Logic-Device-Inspired Mechanical Computing System Based on Three- Dimensional Active Components

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However, its reliance on passive mechanical displacement limits its applicability for complex computations. This study presents a novel system that enables active light signal modulation through reversible mechanical deformation by integrating soft and 3D electronics. The proposed system features: 1) Optical fibers with optimized 3D cracks embedded in a low-modulus, high-elongation material, enabling strain-induced multimodal transitions. 2) Maximized stress concentration on the cracked fibers under strain, allowing them to function as active components for light modulation, which facilitates complex logic calculations and validates truth tables. 3) Multifunctional vibration sensing capabilities, illustrating the scalability of strain inputs and the potential for dynamic applications, such as soft robotics. These findings underscore the potential of this approach as a computational platform for mechanical motion-based technologies. Physical sciences/Engineering/Electrical and electronic engineering Physical sciences/Materials science/Materials for devices mechanical computing mechanical buckling process optical fiber electronic components mechanical transistor Figures Figure 1 Figure 2 Figure 3 Figure 4 INTRODUCTION Mechanical computing is a data processing and calculation strategy that relies on the physical displacement and interaction of mechanical devices 1 . Owing to the operation mechanism based on mechanical motion, mechanical computing systems can maintain reliable performance even under harsh environmental conditions, such as extreme temperatures 2 , radiation exposure 3 , and signal interference 4 , 5 . In addition, the precise and sophisticated design of these systems ensures consistently high calculation accuracy, enabling computations with minimal errors and enhancing robustness against external changes 6 – 9 . These advantages have made mechanical computing an attractive technology for applications requiring precise mechanical deformations, such as advanced manufacturing systems and space engineering. Despite these advantages, several intrinsic challenges remain in expanding the accessibility and applicability of mechanical computing. Conventional mechanical computing systems primarily employ high-modulus, low-elongation materials throughout the entire system, except for specific deformable elements, such as joints 10 , 11 . This design provides high strength and stiffness but makes the system susceptible to repetitive deformation and material fatigue. Moreover, the inherent limitations of systems composed of high-modulus materials 12 – 15 pose significant challenges for dynamic applications, such as wearable devices and soft robotics involving repetitive movements and complex motions with multidimensional nonlinear deformation. In this context, adopting low-modulus, high-elongation materials in mechanical computing systems presents a promising solution 16 – 19 , offering flexibility and stretchability. Integrating low-modulus materials throughout the system ensures reliability even under repetitive displacement and prolonged loading while achieving greater spatial freedom of operation under multidimensional nonlinear deformations 20 , 21 . In addition, system configurations with low-modulus materials enable high sensitivity to environmental changes, supporting sophisticated and rapid data processing essential for dynamic applications. Electronic computing systems are typically designed by combining passive and active components based on the required functions 22 – 24 . Passive components 25 , 26 , such as resistors and capacitors, are suitable for transmitting or regulating signals but cannot modulate or amplify signal flow. By contrast, active components 27 – 29 , such as diodes and transistors, perform the functions of passive components and enable advanced signal processing and complex logic calculations by modulating and amplifying signal flow 30 – 34 . In comparison, mechanical computing systems typically rely on passive computation derived from the deterministic behavior of mechanical components 35 , 36 . Thus, they are optimized for specific tasks but face challenges in implementing the active signal modulation capabilities provided by active components of electronic computers. This limitation leads to challenges with data processing, dynamic adjustments, and executing complex operations. Therefore, integrating active components into mechanical computing systems is necessary to meet the demands of increasingly complex modern computing tasks and provide adaptable, dynamic operations in diverse environments. This study introduces a mechanical computing system integrating soft and three-dimensional (3D) electronics. The system employs mechanically guided 3D optical fibers as active components to modulate light transmission for highly complex computations while functioning as a vibration sensor. The key features of the proposed mechanical computing system are as follows: ⅰ) The first mechanical computing system incorporating soft electronics. The intrinsically flexible optical fiber-based mechanical computing system is built on a stretchable silicone elastomeric substrate, which induces mechanical deformation of optical fiber through substrate elongation. Incorporating low-modulus and high-elongation materials throughout the entire system enables nonlinear deformation in multidimensional space. ⅱ) An active signal modulation capability similar to that of a diode in electronic computing systems is first demonstrated through the mechanically guided 3D deformation of optical fibers with cracks. The 3D structural transitions of the cracked optical fiber facilitate multimodal conversion between the on/off states of light transmission, enabling active light modulation. The morphology of the cracks is precisely designed to efficiently alter the light transmission path through stress concentration, as supported by simulation studies. In addition, multiple 3D multimodal optical fiber diodes are integrated to successfully execute several complex logical computations. ⅲ) Multifunctionality as a vibration sensor is demonstrated by detecting vibrations along different axes induced by intentional mechanical deformation, highlighting its scalability for multiaxis strain input. Mechanical computing systems incorporating low-modulus and high-elongation materials enable flexible and stretchable innovative computing devices for technologies relying on the mechanical deformation of materials, such as wearable devices and soft robots. Furthermore, mechanical computing systems integrating active components hold significant potential for advancing automation and adaptive systems through complex signal processing. RESULTS Logic-Device-Inspired Mechanical Computing System Based on 3D Cracked Optical Fiber Mechanical computing device operation follows a conceptual flow where unit cells constituting the device interact through the input mechanical deformation and output a transformed state based on a deterministic nature (Fig. 1 a). This study proposes a novel mechanical computing system in which the morphological state of optical fiber cracks is determined by input strain applied to the substrate 37 – 41 , and light output with controlled attenuation is generated. Consequently, these cracked optical fibers function as diodes, actively modulating light transmission and distinguishing between on and off states, serving as active components within the mechanical computing system. A diode is an active component in a semiconductor device that allows current to predominantly flow in one direction by controlling the carrier (hole or electron) concentration in the depletion region with an applied voltage bias, as shown in Fig. 1 b. The on/off state of the diode is differentiated according to the threshold voltage, defined as the minimum forward bias required for the current to start flowing, beyond which the current begins to flow. Inspired by this operating mechanism, the cracked optical fiber switches the on/off state of light output by controlling the depletion level of light-carrying carriers (Fig. 1 c). Carrier depletion occurs in cracks intentionally created on the optical fiber surface and is regulated by the state of the three-dimensional (3D) crack, which varies with the applied strain. The strain-light-driven optical fiber diodes 42 , 43 can exhibit a rapid light attenuation behavior at the threshold strain, establishing a criterion to distinguish between the on and off states. The strain-light-driven optical fiber diode operates through the deformation of cracked optical fibers attached to a low-modulus and high-elongation elastomeric substrate 44 – 49 . The mechanical properties of the elastomeric substrate enable it to endure reversible and repetitive deformation. Consequently, the architecture and operational mode of the cracked optical fibers are altered with the strain applied to the substrate, as shown in Fig. 1 d. The crack of the optical fiber is formed in 3D 50 – 53 on the surface through a simple laser-cutting strategy, which is discussed in the succeeding section. The strain release exposes the optical fiber core region, which determines the light propagation path, leading to the attenuation of light transmission intensity 54 – 57 . The light transmission behavior of cracked optical fibers under varying strain applied to a prestretched elastomeric substrate is observed in bright field (Fig. 1 e, left column) and dark field (Fig. 1 e, right column). The transmitted light intensity attenuates owing to crack-induced light scattering and light carrier depletion as the applied strain to the substrate decreases (500%, 250%, and 0% strain). Moreover, nearly no light is transmitted into the fiber beyond the crack at conditions below approximately 180% strain (Fig. 1 c). Consequently, the availability of cracked optical fibers as components of strain-light-driven mechanical computing devices is confirmed by inducing mechanical deformation and changing the state of individual cracked optical fibers independently or in combination by controlling the strain applied to the substrate (Fig. 1 f). Morphological Optimization of 3D Cracks for Effective Light Attenuation Mechanical cracks are typically associated with structural weaknesses owing to stress concentration. Two-dimensional (2D) cracks weaken the strength and durability of materials and increase the risk of crack propagation, causing various challenges related to system stability. To address these problems, significant efforts have been made to effectively eliminate 2D cracks and maintain the structural integrity of materials. However, the potential of mechanical cracks as a strategic design element for systems requiring precise signal control, such as electronic sensors 58 , 59 , has been explored. In particular, 3D cracks offer the advantage of precise control over stress distribution owing to their high spatial degree of freedom. This enables nonlinear responses to deformation and effective modulation of physical elements, such as light, vibration, and heat. In addition, 3D cracks enhance adaptability to complex mechanical stresses, ensuring stable performance under various deformation conditions. Consequently, systems using 3D cracks achieve superior sensitivity and precision under micro deformation, making them ideal for applications requiring finely tuned mechanical responses. In this context, 3D cracks have been adopted as a structural strategy to achieve effective light attenuation and rapid on/off switching in optical fibers. Morphological optimization of cracks has been performed to maximize performance. The 3D cracks were formed by ablating a finite region of the fiber cladding using a straightforward and controllable laser-cutting method. Differences in the ablation of the fiber cladding area were induced by controlling the laser power; higher power intensities resulted in greater ablation, as shown in Fig. 2 a-c. Subsequently, in-depth morphological analysis was performed to verify the 3D structural modification of the optical fiber after laser cutting. A 3D anisotropic crack was formed, exposing the core area—the primary light transmission path—under deformation (Fig. 2 d-e). To further understand the impact of 3D cracks, simulations were performed to obtain the stress distributions of the cracked optical fiber sensors. The simulations reveal the size and shape of the crack and the effect of that shape on the stress distribution. The stress distributions were evaluated for various crack shapes, including V-shape, two-point V-shape, and four-point V-shape (Fig. 2 f-h). All stresses applied were below 4 MPa. Stress concentration is observed in the cracks, with the V-shaped cracks exhibiting more concentrated stress (Fig. 2 f) compared with the more relaxed stress distributions observed in the two-point and four-point V-shaped cracks (Fig. 2 g-h). Replicating experimental conditions, the optical fibers were fixed at both ends of the prestretched substrates elongated by up to 500%, followed by a controlled release to 300%. The stress distribution in each case was simulated around the cross-section of the 3D crack. These simulations demonstrate how V-shaped cracks influence the stress distribution based on the substrate strain (Fig. 2 i-k). In particular, stresses in the V-shaped cracks remain within safe limits, peaking at 13.3 MPa. This result aligns closely with experimental findings, highlighting the influence of anisotropic 3D crack geometry, generated through fiber cladding ablation, on stress concentration. During mechanical deformation of the optical fiber, stress tends to accumulate in uncut regions owing to this geometry. Upon substrate strain release, these concentrated stresses expose the fiber core, enhancing light attenuation and enabling efficient and swift transitions between the on/off states. Logic Computation Using an Active Signal Modulation Optical-Fiber-Based Mechanical Computing System Leveraging the light attenuation and clear on/off state switching behavior of the cracked optical fiber diode, the logic computation performance of a mechanical computing system consisting of multiple cracked optical fibers was demonstrated (see details in the Experimental Section). This system defines the elongation state of the substrate as input and the intensity of light transmitted across the optical fiber crack as output (Fig. 3 a). The input is defined as “0” when no change in elongation occurs, with the substrate remaining in a stretched state (Fig. 3 a, upper column). Conversely, the input is defined as “1” when the elongation changes, corresponding to a released substrate (Fig. 3 a, lower column). The output value is determined based on the total light intensity transmitted across the cracked optical fiber, which varies with the elongation state of the substrate. A threshold light intensity was set, adjustable depending on the system. Intensities below this threshold were defined as an output value of “0” (Fig. 3 a, lower column), whereas intensities exceeding the threshold were defined as an output value of “1” (Fig. 3 a, upper column). Subsequently, three cracked optical fiber diodes were interconnected within the mechanical computing system to enable high-level computations. Different colored light sources are introduced into the cracked optical fiber diodes labeled “X” and “Y”, while diode “Z” collects light transmitted through the two cracked optical fibers (Fig. 3 b and c). For example, when no change in elongation is applied to all diodes (all input = "0"), the system outputs light exceeding the threshold intensity (output = "1") (Fig. 3 b). Conversely, when elongation is removed from all diodes (all input = "1"), the output light intensity falls below the threshold (output = "0") (Fig. 3 c). The computational capabilities of various logic gates, comparable to those performed by electronic computers, were demonstrated using the mechanical deformation states of the substrate. A NOT gate was achieved by activating only diode Z (Fig. 3 d). Regardless of the light intensity passing through fibers X and Y, when the "0" state (stretched state) was input to diode Z, the sum of the RGB light exceeded the threshold intensity, resulting in an output of “1”. Conversely, with an input of "1" (released state) to diode Z, the RGB light sum remained below the threshold, yielding an output of “0”. These results are visually discernible (Fig. 3 e), successfully confirming the functionality of the NOT gate (Fig. 3 f). In addition, NAND and NOR logic gates with complex input–output relationships were implemented by activating all cracked optical fibers in X and Y (Fig. 3 g). Figure 3 h-j and Fig. 3 k-m illustrate the computing processes of the NAND and NOR gates, respectively. The computation results are consistent with the values in the logical operation table shown in Fig. 3 g. Notably, the sum of light intensities reaching the end of diode Z, which determines the output value, was similar in the NAND and NOR logic circuit systems. However, both logic gates were successfully implemented by simply modifying the output threshold intensity setting. Multifunctionality as a Multiaxis Vibration Sensor in a Mechanical Computing System In a mechanical computing system, extending the input axis of deformation enables more complex and diverse calculations and improves computing performance by processing more information simultaneously. In this context, the scalability of the input axis for a strain-light-driven mechanical computing system was demonstrated by its ability to detect vibrations along an axis orthogonal to the prestrain applied to the substrate, as shown in Fig. 4 a. Vibrations along this orthogonal axis distort the light transmission path, reducing the intensity of the transmitted light. Notably, the attenuation of light transmission owing to vibration becomes more pronounced when the core of the cracked optical fiber is exposed as the prestrain is released (Fig. 4 b). Accordingly, the light transmitted through the cracked optical fiber under a vibrational environment and the voltage change was observed (Fig. 4 c). Depending on the degree of prestrain release, i.e., the degree to which the 3D crack of the optical fiber is exposed, different voltage changes are observed (Fig. 4 d). When the prestrain remains unreleased, the crack exposure area is extremely small, and light scattering is negligible, even when the light transmission path is distorted owing to vibration. By contrast, with an enlarged crack exposure area owing to increased strain release, a significant voltage change is observed. In addition, increasing the diameter of the cracked optical fiber maximizes light scattering under the same vibration condition, resulting in higher sensitivity to changes in the intensity of the transmitted light (Fig. 4 e). Furthermore, the system demonstrated sufficient temporal resolution to distinguish continuous vibrations alternating between the on/off states at specific time intervals (Fig. 4 f). These findings highlight the capability of the system to sense multiaxis mechanical strain inputs. This implies that strain-light-driven mechanical computing systems have the potential to sense diverse physical changes and perform multifunctional computations on complex inputs. DISCUSSION This study proposed a logic-device-inspired mechanical computing system capable of signal modulation, a typical function of active components, by integrating soft and 3D electronics. The proposed system was designed by integrating 3D cracked optical fibers with a low-modulus, high-elongation elastomeric substrate to enable a multimodal architecture of the 3D cracked optical fibers that responds the reversible deformation of the substrate. The optimized crack morphology was engraved onto the optical fiber using a laser-cutting strategy supported by simulation studies. These engraved cracks induced stress concentration in specific regions when the optical fiber deformed under strain. Stress concentration induced light carrier depletion and rapid attenuation of light output, demonstrating that the cracked optical fiber functioned as a diode, exhibiting on/off state switching behavior. Furthermore, logical calculations were successfully performed by integrating multiple cracked optical fiber diodes into a mechanical computing system. The system demonstrated multifunctional vibration sensing, capable of detecting vibrations with orthogonal axes to the prestrain, highlighting its axis scalability for strain input. Furthermore, this study explored three-dimensional structures, such as helical configurations, demonstrating that the stress concentration and optical attenuation mechanisms induced by cracks can also be applied to optical fibers with non-linear morphologies. This enables their use as mechanical computing elements capable of responding to various types of deformations (Supporting Information S1-S6). The anisotropic nature of the helical structures enable stress concentration under external deformation, induces light attenuation, and offer excellent durability under high strain and stress. Strain-light-driven mechanical computing systems based on optical fibers with structural degrees of freedom are expected to revolutionize applications in various fields, such as robotics and space exploration. These system can perform accurate calculations with deterministic behavior and operate in extreme environments. METHODS Fabrication of Silicone Elastomer PMMA (≈ 100 nm, Microchem INC) was spin-coated on a silicon wafer (3000 rpm for 30 s). After spin-coating, a three-step soft-bake process was conducted. The wafer was sequentially heated on a hotplate at 110, 160, and 180°C, each for 10 min. Subsequently, the silicone elastomer (Ecoflex 0050, Smooth-on) was prepared by mixing the base (Part A) and curing agent (Part B) in a 1:1 ratio. After mixing, 20 g of the silicone elastomer was spin-coated on a the PMMA-coated wafer, followed by spin-coating at 1000 rpm for 1 s, repeated three times. Semi-curing was performed at 110°C on a hotplate for 1 min, followed by full curing at 25°C for 24 h. Fabrication and Characterization of Cracked Optical Fiber A laser cutter (JQlaser, JQ9060) was used to create cracks in the optical fiber (Toray, PGR-FB). The power and speed settings of the laser were adjusted to control the dwell time and intensity of the laser beam to form 3D cracks. The parameters of the laser cutter, including speed (mm/s) and power (W), were optimized to ensure controlled crack formation. The crack patterns were designed considering the interaction between the laser and optical fiber material to achieve precise 3D cracks. Fabrication of Bonding Sites and Integrated Devices Multiple bonding techniques were employed to integrate the elastomeric substrate with the 3D cracked optical fiber. Siloxane bonding was used for optical fibers with diameters ranging from 250 µm to 500 µm. Using photolithography and an e-beam evaporator, 100 nm SiO2 and 100 nm Ti layers were selectively deposited onto the 3D cracked optical fibers through a masking process. The elastomeric substrate was heated to 60°C and placed in conformal contact with the optical fibers. A paper towel was placed over the substrate, and a 1 kg weight was applied for 30 min to ensure proper bonding. Polyimide tape was laser cut for fibers exceeding 500 µm in diameter to match the bonding area, facilitating easy integration with stronger adhesion. Siloxane bonding enabled microscale precision, while polyimide tape bonding provided robust adhesion suitable for various fiber sizes. Fabrication and Measurement of Vibration Sensors Vibration sensor experiments were conducted in a dark room to eliminate external light interference. One end of the cracked optical fibers was connected to a light emitter, directing light through the fiber. The other end of the fiber was connected to a photodiode linked to a digital multimeter (2400 SMU, Keithley). The substrate, with the cracked optical fibers attached, was placed on a high-speed motor-equipped stage. As the motor vibrated the substrate, the vibration modulated the light output of the fiber, and the current of the photodiode was measured to quantify the sensor response. Fabrication and Measurement of Logic Gates Three cracked optical fiber diodes were connected using a Y-shaped connector to create logic gate structures. Light sources with three distinct wavelengths (λR = 655 nm, λG = 532 nm, and λB = 460 nm) were used as inputs. The strain applied to the prestrained substrate, adjusted using the X and Y stretchers of the diodes, served as the input signal. Although the color of the output light could be visually observed, quantitative analysis was performed by capturing images and measuring RGB pixel intensities in a defined area using the ImageJ software. Fabrication and Measurement of Helical Optical Fiber Sensors Optical fibers (Toray, FBG-PGR) were coiled around a rod and fixed using polyimide tape. The fibers were then heat-annealed in a vacuum oven at 70°C for 1 h, followed by cooling to room temperature for 10 min. After cooling, the tape was removed, and the fibers were carefully unwound to form helical optical fiber sensors. One end of the fiber was illuminated with a laser pointer to measure strain, while the other was connected to an optical power meter. For pressure measurements, the sensor was encapsulated in PDMS to ensure even pressure distribution (0–50 N) applied using a universal testing machine (UTM). Finite Element Analysis (FEA) Finite element analysis (FEA) simulations were performed using Abaqus to evaluate the mechanical response of the cracked optical fiber sensors. The optical fiber was modeled as a cylindrical structure with a diameter of 0.25 mm, featuring a crack measuring 0.13 mm in width and 0.23 mm in length. The model consisted of 10-node quadratic tetrahedron elements (C3D10) with a global seed size of 0.1, resulting in 12,402 elements. The material properties of the optical fiber were defined based on experimental stress–strain (S-S) data, with a Young's modulus of 1121 MPa and Poisson's ratio of 0.16. The optical fiber was prestretched by 500% and then released to 300%, simulating the experimental conditions. The simulation results were consistent with the experimental data, demonstrating that strain concentration occurred in areas with lower modulus around the cracks, confirming the accuracy of the model. Declarations DATA AVAILABILITY The data that support the findings of this study are either provided in the source data or are available from the corresponding author upon reasonable request. ACKNOWLEDGEMENTS This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (grant Nos. 2022M3H4A1A02046445, RS-2024-00347619, RS-2024-00406240, RS-2024-00407155, and RS-2025-00513522). AUTHOR CONTRIBUTIONS J. H. P., J. H. K., and H. U. 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Technol. 33, 493–501 (2024). Additional Declarations No competing interests reported. Supplementary Files SupportingInformation.pdf Cite Share Download PDF Status: Published Journal Publication published 28 Nov, 2025 Read the published version in npj Flexible Electronics → Version 1 posted Editorial decision: Revision requested 18 May, 2025 Reviews received at journal 09 May, 2025 Reviewers agreed at journal 28 Apr, 2025 Reviews received at journal 27 Apr, 2025 Reviewers agreed at journal 22 Apr, 2025 Reviewers invited by journal 29 Mar, 2025 Editor assigned by journal 21 Mar, 2025 Submission checks completed at journal 21 Mar, 2025 First submitted to journal 11 Mar, 2025 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-6200645","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":442429493,"identity":"0fe4c244-9695-49eb-9ecc-b246b67cf193","order_by":0,"name":"Jun Hyun Park","email":"","orcid":"","institution":"DGIST","correspondingAuthor":false,"prefix":"","firstName":"Jun","middleName":"Hyun","lastName":"Park","suffix":""},{"id":442429494,"identity":"b13bd6ef-50b0-47d6-a294-1e276fe453cc","order_by":1,"name":"Jang Hwan Kim","email":"","orcid":"","institution":"Ajou University","correspondingAuthor":false,"prefix":"","firstName":"Jang","middleName":"Hwan","lastName":"Kim","suffix":""},{"id":442429495,"identity":"6b0fd493-6b67-4042-91fc-a2315cbedf20","order_by":2,"name":"Ha Uk Chung","email":"","orcid":"","institution":"Korea University","correspondingAuthor":false,"prefix":"","firstName":"Ha","middleName":"Uk","lastName":"Chung","suffix":""},{"id":442429496,"identity":"e5a22bf5-fea6-4814-98ec-42eafe9157b5","order_by":3,"name":"Jun Seok Choe","email":"","orcid":"","institution":"DGIST","correspondingAuthor":false,"prefix":"","firstName":"Jun","middleName":"Seok","lastName":"Choe","suffix":""},{"id":442429500,"identity":"9dcd3be0-89c6-4575-b8ba-075abfd1ad10","order_by":4,"name":"Hyokyeong Kim","email":"","orcid":"","institution":"Soongsil University","correspondingAuthor":false,"prefix":"","firstName":"Hyokyeong","middleName":"","lastName":"Kim","suffix":""},{"id":442429501,"identity":"6f7c1baa-019b-4161-ad54-bc4dc6e540b1","order_by":5,"name":"Su Eon Lee","email":"","orcid":"","institution":"DGIST","correspondingAuthor":false,"prefix":"","firstName":"Su","middleName":"Eon","lastName":"Lee","suffix":""},{"id":442429502,"identity":"17ee24a3-929e-4919-a84f-c15bcd8e004f","order_by":6,"name":"Simon Kim","email":"","orcid":"","institution":"DGIST","correspondingAuthor":false,"prefix":"","firstName":"Simon","middleName":"","lastName":"Kim","suffix":""},{"id":442429505,"identity":"7af5b70d-a45b-4e72-8179-9cdce4872ddb","order_by":7,"name":"Ho Jun Jin","email":"","orcid":"","institution":"DGIST","correspondingAuthor":false,"prefix":"","firstName":"Ho","middleName":"Jun","lastName":"Jin","suffix":""},{"id":442429507,"identity":"5fe516b3-4cb1-4dc1-941b-3bcbaea71da5","order_by":8,"name":"Jiwoong Kim","email":"","orcid":"","institution":"Soongsil University","correspondingAuthor":false,"prefix":"","firstName":"Jiwoong","middleName":"","lastName":"Kim","suffix":""},{"id":442429508,"identity":"12ae8037-a644-4a11-bc08-a91ab34069f5","order_by":9,"name":"Heon Lee","email":"","orcid":"","institution":"Korea University","correspondingAuthor":false,"prefix":"","firstName":"Heon","middleName":"","lastName":"Lee","suffix":""},{"id":442429511,"identity":"da8bf535-42f4-48ce-8d3f-f767b2be0724","order_by":10,"name":"Jaehwan Kim","email":"","orcid":"","institution":"Kumoh National Institute of Technology","correspondingAuthor":false,"prefix":"","firstName":"Jaehwan","middleName":"","lastName":"Kim","suffix":""},{"id":442429513,"identity":"efeb529c-e568-4961-b24d-c31744b54594","order_by":11,"name":"Bong Hoon Kim","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA/ElEQVRIiWNgGAWjYBACAyBmBjEkmBkYH/AwSEDFDxCnhdkApIWHeC0MDGwSIOUEtZiz9x5+XVBhkyfZzp1W8eaXhb09A/PDDwxn7uHUYtlzLs16xpm0Ymlm3m035/ZJJPYwsBlLMNwoxu2wGzlmxrxthxPnAbXc5u2RSAA6zIyB4UMCcVqKgVrseRjYvxHSYvwYpGU2UAszzw8Jxh4GHqAtN3Brsew5Y8bMcyYtcWYz72bJuQ1AvxzmKZZIOINbizl7j/FnngqbxBnnz2788OZPnT17e/vGDx+O4dbCAIoOOJOxjQESTXg1AJV8QLD/4Fc6CkbBKBgFIxMAAGDRUBExiNpYAAAAAElFTkSuQmCC","orcid":"","institution":"DGIST","correspondingAuthor":true,"prefix":"","firstName":"Bong","middleName":"Hoon","lastName":"Kim","suffix":""}],"badges":[],"createdAt":"2025-03-11 06:53:10","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6200645/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6200645/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1038/s41528-025-00497-2","type":"published","date":"2025-11-28T15:58:36+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":80917293,"identity":"373763e3-1a48-4b49-bd41-93ea455cc601","added_by":"auto","created_at":"2025-04-18 18:28:45","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":6335835,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eSchematics and Performance Analysis of Fiber-Optic-Based Mechanical Computing Systems.\u003c/strong\u003e \u003cstrong\u003ea\u003c/strong\u003e Schematics illustrating the mechanical computing framework, from input to mechanical computing, output, and conversion. \u003cstrong\u003eb\u003c/strong\u003e Schematic of the depletion region formation in a typical diode, along with intensity and voltage graphs for forward bias. \u003cstrong\u003ec\u003c/strong\u003e Schematic of a fiber-optic-based mechanical computing unit and the strain and attenuation graphs resulting from the shrinkage of the silicone elastomer. \u003cstrong\u003ed\u003c/strong\u003e Schematic illustration of the fabrication method for a mechanical single unit and the components of the optical fiber. \u003cstrong\u003ee\u003c/strong\u003e Single unit cell images under substrain levels of (i) 500 %, (ii) 250 %, and (iii) 0 %, with external light on (left), external light off (right), and zoomed-in view (inset). \u003cstrong\u003ef\u003c/strong\u003e Mechanical computing systems using unit cell arrays with different light wavelengths.\u003c/p\u003e","description":"","filename":"Figure1.png","url":"https://assets-eu.researchsquare.com/files/rs-6200645/v1/5ce322ffe7a1289cf166d86c.png"},{"id":80916931,"identity":"c7439996-49d4-434c-80cb-03b9995d35ba","added_by":"auto","created_at":"2025-04-18 18:20:44","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":7987282,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eCrack Morphology and Stress Distribution in Laser-Cut Optical Fibers.\u003c/strong\u003e OM images of crack sizes according to the power of the laser cutter: \u003cstrong\u003ea\u003c/strong\u003e10 W, \u003cstrong\u003eb\u003c/strong\u003e 15 W, \u003cstrong\u003ec\u003c/strong\u003e 20 W. 3D profiler images of the cracked optical fiber: \u003cstrong\u003ed\u003c/strong\u003e top view, \u003cstrong\u003ee\u003c/strong\u003e side view. Stress distribution caused by different crack shapes: \u003cstrong\u003ef\u003c/strong\u003e V-shape, \u003cstrong\u003eg\u003c/strong\u003e Two-point V-shape, \u003cstrong\u003eh\u003c/strong\u003eFour-point V-shape. Stress distribution simulation of the V-shape unit under varying substrate strain: \u003cstrong\u003ei\u003c/strong\u003e 500 %, \u003cstrong\u003ej\u003c/strong\u003e 250 %, \u003cstrong\u003ek\u003c/strong\u003e 0 %.\u003c/p\u003e","description":"","filename":"Figure2.png","url":"https://assets-eu.researchsquare.com/files/rs-6200645/v1/eb207b9a15c46ea26643fddc.png"},{"id":80916933,"identity":"1d3c463f-7f7f-4a66-9907-9b2767d314d9","added_by":"auto","created_at":"2025-04-18 18:20:45","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":6848425,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eOptical Transistor Logic Gates in Mechanical Computing Systems.\u003c/strong\u003e \u003cstrong\u003ea\u003c/strong\u003e Schematic of the input and output states of the mechanical computing unit cell. Three unit cells are used as switches for three transistors, acting as inputs X, Y, and Z. A laser beam is input into each part to measure the light emitted from other parts. \u003cstrong\u003eb\u003c/strong\u003eSchematic when input = 0 under substrate strain, where light is emitted outward. \u003cstrong\u003ec\u003c/strong\u003e Schematic when input = 1 under substrate strain, where light is not emitted outward. \u003cstrong\u003ed\u003c/strong\u003e RGB value graph detected at point \"S\" under the (01) and (10) logic conditions of a NOT gate. The output state is defined as \"1\" or \"0\" depending on whether the RGB sum exceeds 400. \u003cstrong\u003ee\u003c/strong\u003e Real image, \u003cstrong\u003ef\u003c/strong\u003e Schematic of the optical transistor NOT gate and its (01) and (10) logic conditions. \u003cstrong\u003eg\u003c/strong\u003e Truth table of logic gates defined by various input and output configurations. \u003cstrong\u003eh\u003c/strong\u003eRGB value graph detected at point \"F\" under the (001), (101), (011), and (110) logic conditions of a NAND gate. The output state is defined as \"1\" or \"0\" depending on whether the RGB sum exceeds 400. \u003cstrong\u003ei\u003c/strong\u003eReal image, \u003cstrong\u003ej\u003c/strong\u003e Schematic of the optical transistor NAND gate and its (001), (101), (011), and (110) logic conditions. \u003cstrong\u003ek\u003c/strong\u003e RGB value graph detected at point \"F\" under the (001), (100), (010), and (110) logic conditions of a NOR gate. The output state is defined as \"1\" or \"0\" depending on whether the RGB sum exceeds 500. \u003cstrong\u003el\u003c/strong\u003e Real image, \u003cstrong\u003em\u003c/strong\u003e Schematic of the optical transistor NOR gate and its (001), (101), (011), and (110) logic conditions.\u003c/p\u003e","description":"","filename":"Figure3.png","url":"https://assets-eu.researchsquare.com/files/rs-6200645/v1/ef74c74ec4ea6145644ae6c5.png"},{"id":80916940,"identity":"f328b520-b217-4025-bfbf-48e58a60e179","added_by":"auto","created_at":"2025-04-18 18:20:45","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":5075579,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eVibration Sensing and Voltage Response in Cracked Optical Fiber Systems.\u003c/strong\u003e \u003cstrong\u003ea\u003c/strong\u003e Photographs of the optical fiber under vibration. The mechanical computing array is designed with a pop-up structure using a bi-axis stretcher on a vibration motor. \u003cstrong\u003eb\u003c/strong\u003e Schematic of a single optical fiber unit cell vibrating. \u003cstrong\u003ec\u003c/strong\u003e Schematic of earthquake measurement using cracked optical fiber when Input = 1. \u003cstrong\u003ed\u003c/strong\u003e Voltage difference graph for three repeated cycles of vibration on/off. \u003cstrong\u003ee\u003c/strong\u003e Voltage measurement graph after adjusting the pop-up (0/50/100 %) according to strain. \u003cstrong\u003ef\u003c/strong\u003e Voltage difference graph when vibration is on, based on the diameter of the optical fiber (250/500/1000 μm).\u003c/p\u003e","description":"","filename":"Figure4.png","url":"https://assets-eu.researchsquare.com/files/rs-6200645/v1/863c7fbceabc26099f1b5a06.png"},{"id":97178634,"identity":"7ceed9ea-5924-4059-8eec-8586647b4be7","added_by":"auto","created_at":"2025-12-01 16:11:55","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":38284277,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6200645/v1/1063cdc1-8c5a-4c5a-a4f6-6196fc12384c.pdf"},{"id":80916938,"identity":"2294360f-9f1f-48b1-9899-d9ccd3514eac","added_by":"auto","created_at":"2025-04-18 18:20:45","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"supplement","size":380130,"visible":true,"origin":"","legend":"","description":"","filename":"SupportingInformation.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6200645/v1/bdd0ff5882bb2a44224b9b07.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Logic-Device-Inspired Mechanical Computing System Based on Three- Dimensional Active Components","fulltext":[{"header":"INTRODUCTION","content":"\u003cp\u003eMechanical computing is a data processing and calculation strategy that relies on the physical displacement and interaction of mechanical devices\u003csup\u003e\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u003c/sup\u003e. Owing to the operation mechanism based on mechanical motion, mechanical computing systems can maintain reliable performance even under harsh environmental conditions, such as extreme temperatures\u003csup\u003e\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e\u003c/sup\u003e, radiation exposure\u003csup\u003e\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e\u003c/sup\u003e, and signal interference\u003csup\u003e\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e,\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e\u003c/sup\u003e. In addition, the precise and sophisticated design of these systems ensures consistently high calculation accuracy, enabling computations with minimal errors and enhancing robustness against external changes\u003csup\u003e\u003cspan additionalcitationids=\"CR7 CR8\" citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e\u003c/sup\u003e. These advantages have made mechanical computing an attractive technology for applications requiring precise mechanical deformations, such as advanced manufacturing systems and space engineering.\u003c/p\u003e \u003cp\u003eDespite these advantages, several intrinsic challenges remain in expanding the accessibility and applicability of mechanical computing. Conventional mechanical computing systems primarily employ high-modulus, low-elongation materials throughout the entire system, except for specific deformable elements, such as joints\u003csup\u003e\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e,\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e\u003c/sup\u003e. This design provides high strength and stiffness but makes the system susceptible to repetitive deformation and material fatigue. Moreover, the inherent limitations of systems composed of high-modulus materials\u003csup\u003e\u003cspan additionalcitationids=\"CR13 CR14\" citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e\u003c/sup\u003e pose significant challenges for dynamic applications, such as wearable devices and soft robotics involving repetitive movements and complex motions with multidimensional nonlinear deformation. In this context, adopting low-modulus, high-elongation materials in mechanical computing systems presents a promising solution\u003csup\u003e\u003cspan additionalcitationids=\"CR17 CR18\" citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e\u003c/sup\u003e, offering flexibility and stretchability. Integrating low-modulus materials throughout the system ensures reliability even under repetitive displacement and prolonged loading while achieving greater spatial freedom of operation under multidimensional nonlinear deformations\u003csup\u003e\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e,\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e\u003c/sup\u003e. In addition, system configurations with low-modulus materials enable high sensitivity to environmental changes, supporting sophisticated and rapid data processing essential for dynamic applications.\u003c/p\u003e \u003cp\u003eElectronic computing systems are typically designed by combining passive and active components based on the required functions\u003csup\u003e\u003cspan additionalcitationids=\"CR23\" citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e\u003c/sup\u003e. Passive components\u003csup\u003e\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e,\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e\u003c/sup\u003e, such as resistors and capacitors, are suitable for transmitting or regulating signals but cannot modulate or amplify signal flow. By contrast, active components\u003csup\u003e\u003cspan additionalcitationids=\"CR28\" citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e\u003c/sup\u003e, such as diodes and transistors, perform the functions of passive components and enable advanced signal processing and complex logic calculations by modulating and amplifying signal flow\u003csup\u003e\u003cspan additionalcitationids=\"CR31 CR32 CR33\" citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e\u003c/sup\u003e. In comparison, mechanical computing systems typically rely on passive computation derived from the deterministic behavior of mechanical components\u003csup\u003e\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e,\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e\u003c/sup\u003e. Thus, they are optimized for specific tasks but face challenges in implementing the active signal modulation capabilities provided by active components of electronic computers. This limitation leads to challenges with data processing, dynamic adjustments, and executing complex operations. Therefore, integrating active components into mechanical computing systems is necessary to meet the demands of increasingly complex modern computing tasks and provide adaptable, dynamic operations in diverse environments.\u003c/p\u003e \u003cp\u003eThis study introduces a mechanical computing system integrating soft and three-dimensional (3D) electronics. The system employs mechanically guided 3D optical fibers as active components to modulate light transmission for highly complex computations while functioning as a vibration sensor. The key features of the proposed mechanical computing system are as follows: ⅰ) The first mechanical computing system incorporating soft electronics. The intrinsically flexible optical fiber-based mechanical computing system is built on a stretchable silicone elastomeric substrate, which induces mechanical deformation of optical fiber through substrate elongation. Incorporating low-modulus and high-elongation materials throughout the entire system enables nonlinear deformation in multidimensional space. ⅱ) An active signal modulation capability similar to that of a diode in electronic computing systems is first demonstrated through the mechanically guided 3D deformation of optical fibers with cracks. The 3D structural transitions of the cracked optical fiber facilitate multimodal conversion between the on/off states of light transmission, enabling active light modulation. The morphology of the cracks is precisely designed to efficiently alter the light transmission path through stress concentration, as supported by simulation studies. In addition, multiple 3D multimodal optical fiber diodes are integrated to successfully execute several complex logical computations. ⅲ) Multifunctionality as a vibration sensor is demonstrated by detecting vibrations along different axes induced by intentional mechanical deformation, highlighting its scalability for multiaxis strain input. Mechanical computing systems incorporating low-modulus and high-elongation materials enable flexible and stretchable innovative computing devices for technologies relying on the mechanical deformation of materials, such as wearable devices and soft robots. Furthermore, mechanical computing systems integrating active components hold significant potential for advancing automation and adaptive systems through complex signal processing.\u003c/p\u003e"},{"header":"RESULTS","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003eLogic-Device-Inspired Mechanical Computing System Based on 3D Cracked Optical Fiber\u003c/h2\u003e \u003cp\u003eMechanical computing device operation follows a conceptual flow where unit cells constituting the device interact through the input mechanical deformation and output a transformed state based on a deterministic nature (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ea). This study proposes a novel mechanical computing system in which the morphological state of optical fiber cracks is determined by input strain applied to the substrate\u003csup\u003e\u003cspan additionalcitationids=\"CR38 CR39 CR40\" citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e41\u003c/span\u003e\u003c/sup\u003e, and light output with controlled attenuation is generated. Consequently, these cracked optical fibers function as diodes, actively modulating light transmission and distinguishing between on and off states, serving as active components within the mechanical computing system.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eA diode is an active component in a semiconductor device that allows current to predominantly flow in one direction by controlling the carrier (hole or electron) concentration in the depletion region with an applied voltage bias, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003eb. The on/off state of the diode is differentiated according to the threshold voltage, defined as the minimum forward bias required for the current to start flowing, beyond which the current begins to flow. Inspired by this operating mechanism, the cracked optical fiber switches the on/off state of light output by controlling the depletion level of light-carrying carriers (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ec). Carrier depletion occurs in cracks intentionally created on the optical fiber surface and is regulated by the state of the three-dimensional (3D) crack, which varies with the applied strain. The strain-light-driven optical fiber diodes\u003csup\u003e\u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e42\u003c/span\u003e,\u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e43\u003c/span\u003e\u003c/sup\u003e can exhibit a rapid light attenuation behavior at the threshold strain, establishing a criterion to distinguish between the on and off states.\u003c/p\u003e \u003cp\u003eThe strain-light-driven optical fiber diode operates through the deformation of cracked optical fibers attached to a low-modulus and high-elongation elastomeric substrate\u003csup\u003e\u003cspan additionalcitationids=\"CR45 CR46 CR47 CR48\" citationid=\"CR44\" class=\"CitationRef\"\u003e44\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e49\u003c/span\u003e\u003c/sup\u003e. The mechanical properties of the elastomeric substrate enable it to endure reversible and repetitive deformation. Consequently, the architecture and operational mode of the cracked optical fibers are altered with the strain applied to the substrate, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ed. The crack of the optical fiber is formed in 3D\u003csup\u003e\u003cspan additionalcitationids=\"CR51 CR52\" citationid=\"CR50\" class=\"CitationRef\"\u003e50\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR53\" class=\"CitationRef\"\u003e53\u003c/span\u003e\u003c/sup\u003e on the surface through a simple laser-cutting strategy, which is discussed in the succeeding section. The strain release exposes the optical fiber core region, which determines the light propagation path, leading to the attenuation of light transmission intensity\u003csup\u003e\u003cspan additionalcitationids=\"CR55 CR56\" citationid=\"CR54\" class=\"CitationRef\"\u003e54\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR57\" class=\"CitationRef\"\u003e57\u003c/span\u003e\u003c/sup\u003e. The light transmission behavior of cracked optical fibers under varying strain applied to a prestretched elastomeric substrate is observed in bright field (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ee, left column) and dark field (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ee, right column). The transmitted light intensity attenuates owing to crack-induced light scattering and light carrier depletion as the applied strain to the substrate decreases (500%, 250%, and 0% strain). Moreover, nearly no light is transmitted into the fiber beyond the crack at conditions below approximately 180% strain (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ec). Consequently, the availability of cracked optical fibers as components of strain-light-driven mechanical computing devices is confirmed by inducing mechanical deformation and changing the state of individual cracked optical fibers independently or in combination by controlling the strain applied to the substrate (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ef).\u003c/p\u003e \u003c/div\u003e\n\u003ch3\u003eMorphological Optimization of 3D Cracks for Effective Light Attenuation\u003c/h3\u003e\n\u003cp\u003eMechanical cracks are typically associated with structural weaknesses owing to stress concentration. Two-dimensional (2D) cracks weaken the strength and durability of materials and increase the risk of crack propagation, causing various challenges related to system stability. To address these problems, significant efforts have been made to effectively eliminate 2D cracks and maintain the structural integrity of materials. However, the potential of mechanical cracks as a strategic design element for systems requiring precise signal control, such as electronic sensors\u003csup\u003e\u003cspan citationid=\"CR58\" class=\"CitationRef\"\u003e58\u003c/span\u003e,\u003cspan citationid=\"CR59\" class=\"CitationRef\"\u003e59\u003c/span\u003e\u003c/sup\u003e, has been explored. In particular, 3D cracks offer the advantage of precise control over stress distribution owing to their high spatial degree of freedom. This enables nonlinear responses to deformation and effective modulation of physical elements, such as light, vibration, and heat. In addition, 3D cracks enhance adaptability to complex mechanical stresses, ensuring stable performance under various deformation conditions. Consequently, systems using 3D cracks achieve superior sensitivity and precision under micro deformation, making them ideal for applications requiring finely tuned mechanical responses.\u003c/p\u003e \u003cp\u003eIn this context, 3D cracks have been adopted as a structural strategy to achieve effective light attenuation and rapid on/off switching in optical fibers. Morphological optimization of cracks has been performed to maximize performance. The 3D cracks were formed by ablating a finite region of the fiber cladding using a straightforward and controllable laser-cutting method. Differences in the ablation of the fiber cladding area were induced by controlling the laser power; higher power intensities resulted in greater ablation, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ea-c. Subsequently, in-depth morphological analysis was performed to verify the 3D structural modification of the optical fiber after laser cutting. A 3D anisotropic crack was formed, exposing the core area\u0026mdash;the primary light transmission path\u0026mdash;under deformation (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ed-e).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eTo further understand the impact of 3D cracks, simulations were performed to obtain the stress distributions of the cracked optical fiber sensors. The simulations reveal the size and shape of the crack and the effect of that shape on the stress distribution. The stress distributions were evaluated for various crack shapes, including V-shape, two-point V-shape, and four-point V-shape (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ef-h). All stresses applied were below 4 MPa. Stress concentration is observed in the cracks, with the V-shaped cracks exhibiting more concentrated stress (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ef) compared with the more relaxed stress distributions observed in the two-point and four-point V-shaped cracks (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eg-h). Replicating experimental conditions, the optical fibers were fixed at both ends of the prestretched substrates elongated by up to 500%, followed by a controlled release to 300%. The stress distribution in each case was simulated around the cross-section of the 3D crack. These simulations demonstrate how V-shaped cracks influence the stress distribution based on the substrate strain (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ei-k). In particular, stresses in the V-shaped cracks remain within safe limits, peaking at 13.3 MPa. This result aligns closely with experimental findings, highlighting the influence of anisotropic 3D crack geometry, generated through fiber cladding ablation, on stress concentration. During mechanical deformation of the optical fiber, stress tends to accumulate in uncut regions owing to this geometry. Upon substrate strain release, these concentrated stresses expose the fiber core, enhancing light attenuation and enabling efficient and swift transitions between the on/off states.\u003c/p\u003e\n\u003ch3\u003eLogic Computation Using an Active Signal Modulation Optical-Fiber-Based Mechanical Computing System\u003c/h3\u003e\n\u003cp\u003eLeveraging the light attenuation and clear on/off state switching behavior of the cracked optical fiber diode, the logic computation performance of a mechanical computing system consisting of multiple cracked optical fibers was demonstrated (see details in the Experimental Section). This system defines the elongation state of the substrate as input and the intensity of light transmitted across the optical fiber crack as output (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ea). The input is defined as \u0026ldquo;0\u0026rdquo; when no change in elongation occurs, with the substrate remaining in a stretched state (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ea, upper column). Conversely, the input is defined as \u0026ldquo;1\u0026rdquo; when the elongation changes, corresponding to a released substrate (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ea, lower column). The output value is determined based on the total light intensity transmitted across the cracked optical fiber, which varies with the elongation state of the substrate. A threshold light intensity was set, adjustable depending on the system. Intensities below this threshold were defined as an output value of \u0026ldquo;0\u0026rdquo; (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ea, lower column), whereas intensities exceeding the threshold were defined as an output value of \u0026ldquo;1\u0026rdquo; (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ea, upper column). Subsequently, three cracked optical fiber diodes were interconnected within the mechanical computing system to enable high-level computations. Different colored light sources are introduced into the cracked optical fiber diodes labeled \u0026ldquo;X\u0026rdquo; and \u0026ldquo;Y\u0026rdquo;, while diode \u0026ldquo;Z\u0026rdquo; collects light transmitted through the two cracked optical fibers (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eb and c). For example, when no change in elongation is applied to all diodes (all input = \"0\"), the system outputs light exceeding the threshold intensity (output = \"1\") (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eb). Conversely, when elongation is removed from all diodes (all input = \"1\"), the output light intensity falls below the threshold (output = \"0\") (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ec).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe computational capabilities of various logic gates, comparable to those performed by electronic computers, were demonstrated using the mechanical deformation states of the substrate. A NOT gate was achieved by activating only diode Z (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ed). Regardless of the light intensity passing through fibers X and Y, when the \"0\" state (stretched state) was input to diode Z, the sum of the RGB light exceeded the threshold intensity, resulting in an output of \u0026ldquo;1\u0026rdquo;. Conversely, with an input of \"1\" (released state) to diode Z, the RGB light sum remained below the threshold, yielding an output of \u0026ldquo;0\u0026rdquo;. These results are visually discernible (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ee), successfully confirming the functionality of the NOT gate (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ef). In addition, NAND and NOR logic gates with complex input\u0026ndash;output relationships were implemented by activating all cracked optical fibers in X and Y (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eg). Figure\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eh-j and Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ek-m illustrate the computing processes of the NAND and NOR gates, respectively. The computation results are consistent with the values in the logical operation table shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eg. Notably, the sum of light intensities reaching the end of diode Z, which determines the output value, was similar in the NAND and NOR logic circuit systems. However, both logic gates were successfully implemented by simply modifying the output threshold intensity setting.\u003c/p\u003e\n\u003ch3\u003eMultifunctionality as a Multiaxis Vibration Sensor in a Mechanical Computing System\u003c/h3\u003e\n\u003cp\u003eIn a mechanical computing system, extending the input axis of deformation enables more complex and diverse calculations and improves computing performance by processing more information simultaneously. In this context, the scalability of the input axis for a strain-light-driven mechanical computing system was demonstrated by its ability to detect vibrations along an axis orthogonal to the prestrain applied to the substrate, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ea. Vibrations along this orthogonal axis distort the light transmission path, reducing the intensity of the transmitted light. Notably, the attenuation of light transmission owing to vibration becomes more pronounced when the core of the cracked optical fiber is exposed as the prestrain is released (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003eb). Accordingly, the light transmitted through the cracked optical fiber under a vibrational environment and the voltage change was observed (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ec). Depending on the degree of prestrain release, i.e., the degree to which the 3D crack of the optical fiber is exposed, different voltage changes are observed (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ed). When the prestrain remains unreleased, the crack exposure area is extremely small, and light scattering is negligible, even when the light transmission path is distorted owing to vibration. By contrast, with an enlarged crack exposure area owing to increased strain release, a significant voltage change is observed. In addition, increasing the diameter of the cracked optical fiber maximizes light scattering under the same vibration condition, resulting in higher sensitivity to changes in the intensity of the transmitted light (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ee). Furthermore, the system demonstrated sufficient temporal resolution to distinguish continuous vibrations alternating between the on/off states at specific time intervals (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ef). These findings highlight the capability of the system to sense multiaxis mechanical strain inputs. This implies that strain-light-driven mechanical computing systems have the potential to sense diverse physical changes and perform multifunctional computations on complex inputs.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e"},{"header":"DISCUSSION","content":"\u003cp\u003eThis study proposed a logic-device-inspired mechanical computing system capable of signal modulation, a typical function of active components, by integrating soft and 3D electronics. The proposed system was designed by integrating 3D cracked optical fibers with a low-modulus, high-elongation elastomeric substrate to enable a multimodal architecture of the 3D cracked optical fibers that responds the reversible deformation of the substrate. The optimized crack morphology was engraved onto the optical fiber using a laser-cutting strategy supported by simulation studies. These engraved cracks induced stress concentration in specific regions when the optical fiber deformed under strain. Stress concentration induced light carrier depletion and rapid attenuation of light output, demonstrating that the cracked optical fiber functioned as a diode, exhibiting on/off state switching behavior. Furthermore, logical calculations were successfully performed by integrating multiple cracked optical fiber diodes into a mechanical computing system. The system demonstrated multifunctional vibration sensing, capable of detecting vibrations with orthogonal axes to the prestrain, highlighting its axis scalability for strain input. Furthermore, this study explored three-dimensional structures, such as helical configurations, demonstrating that the stress concentration and optical attenuation mechanisms induced by cracks can also be applied to optical fibers with non-linear morphologies. This enables their use as mechanical computing elements capable of responding to various types of deformations (Supporting Information S1-S6). The anisotropic nature of the helical structures enable stress concentration under external deformation, induces light attenuation, and offer excellent durability under high strain and stress. Strain-light-driven mechanical computing systems based on optical fibers with structural degrees of freedom are expected to revolutionize applications in various fields, such as robotics and space exploration. These system can perform accurate calculations with deterministic behavior and operate in extreme environments.\u003c/p\u003e \u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003cdiv id=\"Sec9\" class=\"Section3\"\u003e \u003c/div\u003e \u003c/div\u003e\n\n "},{"header":"METHODS","content":"\u003ch2\u003eFabrication of Silicone Elastomer\u003c/h2\u003e\u003cp\u003ePMMA (≈ 100 nm, Microchem INC) was spin-coated on a silicon wafer (3000 rpm for 30 s). After spin-coating, a three-step soft-bake process was conducted. The wafer was sequentially heated on a hotplate at 110, 160, and 180°C, each for 10 min. Subsequently, the silicone elastomer (Ecoflex 0050, Smooth-on) was prepared by mixing the base (Part A) and curing agent (Part B) in a 1:1 ratio. After mixing, 20 g of the silicone elastomer was spin-coated on a the PMMA-coated wafer, followed by spin-coating at 1000 rpm for 1 s, repeated three times. Semi-curing was performed at 110°C on a hotplate for 1 min, followed by full curing at 25°C for 24 h.\u003c/p\u003e\u003ch3\u003eFabrication and Characterization of Cracked Optical Fiber\u003c/h3\u003e\u003cp\u003eA laser cutter (JQlaser, JQ9060) was used to create cracks in the optical fiber (Toray, PGR-FB). The power and speed settings of the laser were adjusted to control the dwell time and intensity of the laser beam to form 3D cracks. The parameters of the laser cutter, including speed (mm/s) and power (W), were optimized to ensure controlled crack formation. The crack patterns were designed considering the interaction between the laser and optical fiber material to achieve precise 3D cracks.\u003c/p\u003e\u003ch2\u003eFabrication of Bonding Sites and Integrated Devices\u003c/h2\u003e\u003cp\u003eMultiple bonding techniques were employed to integrate the elastomeric substrate with the 3D cracked optical fiber. Siloxane bonding was used for optical fibers with diameters ranging from 250 µm to 500 µm. Using photolithography and an e-beam evaporator, 100 nm SiO2 and 100 nm Ti layers were selectively deposited onto the 3D cracked optical fibers through a masking process. The elastomeric substrate was heated to 60°C and placed in conformal contact with the optical fibers. A paper towel was placed over the substrate, and a 1 kg weight was applied for 30 min to ensure proper bonding. Polyimide tape was laser cut for fibers exceeding 500 µm in diameter to match the bonding area, facilitating easy integration with stronger adhesion. Siloxane bonding enabled microscale precision, while polyimide tape bonding provided robust adhesion suitable for various fiber sizes.\u003c/p\u003e\u003ch2\u003eFabrication and Measurement of Vibration Sensors\u003c/h2\u003e\u003cp\u003eVibration sensor experiments were conducted in a dark room to eliminate external light interference. One end of the cracked optical fibers was connected to a light emitter, directing light through the fiber. The other end of the fiber was connected to a photodiode linked to a digital multimeter (2400 SMU, Keithley). The substrate, with the cracked optical fibers attached, was placed on a high-speed motor-equipped stage. As the motor vibrated the substrate, the vibration modulated the light output of the fiber, and the current of the photodiode was measured to quantify the sensor response.\u003c/p\u003e\u003ch2\u003eFabrication and Measurement of Logic Gates\u003c/h2\u003e\u003cp\u003eThree cracked optical fiber diodes were connected using a Y-shaped connector to create logic gate structures. Light sources with three distinct wavelengths (λR = 655 nm, λG = 532 nm, and λB = 460 nm) were used as inputs. The strain applied to the prestrained substrate, adjusted using the X and Y stretchers of the diodes, served as the input signal. Although the color of the output light could be visually observed, quantitative analysis was performed by capturing images and measuring RGB pixel intensities in a defined area using the ImageJ software.\u003c/p\u003e\u003ch2\u003eFabrication and Measurement of Helical Optical Fiber Sensors\u003c/h2\u003e\u003cp\u003eOptical fibers (Toray, FBG-PGR) were coiled around a rod and fixed using polyimide tape. The fibers were then heat-annealed in a vacuum oven at 70°C for 1 h, followed by cooling to room temperature for 10 min. After cooling, the tape was removed, and the fibers were carefully unwound to form helical optical fiber sensors. One end of the fiber was illuminated with a laser pointer to measure strain, while the other was connected to an optical power meter. For pressure measurements, the sensor was encapsulated in PDMS to ensure even pressure distribution (0–50 N) applied using a universal testing machine (UTM).\u003c/p\u003e\u003ch2\u003eFinite Element Analysis (FEA)\u003c/h2\u003e\u003cp\u003eFinite element analysis (FEA) simulations were performed using Abaqus to evaluate the mechanical response of the cracked optical fiber sensors. The optical fiber was modeled as a cylindrical structure with a diameter of 0.25 mm, featuring a crack measuring 0.13 mm in width and 0.23 mm in length. The model consisted of 10-node quadratic tetrahedron elements (C3D10) with a global seed size of 0.1, resulting in 12,402 elements. The material properties of the optical fiber were defined based on experimental stress–strain (S-S) data, with a Young's modulus of 1121 MPa and Poisson's ratio of 0.16. The optical fiber was prestretched by 500% and then released to 300%, simulating the experimental conditions. The simulation results were consistent with the experimental data, demonstrating that strain concentration occurred in areas with lower modulus around the cracks, confirming the accuracy of the model.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eDATA AVAILABILITY\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe data that support the findings of this study are either provided in the source data or are available from the corresponding author upon reasonable request.\u003c/p\u003e\n\u003cp\u003eACKNOWLEDGEMENTS\u003c/p\u003e\n\u003cp\u003eThis work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (grant Nos. 2022M3H4A1A02046445, RS-2024-00347619, RS-2024-00406240, RS-2024-00407155, and RS-2025-00513522).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAUTHOR CONTRIBUTIONS\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eJ. H. P., J. H. K., and H. U. C contributed equally to this work. J. H. P., J. H. K., and H. U. C conducted most of the experiments. B. H. K. conceived the idea and supervised the overall work. J. K., H. L., J. K., and B. H. K. conceived of the overall research goals and aims. J. S. C., H. K., S. E. L., S. K., H. J. J. supported the experiments. All authors discussed the results and commented on the manuscript.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eADDITIONAL INFORMATION\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eSupplementary information\u003c/strong\u003e The online version contains supplementary material available at XX.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCorrespondence\u003c/strong\u003e and requests for materials should be addressed to Jiwoong Kim, Heon Lee, Jaehwan Kim, or Bong Hoon Kim.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eReprints and permission information\u003c/strong\u003e is available at http://www.nature.com/reprints\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eYasuda, H. \u003cem\u003eet al\u003c/em\u003e. Mechanical computing. Nature 598, 39\u0026ndash;48 (2021).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLee, T.-H., Bhunia, S., \u0026amp; Mehregany, M. 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Technol. 33, 493\u0026ndash;501 (2024).\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"npj-flexible-electronics","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"npjflexelectron","sideBox":"Learn more about [npj Flexible Electronics](http://www.nature.com/npjflexelectron/)","snPcode":"41528","submissionUrl":"https://submission.springernature.com/new-submission/41528/3","title":"npj Flexible Electronics","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"NPJ","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"mechanical computing, mechanical buckling process, optical fiber, electronic components, mechanical transistor","lastPublishedDoi":"10.21203/rs.3.rs-6200645/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6200645/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eMechanical computing, utilizing mechanical deformation to perform calculations, has attracted significant attention as an innovative computing strategy for achieving high accuracy and exceptional physical robustness. However, its reliance on passive mechanical displacement limits its applicability for complex computations. This study presents a novel system that enables active light signal modulation through reversible mechanical deformation by integrating soft and 3D electronics. The proposed system features: 1) Optical fibers with optimized 3D cracks embedded in a low-modulus, high-elongation material, enabling strain-induced multimodal transitions. 2) Maximized stress concentration on the cracked fibers under strain, allowing them to function as active components for light modulation, which facilitates complex logic calculations and validates truth tables. 3) Multifunctional vibration sensing capabilities, illustrating the scalability of strain inputs and the potential for dynamic applications, such as soft robotics. 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