead of in-plane or out-of-plane buckling modes. Systematic studies involving experimental work, finite element simulation, and analytical theory reveal the underlying mechanisms between three different deformation modes (wrinkling, buckling, and scissoring), for serpentine structures of hard materials on soft elastomeric substrates. Analytical studies of these designs identify key geometric parameters that govern the elastic stretchability and yield optimal values for metallic serpentine interconnects that reach levels of stretchability up to 350%. In Chap. 9, the prebuckling problems of thick serpentine interconnects are considered. A systematic and straightforward theory
- 14. (finite prebuckling deformation, FPD) is developed to analyze the FPD buckling behaviors of beams with the coupling of bending, twisting, and stretch/compression. As a comparison, various theoretical and numerical methods are applied to three classic problems, including lateral buckling of a three-point bending beam, lateral buckling of a pure bending beam, and Euler buckling. The proposed FPD buckling theory for beams can give a good prediction than the conventional buckling theories and numerical methods that always neglected the prebuckling deformation. Finally, an experiment is conducted to observe the actual effects. In Chap. 10, the buckling-driven self-assembly strategy for stretchable electronics is presented. A novel helix electrohydrodynamic printing technique is proposed, without photolithography and transfer printing processes. The buckling behaviors of the serpentine fibers are investigated by combining theoretical modeling, finite element analyses, and experiments. The critical geometric parameter governing the buckling behaviors from local buckling to global buckling is obtained. Finally, the application of the buckling-driven self-assembly strategy in a hyper-stretchable self-powered sensor is displayed to show their distinct advantages. In Chap. 11, a novel Kirigami assembly strategy that can address the conformal challenges of flexible electronics is shown, especially for those made of stiff, non-stretchable materials. Although aimed at forming a 3D curved electronic circuit, this strategy is fully compatible with the conventional 2D circuit designs and fabrication methods. It allows a 2D sheet to wrap a 3D surface conformally and completely, i.e., with a smooth coating surface and high areal coverage. The geometrical design algorithm for 2D-to-3D conformal mapping is elucidated. Finally, several 3D multifunctional sensing systems are fabricated to demonstrate the advantages of the proposed strategy. In Chap. 12, the mechanical behaviors of laminated structure-based flexible electronics are first accurately described. An analytic mechanical model of the laminated structure is established to accurately predict the strain distribution of the structure and the locations of the neutral mechanical planes of the hard layers. A significant finding is revealed that shear deformation dominates in the soft adhesive layers of the laminated structure of flexible electronics
- 15. while the normal strain-induced deformation is negligible. Moreover, the finite element method is used to prove the accuracy of the theoretical model. In addition, the effects of the membrane energy and bending energy of the soft layer are also investigated by incorporating or neglecting the shear energy. In Chap. 13, liquid metals are introduced into the design of stretchable electronics, focusing on microfluidic serpentine antennas for mechanically adaptive frequency modulation. Mechanical tuneability of resonance frequencies of the stretchable antennas is exhibited, including decreasing, stabilizing and increasing the resonance frequencies under stretching. The strain-isolated design and modular assembly of individual antenna sheets are presented to facilitate the practical applications. Furthermore, the serpentine design for liquid-metal antennas is introduced into the design of stretchable RFID tag, which can keep the working frequency stable under high stretching up to 50%. Finally, a ultrathin, flexible electromagnetic metasurface based on liquid metals is demonstrated. In Chap. 14, several representative applications of flexible electronics are displayed. First, the application of flexible electronics as E-tattoos for physiological sensing and therapeutics is given. Large- area, breathable, mechanically robust, and high-fidelity epidermal electrodes are reported. Then, the application of flexible electronics as implantable electronics for the cardiac membrane is demonstrated. Third, an intelligent flexible sensing (iFlexSense) skin, bio-inspired by the powerful sensing capacities of biological systems, is presented for airflow sensing and structural health monitoring of the full-coverage, curved surface. Finally, the application of flexible electronics as robotic interface is shown. This book mainly includes the authors’ achievements in the topic of structural designs of flexible electronics, which is both its strength and its weakness. Many significant progresses by other researchers are covered but not discussed in detail. Though it probably contains many mistakes and misses certain developments and contributions, it can but only reflect the sincere knowledge of its authors. To all distinguished colleagues, collaborators and often friends, we wish to present our apologies for any omissions in our text.
- 16. We are also deeply grateful for the many efforts and contributions from other contributors, including Dr. Wentao Dong, Dr. Xingquan Wang, Dr. Jianpeng Liu, Dr. Lin Xiao, PhD candidate Jiacheng Li, and master candidates Xuejun Liu and Yichen Liu. In addition, we want to express our gratitude to the support from the National Natural Science Foundation of China (Grant Nos. 51925503, 52105575, and 12172359), Natural Science Foundation of Hubei Province (Grant No. 2020CFA028), China Postdoctoral Science Foundation (Grant Nos. 2020M672331 and 2022T150234), CAS Interdisciplinary Innovation Team (JCTD-2020- 03), and the help of the publisher. YongAn Huang YeWang Su Shan Jiang Wuhan, China Beijing, China Hangzhou, China
- 17. Contents 1 Structural Engineering of Flexible Electronics 1. 1 Introduction 1. 2 Applications of Flexible Electronics 1. 2. 1 Wearable Human Healthcare 1. 2. 2 Robotics and Haptic Interface 1. 2. 3 Smart Skin in Aircraft 1. 3 Structural Strategies 1. 3. 1 Wavy Strategy 1. 3. 2 Island-Bridge Strategy 1. 3. 3 Kirigami and Origami Strategy 1. 3. 4 Buckling-Driven Assembly Strategy 1. 3. 5 Structural Designs of Substrate 1. 4 Structural Opportunities by Materials 1. 5 Summary References 2 Buckling of Film-on-Substrate System in Flexible Electronics 2. 1 Introduction 2. 2 Formation of Film-on-Substrate Structure 2. 3 Island-Bridge Structure of Stretchable Electronics 2. 3. 1 Mechanical Model for the Bridge Structure 2. 3. 2 Mechanical Model for the Island Structure 2. 4 Temperature-Dependent Global Buckling Analysis and Structural Design 2. 4. 1 Geometrical Model and Governing Equations
- 18. 2. 4. 2 Structure Design Based on Temperature-Dependent Properties 2. 4. 3 Temperature-Dependent Local Buckling Analysis and Critical Condition 2. 5 Summary References 3 Buckling of Fiber-on-Substrate System in Flexible Electronics 3. 1 Introduction 3. 2 Fabrication of Buckled Fibers 3. 2. 1 Mechano-Electrospinning (MES) Technique for In- Surface Buckled Devices 3. 2. 2 Direct-Writing of Fibers onto a Pre-strained PDMS 3. 2. 3 Materials and Experimental Set-Up 3. 3 Buckling Behaviors of 1D Micro/ Nanowires 3. 3. 1 Out-of-Plane and In-Plane Buckling 3. 3. 2 Mechanics of Out-of-/ In-Surface Buckling 3. 3. 3 Competition of Buckling Modes 3. 4 In-Plane Buckled, Highly Stretchable Devices 3. 5 Performance of the Fabricated Stretchable Piezoelectric Device 3. 6 Summary References 4 Freestanding Fractal-Inspired Design for Stretchable Electronics 4. 1 Introduction 4. 2 Elasticity of Fractal Inspired Interconnects 4. 2. 1 Elastic Analysis of Fractal Interconnects 4. 2. 2 Experiments of the Fractal Structures
- 19. 4. 3 Fractal Designs in Stretchable Electronics 4. 3. 1 Mechanics and Electronics with Peano-Based Geometries 4. 3. 2 Fractal-Based Epidermal Electronics 4. 3. 3 Radio-Frequency Devices with Fractal Layouts 4. 4 Summary References 5 Fractal-Inspired Design on Substrate for Stretchable Electronics 5. 1 Introduction 5. 2 Mechanical Modeling of SSIs on Soft Substrate 5. 2. 1 Maximum Strain of Order-2 SSI 5. 2. 2 The Scale Law Formula 5. 2. 3 FEM Simulation Results 5. 3 Self-Similar Design of Surface Electrodes 5. 3. 1 Electromechanica l Design of Self-Similar Surface Electrodes 5. 3. 2 Electromechanica l Optimization Model 5. 3. 3 Feasible Range of the Geometric Parameters 5. 3. 4 Characterizationof Mechanical Performance 5. 4 Self-Similar Design for Stretchable Wireless LC Strain Sensors 5. 4. 1 Self-Similar Design for Wireless LC Strain Sensor 5. 4. 2 Structural Stretchability of the Self-Similar Strain Sensor 5. 4. 3 Strain-Induced Tunable Inductance 5. 4. 4 Experimental Platform and Sensitivity Analysis 5. 5 Summary
- 20. References 6 Conformal Design on Rigid Curved Substrate 6. 1 Introduction 6. 2 Theoretical Analysis Based on Energy Method 6. 2. 1 Energy Components of Thin Film 6. 2. 2 Energy Components of Substrate 6. 2. 3 Total Energy of Flexible Electronics 6. 3 1D Conformability of Membranes on Rigid Wavy Substrates 6. 3. 1 Analytical Interface Model by Work of Adhesion 6. 3. 2 Analytical Interface Model by Traction-Separation Relations 6. 4 2D Conformability of Island-Bridge Structures on Non- Developable Surfaces 6. 4. 1 Analytical Model 6. 4. 2 Adhesion Experiment 6. 4. 3 Adhesion Experiment for Island on Rigid Surface 6. 5 Summary References 7 Conformal Design on Soft Curved Substrate 7. 1 Introduction 7. 2 1D Conformability on Soft Substrates 7. 2. 1 1D Conformability of Epidermal Electronics on Soft Skin 7. 2. 2 1D Conformability of Epidermal Electronics on Soft Skin Under External Strain 7. 3 2D Conformability on Wavy Soft Substrates 7. 3. 1 2D Conformability of Epidermal Electronics on Soft Skin
- 21. 7. 3. 2 The Effects of the Roughness and Elastic Modulus of the Skin on Conformability 7. 3. 3 The Effects of the Substrate Thickness on Conformability 7. 3. 4 The Effects of the Areal Coverage of Electrode on Conformability 7. 3. 5 The Effects of the External Load on Conformability 7. 4 2D Conformability on Complex Soft Substrates 7. 4. 1 2D Conformability of Island on a Bicurvature Soft Substrate 7. 4. 2 The Effects of Geometry Parameters on Stable Conformal Contact 7. 4. 3 The Effects of Materials Parameters on Conformal Contact 7. 4. 4 Contact Pressure in Conformal Contact 7. 5 Local Failure Analysis of Island During Conformal Process 7. 5. 1 Conformal Strain in Island During Conformal Process 7. 5. 2 Wrinkling and Buckling Delamination During Conformal Process 7. 5. 3 Adhesion Experiment for Island on Soft Surface 7. 6 Summary References 8 In-Plane Design of Serpentine Interconnect on Substrate 8. 1 Introduction 8. 2 Thick Interconnects for Ultra-Large Stretchability 8. 3 Transition Between Wrinkling, Buckling and Scissoring 8. 3. 1 Transition from Wrinkling to Buckling 8. 3. 2 Transition from Buckling to Scissoring
- 22. 8. 4 Criteria for Three Modes 8. 4. 1 Stretchability in the Wrinkling Mode 8. 4. 2 Stretchability in the Buckling Mode 8. 4. 3 Stretchability in the Scissoring Mode 8. 5 Some Applications of Thick Interconnects 8. 5. 1 Interconnects for Stretchable Arrays of LEDs 8. 5. 2 Interconnects for Stretchable Arrays of Solar Cells 8. 5. 3 Traces for Stretchable RF Antennas 8. 6 Summary References 9 In-Plane Design for Serpentine Interconnect Without Substrate 9. 1 Introduction 9. 2 Buckling of Stretchable Serpentine Interconnects 9. 3 FPD Buckling Theory of Beams 9. 3. 1 Geometric Relations for the Finite Deformation of 3D Beams 9. 3. 2 Governing Equations for the FPD Buckling Analysis 9. 4 Application of Three Specific Cases 9. 4. 1 Lateral Buckling of a Three-Point-Bending Beam 9. 4. 2 Lateral Buckling of a Pure Bending Beam 9. 4. 3 Euler Buckling 9. 5 Sample Fabrication and Experimental Verification 9. 6 Summary References 10 Self-Assembly of Self-Similar Fibers for Stretchable Electronics 10. 1 Introduction
- 23. 10. 2 HE-Printing Technique for Fabrication of Self-Similar Nano/ Microfibers 10. 2. 1 HE-Printing Technique 10. 2. 2 Fabrication of Self-Similar Nano/ Microfibers 10. 3 Buckling-Driven Self-Assembly of Self-Similar Fiber-Based Structures 10. 3. 1 Buckling of Serpentine Fibers Under Uniaxial Prestrain 10. 3. 2 Buckling of Serpentine Fibers Under Biaxial Prestrain 10. 3. 3 Self-Assembly by Tuning In-/ Out-of-Surface Buckling 10. 4 Hyper-Stretchable Self-Powered Sensors Based on Self- Similar Piezoelectric Nano/ Microfibers 10. 4. 1 Hyper-Stretchable Self-Powered Sensors 10. 4. 2 Architecture of an HSS and HE-Printing Technique 10. 4. 3 Characterization s of the HSS 10. 4. 4 Applications of the HSS 10. 5 Summary References 11 Kirigami Strategy for Conformal Electronics 11. 1 Introduction 11. 2 Self-Healing Kirigami Assembly Strategy 11. 2. 1 Conformal Criterion for Kirigami Geometry 11. 2. 2 Geometrical Design Algorithm for 2D-to-3D Conformal Mapping 11. 2. 3 Preparation and Characterizationof the Ag/ PCL Self- Healing Materials 11. 2. 4 Kirigami-Based Conformal Heater
- 24. 11. 2. 5 Multifunctional Wind Sensing System 11. 3 Soft-Hinge Kirigami Metamaterials for Self-Adaptive Conformal Electronic Armor 11. 3. 1 Deformation Mechanism of Soft-Hinge Kiri-MMs 11. 3. 2 Stretchability, Flexibility and Conformability of Soft- Hinge Kiri-MMs 11. 3. 3 Electrical Enhancements with Conductive Polymer Composite 11. 3. 4 Functional Soft-Hinge Kiri-MM E-armor Systems 11. 4 Summary References 12 Neutral Layer Design for Flexible Electronics 12. 1 Introduction 12. 2 Mechanics of Neutral Mechanical Plane 12. 3 The Effect of Length on Splitting of the Multiple Neutral Mechanical Plane 12. 4 The Effect of Boundary Conditions on Splitting of the Neutral Mechanical Plane 12. 4. 1 Given Slopes Are Imposed at the Ends of the Hard Layers 12. 4. 2 Given Slopes Are Imposed at the End Sections 12. 5 Effects of the Membrane Energy and Bending Energy of the Middle Layer 12. 5. 1 The Model Incorporating the Shear Energy, Membrane Energy and Bending Energy of the Middle Layer 12. 5. 2 The Model Neglecting the Shear Energy of the Middle Layer 12. 6 Summary References
- 25. 13 Liquid Metal-Based Structure Design for Stretchable Electronics 13. 1 Introduction 13. 2 Microfluidic Serpentine Antennas with Designed Mechanical Tunability 13. 2. 1 Galium-Based Eutectic Alloys 13. 2. 2 The Design of Serpentine Microfluidic Antenna 13. 2. 3 Fabrication of the Serpentine Microfluidic Antennas 13. 2. 4 Characterizationof the Serpentine Microfluidic Antennas 13. 3 Liquid–Metal Antennas with Stable Working Frequency for RFID Applications 13. 3. 1 Serpentine Liquid–Metal Antennas for RFID 13. 3. 2 Design of Stretchable RF Antennas 13. 3. 3 Relationship Between Stretchability and Resonant Frequency 13. 4 Liquid Metal Nanoparticles (LMNPs) for Ultrathin, Flexible Metasurface 13. 4. 1 Liquid Metal Metasurface 13. 4. 2 Sintering Process of LMNPs 13. 4. 3 Electromagnetic Performance 13. 5 Summary References 14 Applications of Flexible Electronics 14. 1 Introduction 14. 2 Application of Flexible Electronics as E-tattoos 14. 2. 1 Low-Cost, μm-Thick, and Tape-Free E-tattoos 14. 2. 2 Characterizationof Wearability and Motion Artifacts
- 26. 14. 2. 3 Applications of the Large-Area Epidermal Electrodes on Human Skin 14. 3 Application of Flexible Electronics as Implantable Cardiac Membranes 14. 3. 1 3D Multifunctional Integumentary Cardiac Membranes 14. 3. 2 Design of Conformability 14. 3. 3 Spatiotemporal Cardiac Measurements 14. 4 Application of Flexible Electronics as Aircraft Smart Skin 14. 4. 1 Design of the Multifunctional, Flexible Sensing Skin 14. 4. 2 External Airflow Multifunctional Perception 14. 4. 3 Internal Structural Health Monitoring 14. 5 Application of Flexible Electronics as Robotic Interface 14. 5. 1 Design and System Architecture of 3D-Shaped E-skin 14. 5. 2 Fabrication of the 3D-Shaped E-skin 14. 6 Summary References
- 27. (1) (2) (3) © Science Press 2022 Y. Huang et al., Flexible Electronics https://doi.org/10.1007/978-981-19-6623-1_1 1. Structural Engineering of Flexible Electronics YongAn Huang1 , YeWang Su2 and Shan Jiang3 State Key Laboratory of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology, Wuhan, China Institute of Mechanics, Chinese Academy of Sciences, Beijing, China Hangzhou Institute of Technology, Xidian University, Hangzhou, China YongAn Huang (Corresponding author) Email: yahuang@hust.edu.cn YeWang Su Email: yewangsu@imech.ac.cn Shan Jiang Email: jiangshan_hust@163.com 1.1 Introduction Over the last two decades, extensive efforts on advanced functional materials and flexible structural designs have been implemented to improve flexible electronics. Structural engineering of flexible electronics that contain conventional stiff, non-stretchable, and even brittle materials such as piezoelectrics and silicons has proven its unique advantages compared to the intrinsically flexible and stretchable materials. Despite low yield strain (typically below 1%), such conventional materials can provide high performance and
- 28. reliability. The structural engineering can bridge the gap between the large deformation and inorganic materials, by which low-modulus mechanics of high-modulus materials can be achieved to accommodate extreme mechanical deformations. While applied research in this area has been abundant in recent years, review from the standpoint of fundamental mechanics is needed to advance the field in new directions. For example, the new opportunities and challenges of flexible electronics derived from the conceptual breakthroughs of emerging mechanical metamaterials. The rest of this chapter is organized as follows. In Sect. 1.2, several representative application scenarios are demonstrated to show the significance of flexible electronics. In Sect. 1.3, an overview of historical developments of structural engineering of flexible electronics is presented with a focus on the pioneering achievements, from initial wavy strategies to subsequent self-assembly strategies and then to flexible mechanical metamaterials. In Sect. 1.4, from the view of structural opportunities, several common advanced functional materials are discussed. Finally, in Sect. 1.5, perspectives on the remaining challenges and open opportunities in the mechanically- guided structural engineering of flexible electronics are offered. 1.2 Applications of Flexible Electronics Flexible electronics that can apply on complex curvilinear surfaces have aroused extensive interest and become one of the greatest concerned, cutting-edge interdisciplines. They have broad innovative application prospects like wearable electronics [1], epidermal electronics [2], robotic skin [3], and aircraft smart skin [4]. The requirements of flexible electronics differ from application to application, from bendability and rollability for easier handling of large area photovoltaics, to conformability onto irregular shapes, and to hybrid of stretchability, twistability, foldability, and deformability for electronic skin. This section will present some representative application scenarios, offering insights into the significance of structural engineering of flexible electronics. 1.2.1 Wearable Human Healthcare
- 29. Flexible electronics can be built into our clothes and accessories, attached to our skin, and even implanted in our bodies. The corresponding branches are wearable electronics [5, 6, 7], epidermal electronics [2, 8, 9], and implantable electronics [10–13], respectively (Fig. 1.1). Such bioelectronics have been changing conventional medical diagnoses by endowing them with combined features of wearability, comfortability, remote operation, and timely feedback. Specifically, they can be utilized for continuous, noninvasive, real-time, and comfortable monitoring of vital biometric signs, which provide important clinically related information for disease diagnosis, preventive healthcare, and rehabilitation care [14, 15]. In a word, flexible electronics offer bright promise for next-generation healthcare and biomedical applications.
- 30. Fig. 1.1 Flexible electronics can be used as wearable electronics [5–7], epidermal devices [2, 8, 9], and implantable electronics [12, 13] Various physical and physiological signals can be measured by wearable electronics, such as electrophysiological signals [16, 17], body motion [18], and muscle movement [19] (e.g., walking, jogging, and eye blinking). Such real-time monitoring of muscle activities is useful for clinical gait analysis and muscle fatigue evaluation, which can improve exercise performance and even prevent unexpected catastrophic situations. With epidermal electronics, vital physiological signals, such as pulse, heart and respiration rate, body temperature, and skin and breath moisture, can be continuously and long-timely tracked in a mechanically unfeelable manner [20, 21]. In this way, chronic diseases like diabetes and glaucoma can be effectively diagnosed and managed with noninvasive, transcutaneous therapeutic treatment. Moreover, with the advent of biocompatible and bioresorbable materials, implantable electronics have been developed for in vivo recording of internal conditions, such as intracranial pressure [22], biochemical constituents (e.g., metabolites and electrolytes) [23], and electrophysiological signals [24] (e.g., electrocardiogram, ECG; electromyogram, EMG; electroencephalogram, EEG; electrooculogram, EOG; and electroglottogram, EGG). Direct contact with the dynamic curvilinear tissues and organs can provide accurate neural and physiological signals. One of the most challenges of flexible electronics for human applications is how to maintain intimate and effective contact with the complex, time-dynamic surfaces of skin, tissues and organs during service [25]. For example, organs such as the heart, arteries, and alveoli undergo periodic areal strains of up to several tens of percent. Structural engineering and materials engineering are two main strategies. Structural engineering can circumvent the high threshold of intrinsically flexible/stretchable materials. Moreover, rational structural designs can not only enable the stretchability of conventional stiff, non-stretchable, and even brittle materials, but realize the programmable deformability of such materials to better adapt the targeted surfaces. 1.2.2 Robotics and Haptic Interface
- 31. The research of robotics has grown into a popular field in the past few years (Fig. 1.2a) [26]. Electronic skin (E-skin) is the most intuitive application of flexible electronics in robotics to enhance perceptibility and interactivity, which is emerging rapidly with the goal of matching or even surpassing the performance of human skin (Fig. 1.2b, c) [27, 28]. Moreover, soft robots can integrate E-skin and soft actuators to achieve integrated control of sensing and driving (Fig. 1.2d, e) [29–32], and programmability and multifunction [33]. With the increasing demand, flexible electronics have broad application prospects in the field of soft robots [34]. Mechanical compliance is a prerequisite for E- skin to accommodate complex dynamic environments while maintaining its multiple functionalities. In this regard, structural engineering of E-skin has been developed for compliant designs, enabling the integration of imperceptible sensing systems with great conformability to 3D surfaces.
- 32. Fig. 1.2 Flexible electronics in soft robotics. a Human–machine interaction [26]. b Electronic skin [28]. c Prosthetic skin [27]. d Self-powered soft robot [31]. e Soft, autonomous robots [32]. f Programmable, reprocessable multifunctional soft robots [33] More importantly, analogy to human skin, E-skin should exhibit extraordinary sensing abilities for numerous tactile and thermal stimuli, object recognition, texture discrimination, slip detection, sensory-motor feedback, etc. The flexible sensors are the key to realizing this goal. Taking the flexible pressure sensors as examples, microstructural engineering of the active layers is one of the most
- 33. admirable strategies to enhance the performance of flexible sensors like sensitivity, linearity, and sensing range. Common microstructural designs include regular pyramids [29, 35], hemispheres [30], and pillars [36, 37]. Moreover, bioinspired hierarchical structural arrays [38], randomly distributed spinosum [39], and bioinspired cone arrays [40] have been proposed successively. Recently, Bai et al. reported an iontronic pressure sensor with ultra-broad-range high sensitivity based on graded intrafillable architecture [41]. Ji et al. synergistically optimized the sensitivity and linearity of flexible pressure sensors via double conductive layer and porous microdome array [42]. Not long ago, Liu et al. introduced Origami designs to broaden the sensing range of flexible sensors [43]. In the future, continuous breakthroughs of structural engineering for the applications of flexible electronics in soft robotics will appear, such as the introduction of emerging mechanical metamaterials [44, 45], and the structural design of a driving-sensing integrated strategy suitable for soft robots. 1.2.3 Smart Skin in Aircraft Recently, the demands of flexible electronics applied in the field of aeronautics are increasing such as the flexible smart sensing skin [4, 46–49]. The flexible smart sensing skin can realize the in-situ measurement of aerodynamic parameters without changing the structure attributes and flow field environment, making it a promising candidate in wind tunnel test, unmanned driving, morphing aircraft, and other related fields. Compared with the traditional method of pressure taps [50], the pressure-sensitive paint [51], and the conventional smart skin [52], recent significant technical advances in flexible electronics have overcome many historic drawbacks, e.g., avoidance of the inevitable structural damage and significant increase of weight, real-time and in-situ measurement, and high-density sensing network. However, unlike the applications in human and robots, the extreme operating environments of aircrafts impose strict limitations to the materials. The widely used intrinsically flexible/stretchable materials, such as PDMS and Ecoflex, are incompetent and unsuitable for such situations due to insufficient strength, temperature sensitivity (low glass-transition temperature), high-frequency fitration, and so on. Therefore, the structural engineering of flexible electronics made of
- 34. conventional stiff, stable, and high-performace materials is natural and sagacious choice. Furthermore, the intelligent flexible sensing (iFlexSense) skin is a key enabling technology for the wind tunnel test and the future “Fly-by- Feel” control of morphing aircraft (Fig. 1.3). It represents the next- generation skin of aircraft that can exhibit more powerful sensing functions. The smart skin can “feel”, “think”, and “react” in real time based on high-resolution state-sensing, awareness, and self-diagnostic capabilities, endowing the aircraft with the ability to change shape according to the fly states and structural health [4]. Undoubtedly, such advanced functions pose great challenges to the mechanical properties of the flexible smart sensing skin, especially for the deformability. It should hold extra features: (i) capability of adaptive deformation with the infrastructural skin, (ii) low membrane stiffness to allow small actuation requirement, (iii) effectively sensing air loads while maintaining initial surface geometry, and (iv) high elasticity and recovery to allow multiple cycles of deformation [53]. Empirically and reasonably, the realization of these targets mainly relies on the structural engineering of flexible electronics. Predictably, future aircrafts with more controlled systems will lead to the increasing need for flexible electronics applied on the aircraft surface. Fig. 1.3 Intelligent flexible sensing (iFlexSense) skin for aircraft [54] 1.3 Structural Strategies
- 35. 1.3.1 Wavy Strategy The wavy strategy was first proposed in the pioneering work of flexible electronics in 2006, in which flexible devices made of single-crystal silicon were buckled into microscale, periodic, and wavy shapes [55]. Thin silicon ribbons (20 ~ 320 nm) were firstly fabricated by lithographic processing and then transferred to the surface of a pre- strained elastomer substrate (e.g., PDMS). After releasing the pre- strain, the silicon ribbons were compressed to wavy structures. Wavy silicon can be reversibly stretched and compressed to large levels of strain without damage. The strains of the whole system during deformation are accommodated mainly through changes of the wavelengths and amplitudes of the wavy structures rather than the mechanical properties of materials. The wavy silicon ribbons of 100 nm thickness can be stretched up to 30% that overwhelms the 1% strain limit of silicon. Such strategy renders the conventional stiff, nonstretchable, and even brittle materials sufficiently deformable to act as flexible electronics. It not only allows large-scale stretchability without degradation in electronic performances, but also realizes good conformability on complex surfaces. The wavy strategies pave the new way for the structural engineering of flexible electronics. Many mechanical models have been established to analyze the configuration of wavy structures. In the beginning, under the small- deformation assumption (<5%) and the principle of minimum potential energy, Khang et al. [55] and Huang et al. [56] developed an energetic method to describe the buckling behaviors, in which the out-of-plane displacement is assumed as a sinusoidal profile. Afterward, considering the practical large deformations (>5%), Jiang et al. [57] and Song et al. [58] developed a nonlinear finite-deformation model, by which the wavelength and amplitude of wavy profile can be predicted. Following this direction, the theoretical framework is gradually and continuously improved, and more and more situations are considered, including post-buckling [59], finite-width effect [60], local versus global buckling [61], thermomechanical analysis [62, 63], adhesion-governed buckling [64], rigid/soft wavy surfaces [65, 66], 1D/2D wavy surfaces [67, 68], and moderately large-deflection theory [69]. Relying on the underlying mechanisms, the wavy designs are widely applied in flexible electronics. Initially, Khang et al. presented a stretchable single-crystal
- 36. silicon p-n diode on a PDMS substrate at −11%(top), 0% (middle), and 11% (bottom) applied strains [55]. Furthermore, Kim et al. demonstrated stretchable and foldable silicon integrated circuits based on 2D wavy designs [70]. Ko et al. realized the wrapping of a silicon membrane circuit on a golf ball (Fig. 1.4a) [71]. Noteworthily, except for the full bonding method, the selective bonding method is also widely used to generate wavy structures on the elastomeric substrates. For example, Sun et al. constructed metal–semiconductor field-effect transistors based on buckled wavy GaAs ribbons [72]. Fig. 1.4 Various structure strategies in stretchable electronics: a Wavy [71], b serpentine [73], c self-similar [74] strategies 1.3.2 Island-Bridge Strategy Originating from and then beyond the wavy strategies, the island- bridge strategies were proposed to achieve higher levels of stretchability. The non-stretchable functional components reside at the low-strain islands and the stretchable interconnects form the bridges to accommodate the mechanical stretchability and electrical conductivity. Due to the much lower stiffness of the bridges than the islands, the islands and adhered functional devices are mechanically isolated. In other words, the key point of island-bridge strategies lies in the design of bridges. By now, there are three representative successful cases, namely arc-shaped [75, 76], serpentine [77–80], and fractal interconnects [74, 81–83]. Since the arc-shaped designs are very similar to the wavy strategies in the previous section, here we mainly introduce the latter two.
- 37. Arc-shaped interconnects. Under stretching and compression, switch- on/off of out-of-plane buckling of arc-shaped interconnects can accommodate the applied strain. Initially, the arc-shaped interconnects were usually treated as clamped beams or films, and the out-of-plane buckling displacement was assumed as sinusoidal profiles [75]. After that, to break the limitation of the sinusoidal assumption for the large displacements, a finite-deformation theoretical model was developed, which can offer a more accurate prediction of the amplitude [84]. Wang et al. presented a systematic analysis for the buckling behaviors and gave the critical criteria, by which the buckling behaviors are determined by the relationship between pre-strain and adhesion and the modes can be subdivided into global buckling, local buckling, and no buckling [85]. Serpentine interconnects. The serpentine strategy was firstly applied in the milestone work of epidermal electronics in 2011 [2], in which the concept of epidermal electronics was defined. With the filamentary serpentine designs, the system provided elastic, reversible responses to large-strain deformations with effective moduli (<150 kPa), bending stiffnesses (<1 nN/m), and areal mass densities (<3.8 mg/cm2 ). Those merits are in orders of magnitude smaller than those possible with conventional electronics or even with recently explored flexible devices. Thereafter, the filamentary serpentine interconnects have been widely explored in flexible electronics. A representative example is the soft microfluidic assemblies of sensors, circuits, and radios for the skin, in which strain-isolated device components are connected by a freestanding serpentine interconnecting network (Fig. 1.4b) [73]. A systematic and comprehensive investigation of mechanical behaviors in such serpentine interconnects has been performed by researchers. In earlier research, the serpentine interconnects were mostly freestanding and the stretchability relies on the folding, tenuous, and thin designs. Zhang et al. developed analytical models to reveal the buckling mechanisms in such stretchable serpentine microstructures, including the buckling and post-buckling behaviors [80]. A scaling law was established to determine the critical buckling strain, by which symmetric and anti-symmetric buckling modes were identified. Soon after, Zhang et al. further proposed a pre-strain
- 38. approach that can significantly improve the stretchability (more than two times) compared to the situation without pre-strain [86]. The analytical model can not only effectively predict the wavelength but also explain the influence of thickness, offering a rational method to obtain the desired stretchability. Moreover, in 2016, Su et al. introduced a different route to design the serpentine interconnects, where tenuous and freestanding geometries were substituted by thick and bonded layouts to enhance the mechanical and electrical performance [87]. The in-plane and out- of-plane buckling modes were replaced by pure in-plane scissor-like deformations. More specifically, with the increase of thickness, the deformation mechanisms change from wrinkling (localized, multiwave, out-of-plane buckling) to buckling (coupled out-of-plane buckling and twisting) and then to scissoring (pure in-plane bending deformation). The scissor-like deformations significantly increased stretchability from 20% for thin, buckling interconnects to ~ 100% for thick, scissoring interconnects. The findings provide a significant supplement and open a new direction for the design of serpentine interconnects. In addition, Yang et al. proposed a “cut-and-paste” process to manufacture the multiparametric epidermal sensing systems based on the serpentine designs [88]. Pan et al. discussed the effect of substrate thickness and concluded that the reduction of the substrate can improve the stretchability [89]. Fractal interconnects. Aiming to reconcile the mutually exclusive requirements of large stretchability and high-area coverage, fractal design concepts were introduced for stretchable electronics. Before that, Zhang et al. showed the increase of surface filling ratios by increasing the fractal order from 1 to 4 [81]. As with the other strategies, fractal interconnects can also be divided into freestanding and bonding layouts. For the freestanding situation, the deformations can be further divided into pure in-plane stretching for large thickness- width ratio (>1) and spatial buckling for small thickness-width ratio (<1/5). For the former case, Zhang et al. gave recursive formulae to describe the relationship between fractal orders and flexibility and stretchability [81]. For the latter case, Xu et al. propounded ordered unraveling mechanisms to interpret the deformations [82]. In addition
- 39. to the abovementioned serpentine shape, fractal designs can be applied to many other shapes [83, 90], e.g., zigzag, sinusoidal, and horseshoe. Su et al. developed an analytic method to directly compute the elastic energy and the tensile stiffness of fractal interconnects of arbitrary order n and in arbitrary shape [83]. Furthermore, Dong et al. investigated the bonding configuration of such interconnects with the elastomer substrate [91, 92]. By dint of the simultaneous large stretchability and high-area coverage, fractal interconnects used as bridges between mechanically isolated islands have shown unique advantages in stretchable lithium- ion batteries [82], epidermal electronics (Fig. 1.4c) [74], and radio- frequency antennas [93]. Furthermore, fractal designs can also enhance conformability on soft, curvilinear surfaces, which are meaningful for applications in bio-systems. Xu et al. presented a fractal electrode array distributed over a rabbit heart circumference to deliver cardiac electrical stimulation and sense cardiac electrical activity [94]. Moreover, fractal electrodes are conformable to more complex biological surfaces, in which the fractal electrode meshes can be directly and chronically mounted on the complex surfaces of the auricle and the mastoid [95]. The case of the auricle proved another advantage of fractal interconnects, namely directional guided deformability to match the complex topology of the auricle. Specifically, all-vertical Peano curves were used to get selective high stretchability along with the longitudinal coordinates. 1.3.3 Kirigami and Origami Strategy Recently, the concept of Kirigami mechanical metamaterials (Kiri-MMs) has been introduced into the design of flexible electronics [54]. The salient structural traits including negative Poisson’s ratio [44, 96], ultra-stretchability [97–100], mechanical programmability [101–105], and transformability from 2 to 3D [106–108] provide a brand-new research strategy. Specifically, the programmability enables the possibility to fit arbitrary curvilinear surfaces [105], and the transformability from 2 to 3D is a perfect solution to the contradiction between 2D planar processing technology and 3D conformal demands [106, 109]. Compared with other thin open-mesh serpentine or island- bridge strategies introduced above, Kirigami structures have a high fill
- 40. factor, which are particularly desirable for high-density sensing or high- resolution imaging [110]. In the early stage, graphene Kirigami was an impressive example to demonstrate the salient traits of Kirigami [111], by which one-atom-thick graphene sheets were transformed into resilient and morphing structures without sacrificing electrical performance. By now, Kirigami-inspired creative applications have become abundant, including self-powered strain sensor (Fig. 1.5a) [112], soft crawler (Fig. 1.5b) [113], morphable stent (Fig. 1.5c) [114], shoe grip (Fig. 1.5d) [115], adaptive imager (Fig. 1.5e) [110], and flexible car shell [116]. The underlying mechanism of Kirigami structures relies on the local buckling of hinges under low-energy loads to empower the whole structural reconfigurability. Rafsanjani and Bertoldi investigated the mechanisms of the buckling-induced Kirigami and studied how the behavior evolves when the thickness is progressively decreased [109]. However, all these creative buckling-driven traits are poles apart from the fully conformal goals of flexible electronics that require coating as smooth as possible. Current studies mostly directly make use of the buckling-induced traits, but how to restrain buckling while keeping extraordinary mechanical properties of Kiri-MMs remains open. As a note, despite non-stretchable PI used in curvy, shape-adaptive imagers, the ultrathin thickness (~5 μm) makes the devices sufficiently compliant [110]. To address this challenge, we show that using soft material at the hinges of Kiri-MM can restrain this local buckling effect and improve conformability [117], which will be presented in the following chapter.
- 41. Fig. 1.5 Kirigami strategy: a self-powered strain sensor [112], b soft crawler [113], c morphable stent [114], d shoe grip [115], and e adaptive imager [110] As for the design methods, fractal Kirigami can further enhance the stretchability. Programmable Kirigami mechanical metamaterials are becoming popular. Choi et al. propounded a meaningful inverse Kirigami design method, in which the cutting path was determined by objective and constrained functions derived from targeted conformal shapes [105]. Most recently, based on the computer graphics, Jiang et al. presented an affirmative solution to realize the targeted programmability of Kirigami sheet between arbitrary shapes, in particular between a 2D sheet and a 3D curved surface [118]. This so- called inverse problem for Kirigami cut and fold patterns is solved by drawing on a differential-geometric interpretation of the morph and progress in geometric computing. Therefore, it is convinced that Kirigami will be a powerful strategy to design the flexible electronics. As the twin concept of Kirigami, Origami is another admired strategy to build wonderful structures. Because of the ability to hold creases and bend at will, a 2D sheet can be folded into arbitrary shapes. The mechanisms of Origami have been widely studied for a very long time, including mathematics [119], geometry [120], and compliant mechanisms [121]. Many Origami strategies have been proposed like
- 42. Miura-ori and its variants, Ron Resch’s tessellation, and square twist. Either way, the kernel always roots in the crease patterns. Mechanically, the creases act as soft hinges to connect the stiffer facets, and the low- energy deformation of the creases induces the morphability of the whole Origami structures (Fig. 1.6a) [122]. Similar to previous “island- bridge” strategies, the strain-free facets between the creases are uniquely suited as the integration platform to mount active devices of flexible electronics. Moreover, as Origami-based mechanisms often feature multiple discrete folding motions, they enable the realization of programmable 3D multishapes. In a nutshell, Origami has many ideal characteristics: monolithic preparation, scale-independent, perfect self- assembly compatibility, and unlimited design space based on rich folding patterns, making it very suitable for applications in flexible electronics. Fig. 1.6 Origami strategy. a Transformable Origami with multiple degrees of freedom [122]. b Ori-MMs-based silicon optoelectronics for hemispherical electronic eye systems. Reproduced with permission [128]. c Ori-MMs-based conformal electronics made of non-stretchable materials [131]. d Origami-based electrothermal devices [132]. e Stretchable Origami robotic arm [133]. f Origami- based wide-range flexible capacitive pressure sensors [43] Recently, Origami has been explored for applications in many engineering fields, e.g., compactly deployable solar arrays for space applications [123], self-folding crawling robots for machine manufacturing [124], and medical stents for biomedical applications [125]. Its strut in flexible electronics may start from the Origami
- 43. lithium-ion batteries proposed in 2014 [126]. This Origami battery exhibited stable and reliable performances under large cycles of mechanical deformations. By utilizing printable ZnO nanowires and carbon electrodes, Lin et al. developed a stretchable and deformable Origami photodetector array based on the Miura-ori strategy [127]. The Origami photodetector array can provide excellent capabilities of omnidirectional photodetection. Furthermore, Zhang et al. developed Origami silicon optoelectronics for dense, scalable, and compact hemispherical electronic eye systems [128] (Fig. 1.6b), which were compatible with mature complementary metal–oxide–semiconductor (CMOS) technologies that enable deployments in extremely high density. In the same period, Origami was introduced to fabricate a flexible and foldable thermoelectric nanogenerator [129]. Most recently, Qi et al. displayed reconfigurable flexible electronics driven by Origami magnetic membranes [130]. In addition, Origami can be adopted to realize full wrapping of conformal electronics made of non- stretchable materials (Fig. 1.6c) [131], to structure electrothermal devices with controllable multi-degrees-of-freedom shape morphing (Fig. 1.6d) [132], to enable stretchable robotic arm with omnidirectional bending and twisting soft robotics (Fig. 1.6e) [133], and to devise wide-range flexible capacitive pressure sensors (Fig. 1.6f) [43]. Incidentally, a number of computer-aided tools to Origami such as TreeMaker and Oripa have been developed. TreeMaker allows new Origami bases to be designed for special purposes and Oripa tries to calculate the folded shape from the crease pattern. All these achievements demonstrate the potential of the Origami to develop spatial flexible electronics. 1.3.4 Buckling-Driven Assembly Strategy Buckling-driven assembly strategy is another milestone of structural engineering of flexible electronics (Fig. 1.7) [134]. It relies on the control of buckling to realize 2D-to-3D transformation, with the release of prestrained elastomer substrate to provide initial mechanical drive and vice versa. It can be reversibly stretched and buckled between 2D and 3D configurations without degradation of performance even with a large number of cyclic loadings [106, 135, 136]. The 3D stretchable multifunctional photodetector is a convincing paradigm for the
- 44. effectiveness of the buckling-driven assembly strategy [137]. The interconnects of the device exploit a sandwich configuration, with the graphene encased by two SU-8 layers, and then the SU-8 layers are buckled into a hemispherical structure, rendering a 3D arrangement of the MoS2 patches that serve as photodetecting elements. The advantages include (i) the concurrent tracking of the direction and intensity of the incident light, (ii) optically transparent system allowing the detection of incident angles, and (iii) high geometrical extensibility like an octagonal prism and an octagonal prismoid. Note that these merits cannot be easily achieved by photodetector arrays in planar layouts. Fig. 1.7 Buckling-driven assembly strategy. a Schematic illustration of the assembly process guided by controlled buckling [134]. b 3D Origami micro/nanostructures [138]. c 3D Kirigami mesostructures [106] Except for the compressive buckling, the 3D assembly can be also realized by tensile buckling that can circumvent the pre-stretching limit [139]. When the substrate is stretched uniaxially, the nonbonded regions of the 2D precursor are delaminated from the substrate, resulting in a 3D transformation through coordinated bending/twisting deformations and translational/rotational motions. The derivative
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