Hierarchical Wrinkling‐Cracking Architectures for Flexible Pressure Sensors

Inspired by butterfly wing architectures, a facile but efficient approach is developed to realize three sensing characteristics in a single pressure sensor by harnessing hierarchical wrinkling‐cracking architectures, including i) wrinkling‐dominant (WD) mode, ii) wrinkling and cracking‐dominant (WCD) mode, and iii) cracking‐dominant (CD) mode. The pressure sensor can exhibit distinct sensing performances for various specific applications, depending on the working mode. In a WD mode, the sensor reveals an ultrahigh sensitivity (≈20 kPa−1) and a low limit of detection (0.6 Pa), capable of sensing acoustic vibrations, subtle pulses, and tiny motions. The sensor in WCD mode can monitor the full‐range human motion from the subtle pulse to human gait during walking/jogging. Moreover, the sensor in CD mode exhibits high sensitivity (1420 MPa−1) and excellent linearity over the ultrahigh pressure range (greater than 20 MPa), and are able to detect the movement of a car and distinguish the embarkation/debarkation of an adult passenger. The underlying mechanisms for the three sensing modes have been clearly elucidated, respectively. These findings open up new possibilities to design flexible pressure sensors by harnessing wrinkling‐cracking architectures.


Introduction
Flexible pressure sensors hold great promise for a variety of domains such as implantable or skin-mounted electronics, wearable robotics, artificial intelligence, and prosthetic manipulation. [1][2][3] Based on transduction mechanisms, the pressure In fact, there is no concrete guideline as to what constitutes a high or low sensitivity and a broad or narrow sensing range. [40] The exact sensitivity required depends on the target application scenarios of different strain ranges. For instance, a high sensitivity (>10 kPa −1 ) is required to monitor the subtle vibrations and sound waves (a pressure range of <10 Pa). To mimic the tactile sensing capabilities of the human skin, from pulse pressure to foot pressure, a moderate sensitivity (>1 kPa −1 ) over a pressure range of 10 Pa to 300 kPa is usually sufficient. Additionally, the relatively low sensitivity (≈1 kPa −1 ) over a pressure range of >300 kPa, even up to several MPa, meets the demand of detecting strong pressures when robot hands manipulating heavy objects. It is challenging for a single sensor to achieve a high sensitivity over an ultra-broad sensing range, and thus persuading a pressure sensor system with adjustable sensitivity under different sensing ranges is desirable for various applications. Yet, until now, how to effectively design and facilely fabricate such a pressure sensor is rarely reported.
Nature-inspired materials with intriguing hierarchical architectures over several length scales often exhibit remarkable physical, chemical and mechanical properties. [41][42][43] For instance, the 3D hierarchical micro/nanostructures on scales of butterfly endow its wings with excellent physical properties, which have been mimicked or replicated for various applications, such as photonic crystals, [44] superhydrophobicity, smart adhesion [45] and vapor sensors. [46] The scales are composed of periodic sub-microscale cuticle ridges, and a single cuticle ridge consists of nanoscale densely packed chitin ridges (Figure 1a). Inspired by the hierarchical micro/nanostructures of Morpho butterfly, we developed a novel and facile strategy to fabricate the metal film/soft substrate bilayers with hierarchical wrinkling and cracking architectures, in which ordered cracks divide the metal film into "scales" and the hierarchical wrinkles mimic the "densely stacked ridges" on scales. A flexible pressure sensor based on the bio-inspired bilayers is further developed, capable of detecting an extremely broad pressure range including acoustic sound recognition (<∼1 kPa), human physiological activities (≈1-300 kPa) and heavy object manipulation (≈20 MPa). The novelty of this work lies in i) introducing controlled cracks in pressure sensor to enhance the sensitivity of pressure sensor in the high-pressure region and significantly broaden the sensing range; ii) achieving three kinds of sensing characteristics based on the same material systems but different configurations (modes).

Design and Preparation of the Pressure Sensor
Cracking and wrinkling, common failure modes under tension and compression in bilayer heterogeneous systems, www.advmatinterfaces.de respectively, are usually considered as defects to be avoided. Recently, the spontaneously formed wrinkling and cracking patterns have been widely exploited to achieve various functionalities, such as smart stretchable electronics, [47] tunable adhesion [48] and wetting, [48] optical properties, [49] nanoplatelet fabrication, [50] and measurement of film/substrate properties. [51] Here, we present a cracking-and wrinkling-engineering strategy to design a flexible pressure sensor. A schematic of the fabrication process is illustrated in Figure 1b. In step i), a poly(dimethyl siloxane) (PDMS) sheet was uniaxially stretched and then exposed to ultraviolet/ozone (UVO) radiation. After releasing the prestrain, periodic stripe wrinkles spontaneously formed perpendicular to the prestrain direction due to the formation of a thin and rigid oxidation layer of SiO x on PDMS. The wrinkled SiO x /PDMS system was used as a template to replicate a pattern of microscale wrinkles (3rd generation, G3) on another PDMS surface. In step ii), the replicated PDMS sheet was stretched and exposed to oxygen plasma (OP), followed by two steps of prestrain relaxation. Upon the sequential release of 20% and 20% prestrain, the nanoscale (1st generation, G1) wrinkles and microscale (2nd generation, G2) wrinkles were generated on the greater (G3) wrinkles, respectively, constructing a nested hierarchical wrinkling structure (Figure 1c-e). The smaller wrinkles rest parallel to and on the larger wrinkles. Both scanning electron microscopy (SEM) and atomic force microscopy (AFM) observations reveal that the wavelengths λ are ≈900 nm for G1, ≈3 µm for G2 and ≈63 µm for G3, respectively. Simultaneously, crack arrays parallel to the prestrain direction can be controllably created in a spontaneous manner due to the mismatch in Poisson's ratio between the oxidation layer and the PDMS sheet. In step iii), Ag films were deposited on the hierarchically wrinkled PDMS substrates via magnetron sputtering. More details on the materials and sensor preparation are provided in Methods Section (Supporting Information). Note that the dimensions of multiscale wrinkles can be independently manipulated, e.g., the G3 wrinkle dimensions depend on the UVO treatment time and prestrain magnitude, and the G1 and G2 wrinkle dimensions rely on the OP treatment time and prestrain magnitude ( Figure S1, Supporting Information).

Wrinkling-Dominant Sensing Characteristics and Mechanism
The sensing mechanism originates from the pressing forcedependent contact between the top and bottom hierarchical nested wrinkles (Figure 2a). At the pristine state, the top and bottom wrinkled Ag/PDMS sheets only partially contact each other. Upon applying a subtle pressure, the contact area of the interlocked ridges (wrinkles) significantly increases, leading to more conductive pathways and thus a decrease in resistance. To investigate the sensing characteristics, the electrical resistance (R) was measured in real-time as a function of the applied pressure (P) under constant operating voltage. Figure 2b shows the relative resistance change ( / 0 R R ∆ ) as a function of pressure (P), where / 0 R R ∆ first decreases rapidly and then slowly as P increases, in accordance with the common phenomenon in pressure sensors. [11] The S is the change in resistance divided by the product of the initial resistance and the mechanical pressure, i.e., ( / )/ 0 S R R P = ∆ ∆ . Our sensor exhibits a high sensitivity of −18.2 kPa −1 at a low-pressure range from 0.06 Pa to 0.2 kPa and a low sensitivity of −1.2 kPa −1 within the pressure range from 0.2 to 2.0 kPa. An ultralow detection limit of 0.06 Pa was demonstrated by using a Platanus orientalis seed ( Figure 2c). Here, the wrinkle orientations of the upper and lower sheets are parallel to each other, because the parallel assembled sensor shows higher sensitivity than the perpendicularly assembled sensor ( Figure S2, Supporting Information). The interlocked wrinkles are reminiscent of the interlocked ridge structures between the dermal and epidermal layers in human skin, which enhances the tactile perception of mechanoreceptors. [39] The hierarchical nested wrinkles endow the pressure sensor with much higher sensitivity than single-scale wrinkles ( Figure S3, Supporting Information), which should be attributed to the strengthened interlock effect. [52] Finite element analysis (FEA) reveals a high stress concentration at the contact spot between interlocked wrinkles ( Figure 2d). The hierarchical nested wrinkles enable more effective stress concentration than the single-scale wrinkles ( Figure S4, Supporting Information), leading to a more dramatic increase in contact area ( Figure S5, Supporting Information) and a sharper reduction in electrical resistance at a given pressure. Besides, the sensitivity of pressure sensor depends on the wrinkle dimensions for single-scale, double-scale, and three-scale wrinkles, i.e., the sensitivity generally increases with increasing wrinkle dimensions ( Figures S6 and S7, Supporting Information).
Additionally, our pressure sensor exhibits stable frequency responses in frequency range from 0.05 to 0.2 Hz for a 1.0 kPa pressure (Figure 2e), good real-time responses under different pressures from 7 Pa to 1.8 kPa ( Figure 2f) and a high response speed of 20 ms under a pressure of 0.5 kPa (Figure 2g). To evaluate the mechanical stability, the pressure sensor was subjected to over 8000 compression/release cycles at a peak pressure of 500 Pa ( Figure 2h). Furthermore, the sensing performance is almost insensitive to the ambient temperature and humidity ( Figure S8, Supporting Information). Note that the temperature will induce the larger relative change in resistance under the low pressures. The temperature improves the deformation ability of Ag/PDMS, which promotes more conformal multiscale contact between the face-to-face assembled Ag/PDMS sheets to form more conductive paths. Although encapsulated with polyurethane tape, the pressure sensor cannot work in hydrated conditions for long periods of time. The device performance will be further enhanced by surface wettability design, including waterproof, self-clean, moisture management, sweat collection/analysis and self-powered system. [53,54] A classic music sound (Poem of Chinese Drums) can also be continuously and precisely detected ( Figure 2i). Thus, the high sensitivity, low limit detection and good durability make the wrinkling-dominant pressure sensor promising for subtle pressure/ vibration detection.
We have also measured the electrical signals under different mechanical stimuli. As shown in Figure S9 (Supporting Information), each of the electrical signals under different mechanical stimuli provides a unique output pattern specific to the mechanical input. The pattern of resistance variation can be www.advmatinterfaces.de differentiated by the different magnitude, shape, and response/ relaxation times. However, it is difficult for the present sensor to distinguish the simultaneously applied input stimuli as they may interact with each other. Some strategies have been proposed to decouple different input physical and mechanical stimuli, including the suppression of the interference, integrated multisensing platforms, single sensing units with multiple sensing mechanisms, materials with different response times to different input stimuli, and combined structure and material innovations. [14]

Wrinkling and Cracking-Dominant Sensing Characteristics and Mechanism
Although high sensitivity can be achieved by engineering the films with microstructured surfaces, the pressure sensors usually suffer from limited or saturated response under higher pressure due to the increasing structural stiffening of microstructures. [1,36] Crack engineering is an effective approach to achieve an ultra-high sensitivity while simultaneously maintaining wide stretchability in metal films-based stretchable strain sensors [55][56][57][58] if film cracking occurs in a controlled manner. Here, we utilize the crack-based strategy to enhance the sensitivity of pressure sensor in the high-pressure region and thereby broaden the sensing range. As mentioned in step (ii) of the preparation process, arrays of parallel cracks form spontaneously along the prestrain direction on the oxidized PDMS, instead of on the flat Ag films (Figure 3a). To experimentally visualize the cracking behavior, in situ optical microscopy (OM) compression tests were performed. As the pressure increases, the sample expands isotropically due to the Poisson's ratio effect. As shown in Figure 3b-d, film cracking preferentially occurs at the locations where cracks already exist on the oxidized PDMS surfaces because of the stress concentration when P increases to 50 kPa. However, these primary cracks (marked by red arrows) play a negligible role in the resistance because they align with the current pathway direction. Upon further pressuring to 150 kPa, another array of cracks (secondary cracks marked by green arrows) perpendicular to the primary cracks start to form, which would break the current pathway and affect the resistance. The statistical results reveal that both the secondary crack density ρ c and the crack width W c increase with increasing pressure (Figure 3e). The crack www.advmatinterfaces.de density gradually attenuates when the pressure reaches ≈300 kPa, indicative of the reduced cracking rate, which is attributed to the crack interaction. [59] After preloading pressure relaxation, the cracks are approximately closed due to the elastic recovery of the PDMS and no adjacent film fragments overlap each other. Figure 3f shows the relative resistance change as a function of applied pressure. Contrary to the wrinkling-dominant electrical responses, / 0 R R ∆ of the pressure sensor with wrinkling-cracking patterns increases rapidly with increasing P, and then gradually attenuates. We derived a simple model to describe the strain-dependent electrical response by correlating the resistance with the crack-related parameters (sec-ondary crack density ρ c and crack width W c ) (see Note S1 and Figure S10, Supporting Information). The theoretical calculations agree with the experimental observations well within allowable error (Figure 3f). The small discrepancy within the pressure range of 30-100 kPa is due to the non-uniformly distributed cracks. Accordingly, the sensor exhibits a high sensitivity of 3.5 kPa −1 at a low-pressure range (<10 kPa), and a moderate sensitivity of 0.9 kPa −1 at a pressure range from 10 to 250 kPa. These sensing characteristics can be rationalized by the wrinkling and cracking-dominant mechanism. As a subtle pressure is applied, the mutual contact induced by wrinkles gives rise to a decrease in resistance, while the disconnection Figure 3. Performance characteristics and mechanism of the pressure sensor in the wrinkling and cracking-dominant (WCD) mode. a-d) In situ OM images of the cracking patterns at the pressure of 0, 50, 150, and 350 kPa, respectively. e) Evolution of crack density (ρ c ) and crack width (W c ) with pressure. f) Evolution of relative resistance change with pressure. g) Schematic of the sensing mechanism in the WCD mode and the corresponding equivalent circuit. Applications of the pressure sensor for various signal detection, including the h) artery pulse, i) throat vibration when saying the "Hello" in Chinese, j) facial movement (swallowing), k) finger bending, l) jogging, and m) walking.

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induced by cracks causes a more pronounced increase in resistance, consequently leading to the increasing resistance with pressure. The two competing effects lead to a relatively low sensitivity, compared with the wrinkling-dominant sensitivity, but are still high enough for monitoring human health and motion. Upon further compression, the adjacent film strips sequentially lost their contact and broke the current pathway, resulting in an increase in resistance. Although the crack gap (width) increases with increasing pressure, the upper and lower Ag fragments still can form a complete electrical circuit (Figure 3g). Thus, the resistance gradually attenuates at high pressure (Figure 3f). Note that the primary cracks figure prominently in the formation of roman-bricks crack patterns in the present pressure sensor, related to the two-stage cracking behavior. First, parallel primary cracks preferentially form along the cracks in the substrate, causing a strain gradient in the immediate vicinity of cracks perpendicular to the crack propagation direction. [60] The variation in local strain field dictates the cracking behavior. As the tensile stress (parallel to the primary cracks) gradually increases and exceeds the film fracture stress, the secondary cracks perpendicular to the primary cracks appear inside the existing fragments, forming the roman-brick-like crack patterns (Figure 3d). In contrast, random mud-like crack patterns dominate in the Ag/PDMS systems without substrate cracks ( Figure  S11, Supporting Information). These cracks follow a complex trajectory due to the local stress field at the crack tips, [60,61] in the case of quasi-equiaxial tensile stress. Upon continuous pressure, a relatively large film fragment disintegrates producing two or more small fragments separated by meandering cracks, which is induced by sequential dynamic crack branching. The evolution of the average fragment size with applied pressure fits well with a decreasing power-law behavior (Figures S12 and S13, Supporting Information), consistent with previous results on film mud-cracking under equibiaxial tensile strain. [62] The stress field in the films and the crack patterns are intimately dependent on the loading path and fracture sequence. [60] Accordingly, the electrical response ( Figure S14a, Supporting Information) reveals conspicuous fluctuating behavior for the mud-like crack patterns. These fluctuations are far beyond those observed in the roman-brick-like crack patterns (Figure 3f). To gain an in-depth understanding, we took the derivative of the relative resistance change / 0 Q R R = ∆ with respect to the applied pressure P (Figures S13b, Supporting Information). The derivative d /d Q P of the mud-like cracks exhibits much larger fluctuations with negative and positive values than that of the roman-brick-like cracks, related to the disconnection-reconnection events of film fragments. A positive value represents a disconnection event, while a negative value represents a reconnection event. [57] As sketched in Figure S15 (Supporting Information), upon compression shear stress component is induce along the irregular fragment edges, leading to the rotation of the film fragment. Some of the adjacent film fragments would reconnect, and simultaneously some of them disconnect. The fragment rotation-induced disconnection-reconnection events cause the drastic resistance fluctuations for mud-like cracks. [57] A comparison suggests that the pressure-response range is significantly improved from ≈2 to ≈250 kPa almost without sacrificing the sensitivity via crack-based strategy. In addition, our pressure sensor exhibits a low detection limit of ≈15 Pa, good real-time responses under different pressures, good durability for over 3000 loading/unloading cycles, and a fast response time of 20 ms ( Figure S16, Supporting Information). The electrical response shows no obvious signal drift and negligible hysteresis ( Figure S17, Supporting Information). The sensitivity of 3.5 kPa −1 over a pressure range from 15 Pa to 10 kPa, and 0.9 kPa −1 over a pressure range from 10 to 250 kPa is sufficient to detect the full-range vital signs and human motion, from arterial pulse to joint motion and to walking/running. Figure 3h shows the pulse pressure waveforms recorded by the pressure sensor attached to the wrist skin. A pulse frequency of 78 beats per min was obtained, within the normal heart rate range for healthy adults. The typical three peak characteristics in each pulse waveform, i.e., percussion wave (P), tidal wave (T), valley and diastolic wave (D), can be clearly detected, which provide important medical information for clinical diagnosis of cardiovascular and cerebrovascular diseases. Attached to the human throat, the pressure sensor can monitor and distinguish phonation induced epidermis/muscle movements when a disyllabic word "hello" in Chinese was repeatedly spoken (Figure 3i). The pressure sensor can also recognize the swallowing movements ( Figure 3j) and the bending of finger joints (Figure 3k). To evaluate the detection capability at a higher-pressure region, the pressure sensor was placed and attached inside the shoe and under the sole of feet to monitor the walking or jogging states. Periodic and stable waveforms can be recorded during continuous jogging (Figure 3l) and walking (Figure 3m). These outcomes demonstrate the great potential applications of the present pressure sensor in wearable healthcare monitoring devices.

Cracking-Dominant Sensing Characteristics and Mechanism
High sensitivity at pressures over hundreds of kPa even several MPa are also demanded for some specific applications, such as robotic manipulation, pressure tests in high-speed fluids and protective gear for extreme sports. Metal film-based flexible pressure sensors capable of detecting pressure over 1.0 MPa have rarely been reported. To further extend the sensing range, the bridge connection between the upper and lower Ag film fragments should be avoided. Here, we constructed a pressure sensor by the face-to-face assembly of one wrinkled Ag/ PDMS sheet and one wrinkled PDMS sheet using the coplanar electrode design (Figure 4a). As shown in Figure 4b, the relative resistance change keeps increasing with applied pressure, and steeply escalates even when P> ≈15 MPa. To quantitatively understand the strain-dependent electrical response, a simplified resistance model based on Simmons' formula [63] was developed (Note S2 and Figure S18, Supporting Information). There is good agreement between the theoretical and experimental results (Figure 4b). Accordingly, the pressure sensor exhibits an ultrawide dynamic pressure range, from ≈30 to ≈12 MPa with a sensitivity of 40 MPa −1 and from ≈12 to ≈20 MPa with a high sensitivity of 1420 MPa −1 . The almost linear sensitivity over a wide range also facilitates the direct acquisition of accurate pressure information without additional signal processing.
In addition, the sensor can maintain its functionality over 500 cycles of repeated loading/unloading at 13 MPa (Figure 4c).

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To demonstrate the sensing capability for robot manipulation, we installed a pressure sensor on the index finger and then grasped a bottle with different volumes of water. As the water volume linearly increases, the resistance change linearly increases accordingly (Figure 4d). Attached on the boxing gloves (Figure 4e), the pressure sensor is capable of monitoring the two punches using the left and right straight combination (Figure 4f), demonstrating the potential application in protective gear for extreme sports. To further demonstrate the sensing capability under extremely high pressure and good mechanical robustness under adverse conditions, a pressure sensor was placed under the front tire of a car (≈1200 kg) (Figure 4g), and the resistance changed significantly when the wheel ran over the pressure sensor (Figure 4h). Furthermore, the embarkation/debarkation of a 70 kg male passenger was clearly detected, as shown in Figure 4i (enlarging of the red dotted frame in Figure 4h), proving the high pressure resolution at an extremely high pressure.
We compared the sensing performances of our sensor to other metal film-based resistive pressure sensors (Figure 5). Our sensor exhibits a high sensitivity over an unexpectedly broad pressure range, outperforming the metal film-based [21,22,[64][65][66][67] and metal NWs film-based [20,29,[68][69][70] pressure sensors reported in the literature to the best of our knowledge. The multiscale wrinkles enable a very high sensitivity in the low-pressure region. The controlled crack patterns dictate the ultrabroad sensing range while maintaining a high sensitivity. In the WD and WCD modes, the sensor sensitivity is comparable to the best ability of the existing metal film-based resistive pressure sensors. Although the sensitivity is lower than some pressure www.advmatinterfaces.de sensors based on new material or architecture designs, [71,24,72] our metal film-based pressure sensor has a lower initial resistance and power consumption, which could work even at an extremely low voltage of 1 mV with a sensitivity of 3.2 kPa −1 ( Figure S19, Supporting Information). The response/relaxation times and the limit of detection are decent, better than most of the resistive pressure sensors under the similar conditions. Strikingly, our sensor in the cracking-dominant mode possesses an ultrabroad sensing range that is two orders of magnitude larger than that of conventional piezoresistive sensors while maintaining an equivalent sensitivity, which define a new space in the sensitivity-sensing range map for the MPa range pressure. Only a few reported pressure sensors [1,73] show a sensing range over 2 MPa, but the sensitivity is below 0.05 MPa −1 . Like most of the existing pressure sensors, the present sensor shows a relatively narrow linear pressure range, which would be improved by structure designs (such as porous structures, multilayers, gradient structures). [39,43,74] Note that the sensing performances can also be readily tuned by changing the metal film thickness ( Figure S20, Supporting Information). In addition, a drawback of our sensor is the external power supply, and it reduces the portability option of the sensing devices. More effort is needed to integrate the present materials and structures into the self-powered systems in the future. [75,76]

Conclusions
In summary, we proposed a cracking-and wrinkling-engineering strategy to design a flexible pressure sensor. The pressure sensors could exhibit different pressure sensing characteristics based on the same Ag/PDMS material systems but different configurations (modes). The three different sensing models cannot co-exist in a sensor. The wrinkling-dominant mode enables an ultrahigh sensitivity (18.2 kPa −1 ) and a low limit of detection (0.6 Pa), which makes the sensor an ideal candidate for precisely monitoring very subtle vibrations. The wrinkling and cracking-dominant mode endows with a sufficiently high sensitivity (3.5 kPa −1 ) and a broad pressure range from 15 Pa to 300 kPa, which will be applicable to detect the full-range vital signs and human motion. The cracking-dominant mode promotes a high sensitivity (1420 MPa −1 ) over an ultrabroad pressure range up to 20 MPa, holding promise for sensing ultrahigh pressures. Moreover, the pressure sensor exhibits good long-term stability and repeatability in all three modes. The present strategy is extremely simple, cost-efficient, and universally applicable to other metal film/polymer substrate systems for flexible pressure sensors.

Experimental Section
Preparation of PDMS Sheets with Hierarchical Wrinkles: In step (i), the PDMS base and curing agent (Sylgard 184, Dow Corning) were mixed thoroughly at a weight ratio of 10:1. After being degassed for 30 min, the mixed base/curing agent was poured into a custom-built PMMA mold with a depth of 1 mm and cured at 70 °C for 4 h. In step (ii), the PDMS sheets (30 mm × 15 mm × 1 mm) were pre-stretched uniaxially to 40% using a custom-built apparatus and exposed to ultraviolet/ozone (UVO) for 4 h. After prestrain relaxation, microscale wrinkles formed simultaneously. In step (iii), we used the wrinkling patterns as a template and poured fresh PDMS base-curing agent mixtures onto the template to replicate microscale features. After curing at 70 °C for 2 h and being peeled off carefully, a 0.8 mm-thick PDMS sheet with inverted wrinkling patterns was fabricated (denoted as G3), which precisely replicates the microstructures of the template. The average wrinkle wavelength is ≈63 µm, and the average wrinkle amplitude is ≈8 µm. In step (iv), the PDMS sheets (25 mm × 10 mm × 0.8 mm) were stretched to 40% strain and treated with oxygen plasma (OP) for 5 min at 50 W. After releasing the prestrain from 40% to 20%, nanoscale wrinkles formed (denoted as G1). The wrinkle wavelength is ≈900 nm, and the wrinkle amplitude is ≈120 nm. Immediately after the previous step, the PDMS sheets were maintained at 20% prestrain and treated by OP at 50 W for 30 min. After the complete relaxation of prestrain, wrinkles with a wavelength of ≈3 µm and amplitude of ≈700 nm were engendered. Finally, we fabricated hierarchical three-scale wrinkles on the surfaces of PDMS sheets. Note that the crack arrays parallel to the prestrain direction were created spontaneously in the oxidation layer when the prestrain was released.
Preparation of the Metal Films: The three-scale nested wrinkling PDMS substrates were cut into small pieces with a size of 13 mm × 10 mm × 0.8 mm, and then Ag films with a thickness of 50 nm were deposited on the PDMS substrates using direct current magnetron sputtering at room temperature. The chamber base pressure was kept at ≈5 × 10 −5 Pa before sputtering. During sputtering, the power was 120 W, and the argon pressure was 0.5 Pa. The substrates were rotating at a speed of 20 r.p.m. to ensure film uniformity.
Fabrication of the Pressure Sensors: The silver wires with a diameter of 0.1 mm were fixed on the Ag film surfaces using silver paste. For the wrinkling-dominant (WD) mode and wrinkling and cracking-dominant (WCD) mode, we constructed the pressure sensor by a face-to-face assembly of two wrinkled Ag/PDMS sheets. For the cracking-dominant (CD) mode, we constructed the pressure sensor by a face-to-face assembly of one wrinkled Ag/PDMS sheet and one wrinkled PDMS sheet. Finally, pressure sensors with a face area of 10 × 10 mm 2 were encapsulated with PU tape.
Characterization of the Wrinkling-Cracking Structures: The surface morphologies and microstructural features of Ag/PDMS systems were characterized by field-emission scanning electron microscopy (SEM, HITACHI SU6600), atomic force microscopy (AFM, Bruker Dimension Icon), confocal laser scanning microscopy (CLSM, Olympus, LEXT OLS4000) and optical microscopy (OM, Zeiss Axiolab 5). The wavelength and amplitude of multiscale wrinkles were statistically obtained from both AFM and CLSM measurements.  Figure 5. Performance comparison between this work and previously reported resistive pressure sensors based on various nanomaterials, such as metal films, [22,65,66] CNTs, [73,[77][78][79] metal NWs, [29,69,70] graphene, [80][81][82] conductive polymers, [33,83,84] Mxene-based [71,85] and silkbased materials. [86,87] www.advmatinterfaces.de To monitor the fracture process of the Ag films in situ, a piece of Ag/PDMS sheet with a size of 13 mm × 10 mm × 0.8 mm was placed between two PMMA sheets with a size of 90 mm × 20 mm × 1 mm. The pressures were applied with custom-made weights on both sides of the PMMA sheets ( Figure S21, Supporting Information). In situ CLSM and/or OM observations were performed by focusing through one transparent PMMA sheet onto the film surfaces. The crack density and crack width were obtained by averaging over 200 cracks. Note that the maximum pressure applied is 1500 kPa due to the limitation of weight and volume of standard weights.
Performance Testing of Pressure Sensors: The compression tests and the cyclic stability tests were examined using a Kammrath & Weiss mechanical stage. The electrical signals of the pressure sensors were recorded by a digital source meter (Keithley 2601) and a digital nanovoltmeter (Keithley 2182A). Sensing performance measurements were performed in a controlled temperature and humidity atmosphere by using a programmable temperature/humidity chamber. Informed consent was obtained for all participants involved in the experiments testing the potential applications of the sensors. In addition, institutional review board approval was not required to perform these experiments.
Finite Element Simulations: 2D nonlinear finite element analysis was carried out for calculating the strain distribution and contact area using general surface-to-surface contact interactions, implemented in the commercial software ABAQUS. While the bottom film was fixed, a vertical displacement was applied in the top film to induce pressures in the double-layer system with interlocked hierarchical wrinkles or singlescale wrinkles. In all cases, periodic conditions were used in lateral boundaries and four-node 4-node bilinear plane strain quadrilateral elements with reduced integration were adopted. The geometries in the wrinkles follow those in the experiments. PDMS was modeled as a homogeneous isotropic elastic material with a density ρ = 965 kg m −3 , and Young's modulus E = 800 kPa. Poisson's ratio was set to be ν = 0.475 for modeling the property of incompressibility.

Supporting Information
Supporting Information is available from the Wiley Online Library or from the author.