Strain Visualization in Flexible Sensors with Functional Materials: A Review

Here, in comparison to indirect and nonvisualizable detections that usually convert strains from electrical signals, the strain sensors that show visible signals with operation simplicity and intuitive perception for practical applications in flexible, printed, and hybrid microelectronics are summarized. The sensors are categorized into four mechanisms of optical phenomena (diffraction, reflection, interference, and photonic crystal), fluorescent mapping (mechanochromism and mechanoluminescence), Moiré effect, and thermal imaging. In addition to their operating principles, three characteristics of sensitivity, dynamic window, and spatial resolution are examined. Furthermore, three types of strains (uniaxial, biaxial, and multiaxial) with subcategories in strain mode (tensile and compressive) and uniformity (isotropic and anisotropic) that are supported by corresponding sensors are also summarized here. With three potential applications and markets of healthcare and biomedical engineering, human motion detection (sports science), and roll‐to‐roll manufacturing listed at the end, a steppingstone is offered here for those who works or intends to work in this field by revisiting the outcomes from key literature published in recent years.

with color changes in corresponding materials (Figure 1b). Similarly, even though the Moiré effect does not emit light or show color, the change of its fringe patterns indicates deformations, also showing a promising strain visualization solution (Figure 1c). In addition to these, if signals locate outside the visible spectrum, they can still be captured through apparatus and displayed to bare eyes. In such case, thermal imaging is the method that shows energy distributions with various intentionally defined colors on a screen through the Joule heating effect, which can also be considered as a strain visualization solution (Figure 1d).
This article classified strain visualization methods in flexible sensors and investigated their sensitivity, dynamic window, and spatial resolution. After summarizing the detection methodologies, this article lists and forecasts three potential markets. As far as the authors can understand, there is no other literature that summarizes a collection of strain visualization techniques focusing on flexible sensors, function materials, performance indices, and detection methods in one study. This review paper thus provides an in-depth look at several strain visualization methods as well as comparative evaluations of sensor design, material selection, and inspection strategies. By reviewing these ideas in a topical manner, those who are interested in related fields can receive comprehensive notions in a simple, effective, and efficient way.

Mechanisms
In this article, strain detection mechanisms have been categorized into four types, which are optical phenomena, fluorescent mapping, Moiré effect, and thermal imaging, and will be explained in the following subsections and depicted in Figure 1.

Optical Phenomena
Anything that can be observed through bare eyes by various mechanisms, such as diffraction, reflection, interference, and surface plasmon resonance (SPR), can be considered as optical phenomena. These optical phenomena allow users to not only visualize but also localize the strains induced  [36] Copyright 2019, American Chemical Society. b) Fluorescent mapping (mechanoluminescent sensors). Reproduced with permission. [13] Copyright 2009, Elsevier, Thin Solid Films c) Moiré effectbased sensors. Reproduced with permission. [28] Copyright 2012, International Conference on Bridge maintenance, safety and management (IABMAS). [29] d) Thermal imaging (thermoresistive sensors). Reproduced with permission. [33] Copyright 2014, Multidisciplinary Digital Publishing Institute (MDPI) Sensors. without any physical contact or involvement of electrical signals. Additionally, because the responses can be related to the strains, the ability of quantifying strain magnitude is possible.
Sitpathom et al. reported a flexible noncontact optical strain sensor based on a patterned film. [6] A monolayer array of polystyrene microspheres was integrated into patterned polydimethylsiloxane (PDMS), which diffracts lights when the film was applied with strain (Figure 2a). In a demonstration, this film exhibited color variations through diaphragm vibrations in a loudspeaker.
Guo et al. announced dye doped PDMS optical fibers, [14] in which light transmissions depended on reflections. The intensity attenuation in the fiber was a function of dye concentration because the dye molecules show wavelength-dependent absorption. Consequently, quantitative measurements of strains were possible. In a demonstration, this device converted the physical vibrations into visible signals as an application of voice monitoring in human beings (Figure 2b). Because inhalation and exhalation could also be measured in a similar manner, the sensor was claimed applicable for detecting physiological signals as smart clothing.
Another widely adopted strain visualization mechanism is interference. Lo et al. fabricated a multilayer structure that was precisely designed for a Fabry-Pérot interferometer with an air cavity. [9] When the multilayer was deformed with strains, the cavity changes its dimension, which in turn alters the interference. Demonstrations showed that not only the interfered colors but also their areas could be utilized for quantifying and localize the strains.
Apart from these, photonic crystals have also been found promising in strain visualization because they show dynamic color changes by altering their structures. Hu et al. showed a spectrum modulation by SPR [15] from periodical structures in nanometer scales. This work patterned positive circular discs of metallic material above an elastomer (PDMS). The color variation was demonstrated by mechanically stressing the underlying elastomer to isotropically reshape the nanostructures patterned above it (Figure 2c). In contrary, Zhao et al. developed a stretchable strain sensor based on negative patterns on PDMS by nanoimprint technology. [10] This strain sensor shows a color change over the entire visible range under a strain of 30%. It was observed that under normal conditions, the sensor is red. When the sensor is stretched, the lattice constant and shape of the structure changed, which result in color change from yellow, to green and blue gradually (Figure 2d).
Other than these, signal attenuation was also monitored for strain detection. For example, stretchable optical sensors have been used for applications such as human motion detection. Carbon based materials like graphene along with polymers of Figure 2. Photographs of flexible optical strain sensors. a) Diffraction in patterned PDMS film with application of strain. Reproduced with permission. [6] Copyright 2020, OPTICA Publishing group. b) Illuminated light response i) with strain generated due to ii) speech and iii) breathing. Reproduced with permission. [14] Copyright 2017, OPTICA Publishing group. c) Optical response of the nanostructure with and without strain. Reproduced with permission. [15] Copyright 2019, Institute of Physics (IOP) Science. d) Visual strain sensor based on stretchable photonic crystals with i) its sensing performance and ii) comparison of change in color and resistance. Reproduced with permission. [10] Copyright 2019, IOP Science. www.advmatinterfaces.de polyurethane and PDMS have been used for fiber fabrication with high tensile properties as well as good light transmittance. Wang et al. presented a PDMS composite optical fiber-based strain sensor that uses optical loss of the beam to detect strain. It was observed that the attenuation increased with the applied strain when the PDMS optical fiber was doped with graphene. It gives the best response at a graphene concentration of 5 × 10 −4 wt%. [16]

Fluorescent Mapping
Strains can be visualized in fluorescent ways, which are further subcategorized into MC and ML in literature. [17] ML or triboluminescence (TL) are phrases that often used interchangeably. The MC and ML (or TL) show fluorescence from identical compound skeleton structure but different compound aggregation of states, exhibiting different conjugation degrees and thus fluorescent appearances. MC and ML processes are based on their mechanoresponsive organic luminogen materials. Luminogens are atoms or molecules. When they are included in a compound, luminescence or fluorescence will be induced if mechanical forces like stress, pressure, and crushing are applied. [17] Li et al. reported a material that shows force-induced regeneration of conjugation pathway in a dipolar structure. [11] These sensors have two different molecules that can be covalently bonded to an epoxy thermoset network as an MC chemistry. The molecules undergo a force-induced elimination reaction, resulting in a dipolar structure with significant intramolecular charge-transfer effect (Figure 3a), which leads to color variations under strains. Some MC materials also show memory properties (i.e., reversible color change), exhibiting emission intensity variations with external stimuli (such as force and temperature) and are referred as memory chromic polymers. Wu et al. disclosed one memory chromic polymer, [18] in which the spectrum shows clear decline in intensity when the strain was increased (Figure 3b). Hsieh et al. have reported another MC shape memory material based on self-assembled silica colloidal photonic crystals. The position of the reflection peak shifts noticeably toward the blue (654-546 nm) under mechanical deformation or stretching, revealing a considerable color change. The reflection peaks and intensity for the unstretched, stretched, and recovered states amply demonstrate the reversibility of the shape memory deformation and recovery processes. [19] Besides MC, ML or TL is another fluorescent way to visualize strain distribution (Figure 3c). [12,20] Literature divided ML or TL into two subcategories of deformation luminescence (DL) and fractoluminescence (FL). [21,22] Nevertheless, FL usually takes advantage of inorganic and fragile materials that do not fully support strain detection. [21] Thus this article only reviewed the DL, which was further subcategorized into elasticoluminescence (EL) and plasticoluminescence (PL) in literature. [23] When materials are strained into an elastic state, EL and light emission happens. It returns to its original state after the stress is removed. For PL, light emission happens when the materials are strained beyond their elastic limits and physical deformation takes place. [22] Qian et al. examined mechanical deformations using ZnS:M 2+ (Mn/Cu)@Al 2 O 3 microparticles (ZMPs) dispersed into PDMS to form flexible sensors where the elastic modulus is tunable with the help of SiO 2 nanoparticles. [24] ZMPs shows ML Figure 3. Visual changes in various fluorescent strain sensors. a) Development of MC strain sensor i) process along with ii) its stress-strain characteristics and iii) visual optical changes with strain. Reproduced with permission. [11] Copyright 2016, Wiley-VCH. b) Photoluminescence spectra of the film at original, stretched, and recovered state due to application of strain. Reproduced with permission. [18] Copyright 2013, Wiley-VCH. c) Illustration of TL phenomena with i) schematic and ii) real case. Reproduced with permission. [20] Copyright 2018, Elsevier. d) The skin-driven colored ML response at various face positions. Reproduced with permission. [24] Copyright 2018, Wiley-VCH.

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with wavelength shift over the entire visible spectra using different cations doped in ZnS with excellent repeatability and stability as the sensors were tested for 10 000 cycles at 20% strain ( Figure 3d) for electronic skin applications.
A ZnS:Cu phosphor-based optical fiber strain sensor with ML is demonstrated in another intriguing work by Liang et al. More than 10 000 stretch-release motion cycles have been performed to confirm the steady ML signal and reliable sensing. [25] Because the demonstrations were performed repeatedly in the elastic range of the optical fiber, this work was also considered an EL application. The standard deviation for the stretch and release were 0.0091% and 0.0106% respectively which indicates good repeatability for the sensor.
On the other hand, Chandra et al. reported PL for colored alkali halide crystals to examine pressure steps. When pressure is applied to the γ-irradiated crystal, the PL intensity initially increases, reaches a peak value, and subsequently decreases with time, [26] indicating the strain visualization solution of PL.

Moiré Effect
The Moiré effect is a visual illusion that arises when one set of regular patterns is superimposed on another set that shows identical pattern or differs in size, angle, or spacing. Deformation measurement is an interesting application for analysis using Moiré effect and has also gained attention. Strains thus can be analyzed using Moiré effect.
Ding et al. reported a flexible strain sensor based on nonlinear Moiré patterns and image processing. [27] A concentric ring grating was constructed on a piece of PDMS with a line grating superimposed above it with different pitches. As the pitch for the concentric ring grating changes with applied strain, Moiré pattern changes can be observed in overlapped regions as the response (Figure 4a).
In addition to planar applications, Moiré effect also supports strain visualization on curved surfaces. Wang et al. developed a 2D symmetric Moiré grating in titanium alloy. [28] Tensile, compressive, and shear strain can be measured through a series procedure of signal differentiation ( Figure 4b). Along with this, directional strain distribution under different loads is also understandable.
By making these sensors into stickers, Takaki et al. demonstrated sensing applications with simplicity and practicality ( Figure 4c). [29] The visibility and pattern clarity were acceptable for visualization however a trade-off between the magnification and clarity existed. Visibility was achieved by observing characters with line gratings or using character gratings in one of the films. For the pattern clarity, fine gratings were required. A method to extract strain by the use of image processing techniques is also a must. Similar work was done by Umemoto et al. who used strain visualization stickers based on Moiré patterns for concrete surface strain measurement. [30] It allows visual evaluation of rough strain values on concrete surfaces which enables remote as well as noncontact strain measurement.
To further expand its application, Xie et al. used electron beam lithography to fabricate Moiré gratings with high resolution (Figure 4d), [31] which can detect the local deformations in a strain sensor fabricated on a flexible carrier substrate. This proved that the Moiré effect supports not only macroscopic but also microscopic strain visualization and localization with pattern combination varieties.

Thermal Imaging
Thermal variation-based strain imaging exploits the temperature dependency of resistive elements. This Joule heating effect provides quantitative relationships between the thermal power and resistance, which indicates and locates the strains for applications regardless of the mode (compressive or tensile) of strains. To induce the Joule heating, metals are commonly used as resistive elements and subjected to power sources of either current or voltage. Because the thermal response falls out of the visible spectrum, an infrared (IR) detector is usually used to convert the thermal energy into visible colors.
An et al. realized a thermoresistive strain sensor with concealing layer whose results outperformed in terms of detection sensitivity than the sensor without a concealing layer. The loss of thermal energy in terms of heat transfer was suppressed by the concealing layer which helped in generating a larger temperature gradient per unit strain or resistance. [32] There is a significant temperature difference (Figure 5a) between the folded and unfolded regions of the strain sensor with and without the concealing layer, respectively. Another work demonstrated by Liao et al. based on thermoresistive strain sensing not only helps to judge the overall performance, detects localized strain but also differentiates tension and compression. [33] In that work, gold was patterned on polyethylene naphthalate by photolithography as the thermoresistor and strains can be understood through the IR emissions from the sensor. The strain localization is thus achieved because heat accumulated only near the deformed area. The authors claimed that realtime monitoring and off-axis adjustment are possible in R2R manufacturing provided that related control systems are ready.
In case of stretchable electronic devices, rapid thermal heat dissipation is required to enhance its lifetime, durability, and performance. Tan et al. reported a highly stretchable and biocompatible strain sensor based on thermoplastic polyurethane matrix and boron-nitride nanosheets that shows thermoresistive capabilities. Also, rapid heat dissipation into the environment is made possible by the improved thermal and electrical conductivities of the materials employed. A 32% drop in real-time saturated temperature is achieved with a minimum temperature difference of 3.5 °C is seen for a 100% strain. [34] It can be used in applications of human motion detection and health monitoring.
The thermoresistive strain elements on soft and flexible substrates can also be used for biomedical applications, in which conformal deformations exist. Crawford et al. showed a noninvasive technique to characterize the recovery of biological tissue with thermal response on both flat and curved surfaces [35] (Figure 5b).

Characteristics
Strain sensors with different visualization mechanisms have been elaborated in the previous section. In addition to the www.advmatinterfaces.de mechanism, they can also be characterized scientifically in sensitivity, dynamic window, and spatial resolution. As a result, this article reviewed the performances of the sensors on these characteristics in this section. Table 1 compares the characteristics of representative works based on their visualization mechanism.

Sensitivity
Sensitivity is defined as the ratio of incremental output and incremental input with physical quantities. In case of strain detection, the denominator was clearly the strain (ε). However, to quantify the sensitivity, it was not easy to consider the output change in terms of visualizable characteristics such as color or pattern. As a result, other widely used factors were adopted as the numerator of the sensitivity and this subsection summarized practical ones.
Guo et al. used PDMS-based optical fiber with gold nanoparticles (GNP) to observe the diffraction loss in unit of decibel (dB) [36] with the highest sensitivity of 9.54 dB ε −1 (Figure 6a). Another reflection-based fiber optic strain sensor reported by Jauregui-Vazquez et al. shows a sensitivity of 2.4 pm µε −1 . [37] In case of MC-based strain sensors, research groups have observed shift in the wavelengths or changes in color. As a result, the numerator of the sensitivity was the spectral shift in unit of nanometer. For example, with a maximal compressive strain of 49.3%, Li et al. showed the transition of  [27] Copyright 2021, IEEE Transducers. b) Symmetric Moiré gratings and its measurement process for 2D strain distributions. Reproduced with permission. [28] Copyright 2017, OPTICA Publishing group. c) Moiré fringes with different magnification and its tradeoff with clarity. Reproduced with permission. [29] Copyright 2012, IABMAS. d) Schematic principle of formation of Moiré patterns. Reproduced with permission. [31] Copyright 2009, Elsevier.
www.advmatinterfaces.de fluorescent emission from 505 to 630 nm with a sensitivity of 253.54 nm ε −1 . [11] Another MC-based tensile strain visualization was demonstrated by Shauloff et al. with carbon dots embedded in an elastic polymer film. Blueshift in the fluorescence peak along with significant increase in the intensities was observed when the film was stretched. Consequently, the numerator of the sensitivity could also be characterized by the intensity of the signal. [38] In addition to MC, ML is also analyzed with sensitivity. With material modification, Tu et al. developed Li x NbO 3 :Pr 3+ composite material that shows noticeable sensitivity at low strain levels of 1-10 µst (≈103 Pa) [39] (Figure 6b). Consequently, the intensity increment can also be considered as the numerator of sensitivity during characterization in ML and other fluorescent devices.
In case of Moiré effect, it is challenging to define the sensitivity because the pattern changes were analyzed as images without the supports of quantifiable physical quantities. However, some researchers have claimed that the sensitivity depends on the pitch of the grating [40] while other researchers have proposed methods to read fractional fringe orders. [29] One literature reported by Ding et al. shows the peak intensity of various Moiré patterns with respect to the applied stress [27] (Figure 6c).
Lastly, for the thermal image-based sensor that works on Joule heating, the numerator of the sensitivity was described by either a resistance, [33] absolute temperature, [32] or relative temperature change; [32] and the sensitivity was usually termed as a gauge factor (GF) for similar sensors. A GF of 1.46 based on resistance change in a sensor size of 2 mm × 2 mm was once demonstrated in literature as an example. [33] The sensitivity can be further tuned by changing operating parameters such as applied current, voltage, or encapsulating material because thermal energy may accumulate accordingly Reproduced with permission. [32] Copyright 2019, IOP science. b) Thermoresistive sensor i) design for precise characterization of the thermal properties of soft biological tissues such as ii) the skin in noninvasive manner. Reproduced with permission. [35] Copyright 2018, Elsevier.

Dynamic Window
Dynamic window for a strain sensor is another key characteristic. It defines the upper and lower limits of detectable strain, showing the reliable detection range. In most cases, positive and negative strains are used for tension and compression mode, respectively; and the dynamic window should be indicated clearly for the mode of the strain. Table 2 shows the upper and lower strain limits of representative works based on their visualization mechanism. Guo et al. reported one stretchable hydrogel-based optical fibers in a step index core and clad structure. Strain was visualized due to the increase in the propagation loss in the visible range, exhibiting a tensile dynamic window up to +120%. [41] However, usage of hydrogels based optical fibers is restricted to wet environments. When exposed to air, volumetric shrinkage Figure 6. a) Differential loss at dual wavelength along the applied strain. Reproduced with permission. [36] Copyright 2019, American Chemical Society. b) ML response of the Li 1.00 NbO 3 :Pr 3+ sheet during five repetitions of the tensile strain test. The inset shows the ML response of the Li 1.00 NbO 3 :Pr 3+ sheet in the strain range from 0 to 300 µst. Reproduced with permission. [39] Copyright 2017, Wiley-VCH Verlag GmbH and Co. KGaA, Weinheim. c) Representative Moiré patterns formation and the extracted average peak intensity of the Moiré patterns along applied stress on the strain sensor with i) chirped concentric ring grating (CRG) and ii) conventional CRG. Reproduced with permission. [27] Copyright 2021, IEEE Transducers. d) The temperature response of i) various tension and ii) compression bending radii with various applied voltage and current, respectively. [33] Reproduced with permission. Copyright 2014, MDPI Sensors. and structural damage can be observed. To overcome this issue, an optical strain sensor based PDMS optical fibers was fabricated. Along with excellent mechanical properties, it exhibited linear response with repeatability and dynamic window up to +100%. [14] Even though the material composition is different, their latest work based on plasmonic GNP-PDMS optical strain sensors showed a similar dynamic window up to +100%. [36] Previously mentioned MC-based strain sensor disclosed by Li et al. shows a dynamic window up to +49.3%, [11] showing limited dynamic window when compared with the optical fiberbased ones. However, Wu et al. reported a strain sensor that was based on shape memory polyurethane with tetraphenylethylene, exhibiting color responses under strain up to +213%. [42] In comparison to other MC-based strain sensors, this work clearly indicated the lower limit of the dynamic window (+19%). Another memory chromic polymer strain sensor reported by Yenpach et al. uses spiropyran as mechanophores which is responsible for color change with a dynamic range up to +330%. [43] When it comes to ML-based strain sensors, Qian et al. demonstrated a polymer nanocomposite-based sensor also with a lower (+5%) and upper (+30%) dynamic window for tensile strain detections. [24] Similarly, Liang et al. reported polymerbased ML optical strain sensor that shows a dynamic window from 10% to 50%. [25] Even though wider dynamic window is always expected regardless of the operating principle and visualization mechanism, observation on small strain may limit the dynamic window in a trade-off manner. Xie et al. claimed that the dynamic window can be further limited to +5.57% to +14.6% if the application was focused on microscopic strain detections by Moiré pattern. [31] In case of thermoresistive strain sensors, Tan et al. reported a wearable device that shows a maximal temperature variation of 3.5 °C when the sensor was stretched. The dynamic window of the sensor was thus found to be up to +100% under a maximal elongation of more than 700% before break was determined. [34] Besides detections that support tensile strain, solutions that support compressive strain detections are also important. For example, Liao et al. reported a dual mode thermoresistive strain sensor that shows a dynamic window of up to −0.526% when compressive instead of tensile strain should be analyzed. [44] Furthermore, a melamine foam-based strain sensor that takes the advantage of Joule heating with a dynamic window of up to −80% is reported by Cao et al. [45]

Spatial Resolution
Spatial resolution refers to the smallest dimension in a space that can be detected by the sensor. In case of strain sensor, it also refers to the minimal area or maximal resolution.
Lyu et al. demonstrated a polymethylmethacrylate and chirped fiber Bragg grating (FBG)-based strain sensor, which showed a spatial resolution of 1 mm across a gauge length of 40 mm. [46] Using carbon-encapsulated Fe 3 O 4 nanoparticles embedded in a soft copolymer, Hong et al. created a high-performance MC-based strain sensor that demonstrates a dynamic color change from purple to red with a spatial resolution of 100 µm, [47] substantially enhanced the minimal resolvable area when compared with the optical solutions. For the ML-based strain sensor, Wu et al. demonstrated a ZMPs-based device that can detect an area as small as 100 µm (254 dpi) with fast response. [42] For the ML based sensors, Liang et al. shows a spatial resolution of ±1% in terms of strain percentage. [25] In Moiré pattern-based strain sensors, the structure proposed by Ding et al. comprises multiple gratings with various pitches. Because the smallest gap examined in the grating was 50 µm, the spatial resolution in the range of tens of micrometer is implied. [27] Even though the fluorescent mapping and Moiré pattern support high spatial resolution in the range of micrometer, thermoresistive strain sensor failed to demonstrate compatible results because of the physical quantity to be examined is a fluidic matter. Zhang et al. reported a graphene-ecoflex nanocomposite that acts as a stretchable sensor, which resolves an area with side length as small as 0.5 mm based on Joule heating, [48] showing similar spatial resolution to the optical fiber-based sensors.
In short, flexible sensors with strain visualization generally show spatial resolution in millimeter to micrometer scales, supporting most applications regardless of its operating principle and mode of strain.

Examination Strategy
Deformations are not limited to one-directional. Instead, the strains can be applied to two or multiple directions. In case two directions are involved, it is called biaxial strain; in case multiple directions are involved, it can be separated into isotopic and anisotropic multiaxial strains. Consequently, apart from the operating principles and characteristics, the flexible strain sensors can also be categorized into supportiveness on strain types and detection setups. The following subsections thus elucidate what type of deformations (Figure 7) can be examined by these sensors.

Uniaxial Deformation
Uniaxial deformation describes the conditions while the strain is only restricted to one specific direction. However, the applied strain can still be tensile (tension mode), compressive (compression mode), or a combination of both (mixed mode).

Tension Mode
Tension or tensile strain is generated due to the extension of dimension and the operation is usually done by pulling or stretching the device into opposite directions. Scholz et al. reported an in situ characterization system for cellulose-based material cottonid. [49] This work achieved the expected operation by performing scanning electron microscopy and microfocus computer tomography while applying tensile loads. The elastic and plastic regions of the sensor were www.advmatinterfaces.de observed along with the progression of defects such as pores and microcracks. With proper image analysis, defect volume can be calculated and quantified, which indicates strains scientifically.

Compression Mode
Compression or compressive strain is generated due to the reduction of dimension and the operation is usually done in an opposite way to that performed on tension. Structural health monitoring is one of the important areas where compression tests are required. Castro-Caicedo et al. fabricated a FBG strain sensor for uniaxial compression test. [50] Any compression applied onto the FBG can be translated into wavelength shifts, which in turn represent strains. In comparison to those reviewed earlier, which were only limited to tensile strain applications, this work demonstrated the application of compressive strain detection by optical fibers.

Mixed Mode
Even though the examples on strain detection in individual modes of tension and compression were given, it is also important to have a sensor that simultaneously supports detections on both modes because users would not know the strain mode in advance in many applications.
Using the same principle to FBG, one work demonstrated by Rosenberger et al. shows that a planar grating that supports both tensile and compressive strain measurements with integrated waveguide through successive cycles. [51] The sensor showed a spectral redshift and blueshift with the application of tensile and compressive strain, respectively. The sensor showed reproducibility and negligible hysteresis with sensitivity of 2.04 pm per microstrain.
An et al. designed a thermoresistive device with improved detection sensitivity [32] and both tension and compression can be observed with corresponding configurations. To demonstrate the operation flexibility, two modes (tension with voltage and compression with current) were selected from the four possible combinations. The sensitivity of the device was improved from 45.5 to 84.4 °C per 1% strain for the tension detection, and from 62.1 to 83.3 °C per 1% strain for the compression detection.
With the FBG or thermal imaging ideas, users may examine strains without knowing its mode and the need for choosing corresponding sensors in advance does not exist, showing operation practicality.

Biaxial Deformations
Flexible devices, in practice, could deform in more than one direction. As a result, it is crucial to assess strain distributions in both longitudinal (lateral) and transverse (vertical) directions.
Lee et al. used digital image correlation to visualize, quantify, and inspect strains to determine the neutral plane. [52] Axial strains were visualized for both x-and y-directions for a 100 µm thick polyethylene terephthalate (PET) substrate with a bending radius of 6 mm. Comparisons on x-and y-axial strains by numerical analyses were also depicted.

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Meanwhile, Xiang et al. proposed an in-plane biaxial strain sensing technique based on a grating. [53] By understanding the 2D diffraction pattern and reflectance shifts, strains in both directions may be projected. Nevertheless, identical reflectance may appear in both directions, and thus the direction for examination should be identified beforehand. Otherwise, proper decoupling methods to distinguish the strain contributions from both directions should be studied.

Multiaxial Deformations
Stretchable or elastomeric substrates are usually deformed into different directions with strains. When the deformations are identical in all directions in the xy-plane, an isotropic strain with respect to a specific reference point exists. On the contrary, if the deformation is not uniform in all directions, anisotropic strains exist. Here, we summarize solutions that deal with multiaxial deformations.

Isotropic Deformations
Chiu et al. proposed a visualizable SPR sensor, in which materials can uniformly (isotropically) change its dimensions in 360° in the xy-plane. [54] This work implied that when the strain distribution is not uniform, the visible color change in different locations will be different. This work further defined a degree of isotropy, which indicated how isotropic the strain distribution is in 360°.

Anisotropic Deformations
Poisson's effect describes the transverse strain and the longitudinal strain in an integrated way, which leads to the Poisson's ratio that is defined as the ratio of transverse and longitudinal deformations. Consequently, the Poison's effect can be utilized to examine the anisotropic strains in applications, and elastomers such as PDMS are widely used in sensors because they show noticeable Poisson's ratio. [55] Slobodian et al. demonstrated a multiwall carbon nanotube and polyurethane-based sensor which can be compressed in one direction while showing enhancement in the sensitivity as there was an expansion in two other directions perpendicular to the direction of compression. [56] For another example, Lee et al. developed a highly sensitive and transparent solution-processed strain sensor. [57] A metal-insulator heterostructure comprising conducting indium tin oxide (ITO) nanocrystals and insulating zinc oxide (ZnO) nanocrystals was designed. Artificial cracks in the ITO and ZnO were created to enhance the sensitivity due to adequate percolation paths. Cross-shaped patterns with orthogonal cracks realized multiaxial strain detections with gauge factor up to 3000.
These demonstrations provided solutions on monitoring the anisotropic strain distributions wherever needed, which is practical in most cases because strain distribution can be ubiquitous and direction independent.

Potential Applications and Markets
Strain visualization in flexible sensors is an important property that has not been fully explored in applications, regardless of their mechanism, style, shape, material, and fabrication. Due to the operating simplicity of the sensors and intuitive perception of their signals, there are some promising and practical applications which are discussed in this section.

Healthcare and Biomedical Engineering
Flexible, stretchable, and wearable strain sensors have become essential in developing smart devices for healthcare applications. With the advancement of Internet of things, strain sensors can also be used in systems for personalized sports advisor, disease diagnostics, and rehabilitation monitoring. Also, hydrogel materials with photonic functionalities have also recently been investigated for novel biomedical uses (such as monitoring blood oxygen saturation levels in tissues and implants for toxicity sensing).
Guo et al. reported a simple and low-cost stretchable strain sensor with fast response (<12 ms) and high reliability (over 6000 cycles). [36] The strain sensor has been attached to the wrist to measure the pulse. The strain sensors have also been attached to the neck to distinguish speeches with different words and saliva swallowing. In addition, the signals could also decouple the gestures when the sensor is attached to fingers. One similar application based on quantitative analysis of motor disorders in Parkinson's disease (PD) is depicted in (Figure 8a) that shows optical strain sensor attached to fingers of a person for rapid finger tapping test (RFT). Figure 8b-f shows the comparative data analysis of a normal person to a person with PD. Figure 8g,h shows fMRI image with activations in the motor cortex of a PD patient's brain while performing RFT. It was noticeable that synchronous output of optical strain sensor during fMRI appeared. This sensor is suitable for healthcare and biomedical applications since the sensor's signal responses can be visually interpreted without the necessity of additional wire.
Also, the article by Guo et al. shows the design and fabrication of hydrogel fibers based stretchable optical strain sensors that can take axial strain up to 700% and a dynamic strain of 120% still in the elastic region without any plastic deformations. With this supportiveness on strain values and the wide use of hydrogels-based sensors in tissue engineering, these sensors can be used as wearable devices for healthcare applications in terms of drug delivery and wound dressing. [41] Because of their flexibility, stretchability, and biocompatibility, they can be employed as implantable therapy enabling devices in the field of biomedical engineering.

Human Motion Assessment
In case of the human motion assessment, the strain sensors are attached to the skin. For example, measurement of the postures of athletes by strain sensors have been focused lately on www.advmatinterfaces.de the application field of sports science. Zheng et al. published one article, which focuses on a wireless evaluation system for badminton players and can classify them based on their skill levels as well as judge their stabilities and controllabilities. [58] With enough scientific evidence and practical data (Figure 9a), this system outperformed the existing ones.  Reproduced with permission. [58] Copyright 2022, Scientific reports. b) Sensors on the fingers show gradual bending to relaxing with optical loss. Reproduced with permission. [16] Copyright 2019, MDPI Polymers. c) Human motion monitoring tests illustrating i) change in resistance and the stability of the strain sensor even when the joints were ii) extended or iii) flexed. Reproduced with permission. [34] Copyright 2020, Nature Communications.

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Wang et al. reports a graphene added PDMS fiber, which has high tensile properties and good transmittance. When it is stretched, the concentration of graphene per unit volume is constant, and the sensor takes advantage of the optical loss in the fiber to detect the tensile strain. [16] Due to its high flexibility, high sensitivity, and large dynamic window, the sensor can monitor human motion in real-time (Figure 9b).
Another work was reported by Tan et al., in which a wearable strain sensor with advance thermal management is developed that shows promising applications for human motion monitoring. Demonstrations have been given by fixing the sensor on knee, index finger, shoulder, wrists, and elbow ( Figure 9c). [34]

Roll-to-Roll Manufacturing
For flexible, printed, and hybrid microelectronics, R2R manufacturing has been widely used. Before the microelectronic circuits were constructed or the microelectronic components were placed on the substrate, the polymeric substrate was taken out of a stock roll and applied with tension to flatten it during process. Also, after the fabrication, it was rolled again for stock with a calendaring system. Although R2R manufacturing exhibits various benefits such as high throughput, less production waste, and low material cost; the strain engineering on the polymer substrate is challenging.
A work was reported by Liao et al., in which the strain sensor was fabricated by inkjet printing and flashlight sintering. With thermoresistive detection and thermal imaging, noncontact strain measurement by IR inspection is realized. [44] Study of thermoresistive strain sensor with its detection setup was utilized. Both tension and compression have been demonstrated using molds through IR system (Figure 10a). Another work by the same team also shows that all fabrication and detection steps are compatible with R2R manufacturing, and the setup can be integrated for real-time strain measurement with visualization, hence proper adjustment on the misalignment between rollers was claimed achievable (Figure 10b). [33] The sensors in this setup can be used independently and can also be used with various modules to achieve automatic inspection procedures in a modularized way. Compared with existing methods, this solution does not require sensor preprocessing, showing advantages on operation and measurement efficiency.

Conclusion
This paper presented a thorough review on flexible sensors that visualize the strains with the help of functional materials. Diverse mechanisms from optical (diffraction, reflection, interference, and photonic crystal), fluorescent (MC and ML), Moiré effect, to thermal imaging concepts have been categorized. Apart from the operating principle, the characteristics (sensitivity, dynamic window, and spatial resolution) of the strain sensors have also been compared in detail. Detection setups and device supportiveness on quantifying strains in various ways of uniaxial (tensile, compressive, and mixed modes), biaxial, and multiaxial (isotropic and anisotropic) have also been elaborated with representative works. Finally, potential applications Figure 10. a) Demonstrative thermoresistive strain sensor with i) cross-sectional view and ii) detection setups for tension and compression along with iii) R2R fabrication and strain detection steps. Reproduced with permission. [44] Copyright 2019, Mechatronics. b) The R2R manufacturing process with the proposed method with thermoresistive sensing elements. Reproduced with permission. [33] Copyright 2014, MDPI Sensors.

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were discussed, where these sensors can be widely applied in wearable shapes for healthcare monitoring and human motion assessment due to their straightforward signal perception methods, further broadening potential and niche markets such as sports science. In addition, strain visualization has also facilitated the R2R manufacturing with inline and noncontact detection at various production stages.
It is possible to expect that the next generation strain sensing devices and technologies will feature visualization concepts with appropriate detection strategies and advanced materials. This review article thus provides a comprehensive summary on key aspects of strain visualization in flexible sensors regardless of their material and fabrication, for those who works or intends to work in related fields.