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Perforation is used in multilayer tissue products, such as toilet and kitchen papers, as part of the converting process. Perforation facilitates the detachment of consecutive sheets by the user. The compromise between the strength required to detach a perforated sheet and the strength required to break a sheet affects the perforation efficiency. In this work, the mechanical behaviors of 15 commercial papers from different European producers were studied. A morphological analysis of the materials was performed, followed by the determination of their perforation efficiency (through tensile tests). A qualitative analysis of the cuts quality, along with a quantitative analysis of the same cuts dimensions was performed through an optical system. Finally, the stress concentration in the holes and the influence of the cuts distance were analyzed using a finite element model implemented in Abaqus/Standard finite element software. The results showed that a cut distance of 2.0 mm should not be used in these types of papers, and the perforation efficiency increased with the cut distance, regardless of the number of plies in the toilet paper. The stress concentration factor was also determined to have a limit value of 0.11. Papers above this limit value tear at the perforation line, as desired.

Euroresinas produces different types of resin-impregnated paper at their factories. After the paper goes through the resin bath, it undergoes a drying process which is a fundamental step in the process. Although the temperature is controlled by a heating system, the actual values inside the chain of dryers are only measured at a few points away from where the paper is. The company would like to be able to model the temperature profile inside the dryers to better understand problems such as dusting and sticking, as well as the optimization of different variables related to bathing and drying times and energy consumption.

The aging of the transformer oil-paper insulation distributes spatially, which results in changes in paper resistivity in different regions. This paper establishes an iterative inversion algorithm using the finite element method to calculate the oil-immersed paper resistivity in different regions of a transformer. This algorithm sets the transformer dielectric loss factor tan δ at low frequency, the dielectric parameters of the transformer oil as inputs and the oil-immersed paper resistivity as output. The resistivity obtained from inversion can be used as a reference to access the insulation state of the oil-paper insulation. This paper aims at achieving the nondestructive detection of the partial state of the oil-paper insulation.

Purpose. To substantiate the breakdown mechanism of capacitor paper on the basis of numerical-field models with segmented cross-sections of cylindrical volumes of air and water, and also use the proposed models to determine the breakdown strength of air in micron-sized gaps under normal conditions. Methodology. The model bases on a finite element solution to an electrostatic problem in a volume of capacitor paper consisting of cellulose and pores with air and water. First, the possible scenarios for the growth of breakdown in capacitor paper are analyzed and to the conclusion is made, that complete breakdown developed from a partial breakdown in the air cavity. A brand of capacitor paper is chosen in such a way that when its thickness changed, the breakdown strength of the electric field changed over a wide range. Then, for the paper with the lowest average electric field intensity the possibility of explaining the complete breakdown by the breakdown of air segments on the basis of the Paschen dependence is checked. Further points of the obtained dependence by constructing models of papers of the same brand and a different thickness under the assumption of the similarity of electrostatic fields are determined. As such a criterion, the constancy of the equivalent effective permittivity are taken. Results. The dependence of the breakdown strength of the air in the range of 1.36...5.54 μm under normal conditions is determined. The obtained relationship is between the Peschot and Taev curves. Originality. For the first time, the possibility of indirectly estimation the breakdown strength of an insulating material using an electrostatic field model is indicated. Practical value. The proposed method for the numerical calculation of the breakdown voltage of air inclusions in the presence of water inclusions in the thickness of solid insulation can be applied to other types of solid thin-layer insulation., Полученная в работе зависимость напряженности электрического поля воздуха от длины разрядного промежутка удовлетворительно объясняет значения пробивных напряжений образцов конденсаторной бумаги при изменении их марок и толщины. Построена зависимость пробивной напряженности воздуха при нормальных условиях в диапазоне 1,36…5,54 мкм на основании расчета электростатических полей в моделях конденсаторной бумаги с сегментными поперечными сечениями цилиндрических объемов воздуха и воды. Проведено сопоставление полученной зависимости с известными экспериментальными данными. Полученные данные в диапазоне 2…5,54 мкм наиболее близки экспериментальным данным Пешо.

Nowadays, Machine Learning (ML) model of the structure-property relation based on large data from reliable physical models becomes a new and promising approach for material design. The present work demonstrates such approach to examine the variation in microstructure features on mechanical properties of paper materials. After the generation of a “big” dataset of fiber network samples, morphological feature data, including interfiber contact properties were extracted and statistically evaluated. By performing cohesive finite element simulations, the mechanical properties including failure strain, effective stiffness, and maximal stress of fiber networks under tensile test were determined and served along with structural feature data for the ML analysis. Gradient Boosting method achieved a performance score of approx. 0.9 for all mechanical properties of such complex fibrous structure. It was found that “disorderness” represented by the variation of fiber network orientation and the mean contact area size to be the most influential factors to the failure strain and effective stiffness. Whereas the failure strength was driven by the homogeneous distribution of the contact areas. The results validated the strong orientation dependence of fibrous materials in experimental observations and enlighten the importance of sensitivity as feature parameters and the striking potential of ML for material optimization.

This paper reports the effect of process orientation on the mechanical behavior and piezoelectricity of electroactive paper (EAPap) made from natural cotton pulp. EAPap is fabricated by a casting and wet drawing of cellulose film after dissolving cotton with LiCl and DMAc solvent. During the fabrication, permanent wrinkles, a possible factor for performance deterioration, were found in the films. Finite element method was introduced to identify the formation mechanism behind the wrinkles. The simulation results show that the wrinkles were caused by buckling and are inevitable under any conditions. The tensile and piezoelectric tests show that the orientation dependency of the stretched EAPap gives the anisotropic characteristics on both mechanical and piezoelectric properties. In this research, the anisotropic elastic moduli and Poisson&rsquo, s ratios are reported. The piezoelectric charge constant of EAPap in the linear elastic is calculated. The piezoelectric charge constants of EAPap are associated with the alignment angle in the order of 45&deg, &gt, 0&deg, 90&deg, due to the strong shear effect. The higher stretching ratio gives the higher piezoelectricity due to the alignment of the molecular chains and the microstructure in EAPap. The highest piezoelectric charge constant is found to be 12 pC/N at a stretching ratio of 1.6 and aligning angle of 45&deg

The specific energy absorption of a thin-walled tube can be improved by filler. This study examined the potential use of a cheaper biomass filler, paper scraps, to enhance the energy absorption characteristics of the structure while reducing its cost, compared to that with a traditional filler such as foam material. Quasi-static crushing tests and finite element simulations were performed by using the explicit non-linear finite element software LS-DYNA to determine the improvements to the mean crushing force and specific energy absorption of the steel tube when filled with different densities of paper scraps. The mean crushing force and specific energy absorption of the empty tube, the paper scraps, and thin-walled tube filled with paper scraps were determined, and corresponding numerical simulations were performed. The simulation and test results showed that the impact performance of tube filled with paper scraps was greatly improved when paper scraps density was 0.35 g/cm3. By optimizing paper scraps filling structure, a new structure that could further enhance the specific energy absorption was obtained. The optimal scheme could increase the specific energy absorption of Q345 steel tube by 11.35%.

The charge transport and accumulation in oil–paper can cause the insulation degradation. So far, the most widely used model to simulate space charge transport and accumulation is the bipolar charge transport (BCT) model, which can well simulate the space charge dynamics. However, there are two shortcomings in the algorithms for solving the BCT model. One is that there is almost no use of vectorisation technology, which may increase the complexity of the algorithm, the other is the usage of fixed step size which might bring extra computation cost. In view of this, an adaptive time‐stepping transient upstream finite element method (FEM) is developed to solve the BCT model considering trapping/detrapping, as well as the recombination phenomenon under DC condition in this article. Then, a vectorisation technology is used in the method to optimise the algorithm. Moreover, the adaptive time‐stepping method is introduced in simulation to reduce computation time and calculation amount. Simulation results are obtained by programing and later presented, which are basically consistent with the corresponding experimental results. Therefore, the proposed method is expected to promote the optimization design of the oil–paper insulation system.

The thermal response in paper has been studied by thermography. It was observed that an inhomogeneous deformation pattern arose in the paper samples during tensile testing. In the plastic regime a pattern of warmer streaks could be observed in the samples. On the same samples digital image correlation (DIC) was used to study local strain fields. It was concluded that the heat patterns observed by thermography coincided with the deformation patterns observed by DIC. Because of its fibrous network structure, paper has an inhomogeneous micro-structure, which is called formation. It could be shown that the formation was the cause of the inhomogeneous deformations in paper. Finite element simulations was used to show how papers with different degrees of heterogeneity would deform. Creped papers, where the strain at break has been increased, were analysed. For these paper it was seen that an overlaid compaction of the paper was created during the creping process. During tensile testing this was recovered as the paper network structure was strained.

The heat dissipation factor of conventional epoxy impregnated paper bushings is a subject of concern due to the large quantities of power in a High Voltage Direct Current (HVDC) system. The present work deals with the selection of better insulation as a replacement to the conventional resin impregnated material employing nano-hexagonal-Boron Nitride and nano-hexagonal-Boron Nitride added with nano-cellulose-fiber. The bushing of the converter transformer is designed using the Finite Element Method (FEM), and the electrothermal analysis is performed at the loaded working condition. Besides, numerous optimization schemes are also presented for adapting the structure of the thermal conductor enclosed in the inner conductor. The electrothermal performances of the above materials with the optimized structure are compared and an advanced scheme is proposed. Further, the results obtained from the designed system are employed in the form of an Artificial Neural Network to simplify the process of thermal computation characterized by the selected scheme. The internal parameters of the neural network are tuned implementing a hybrid amalgamation of Particle Swarm optimization - Grey Wolf Optimiser and the performance is compared against the actual values. The supremacy of the implemented algorithm is justified by a comparative analysis with other well-established algorithms using various statistical parameters.

The Electric Field and Voltage Distribution (EFVD) are an important parameter for assessing high voltage bushing transformer performance. However, conducting laboratories experiment is dangerous, difficult and expensive due to several aspects. Therefore, Finite Element Method (FEM) software is the best option used as a tool for the assessment of bushing transformer's performance in terms of EFVD. But, before an assessment of analysis could be carried out, an accurate model of bushing transformer must first to be designed. In this research, Computer Aided Design (CAD) software has been employed to design the 145kV bushing transformer based on actual dimension. Upon completion, the design has been exported to FEM software for further analysis. In FEM software, measurement and analysis of electric field and voltage distribution (EFVD) have been carried out. The measurements are performed at various locations of bushing transformer such as of the porcelain surface (both air and oil side), along with aluminum foils, and at oil-impregnated paper (OIP). The results obtained have been compared with other researchers and it is found very satisfactory.

Paper is a complex material consisting of a network of cellulose fibres at the micro-level. During manufacturing, the network is dried under restraint conditions due to tension in the paper web in machine direction. This gives rise to internal strains that are stored in the produced sheet. Upon exposure to a moisture cycle, these strains may be released. This results in permanent shrinkage that may cause instabilities such as curl or waviness of the sheet. The prime objective of this paper is to model this irreversible shrinkage and to link its magnitude to the properties of the fibres and of the network. For this purpose, randomly generated fibrous networks of different coverages (i.e. ratio of the area occupied by fibres and that of the sheet) are modeled by means of a periodic representative volume element (RVE). Within such RVEs, a finite element method combined with a kinematic hardening plasticity model at the scale of the fibres is used to capture the irreversible response. The computational results obtained demonstrate that the magnitude of the irreversible strains increases with coverage until a certain coverage and beyond that coverage decreases in magnitude. This phenomenon is explained by considering the area fraction of free-standing fibre segments relative to bonded fibre segments in the network. A structure–property dependency of irreversible strains at the sheet-level on the micro-structural parameters of the network is thereby established., SCOPUS: ar.j, info:eu-repo/semantics/published

Diplomska naloga opisuje preračun valjev, ki so del kontinuirnega papirnega stroja v podjetju Papirnica Količevo d.o.o. V nalogi je predstavljen celoten postopek od preučevanja obstoječe dokumentacije in računalniškega modeliranja valjev do numeričnega preračuna po metodi končnih elementov. V nadaljevanju je izveden še analitični preračun kritičnih mest in določitev faktorjev varnosti. Vzporedno s praktičnim delom naloge je predstavljeno tudi teoretično ozadje, ki pripomore k razumevanju vsebine izvedenega preračuna. Na koncu naloge so predstavljeni rezultati obeh izvedenih metod (napetosti in pomiki) za vsak valj posebej. This diploma work describes the calculation of rollers, which are part of a continuous paper machine at the company Papirnica Količevo d.o.o. The thesis presents the whole process from the study of the existing documentation and computer modelling of the rollers to the numerical calculation according to the finite element method. Furthermore, analytical calculations of critical sites and determination of safety factors have been carried out. In parallel with the practical part of the task, the theoretical background is also presented, which helps to understand the content of the performed calculations. At the end of diploma, the results of both performed methods (stress and strain) are presented, separately for each roller.

The finite element model for paper honeycomb was constructed, and the finite element method of out-of-plane compression for the paper honeycomb was studied. Then four kinds of paper honeycomb with different structural parameters were simulated and analyzed using finite element software ABAQUS. Moreover, the results obtained from finite element method were verified based on the existing theoretical research results and experimental results, respectively. The results show that stress–strain curves obtained from finite element method clearly show the four deformation stages of the paper honeycomb under out-of-plane compression, which is basically consistent with the trend of the typical curve. The values of initial peak stress, plateau stress and densification strain are close to the theoretical results. The stress–strain curves and deformation contours coincide with experiments well. The differences of initial peak stress σpk, plateau stress σpl and densification strain εD between theoretical, finite element method and experimental results are less than 15%. Therefore, the finite element method can be used to analyze the stress–strain curves and deformation characteristics of paper honeycomb. In addition, the results also show that the thickness of specimen has little effect on the stress and strain. However, people often prefer to use the thicker paper honeycomb to get better cushioning effect in practical applications, which was explained.

Papirnica Količevo Karton d.o.o. želi povečati svojo zmogljivost delovanja papirniških strojev. Stroji in strojni deli bodo zato posledično veliko bolj obremenjeni pod novimi pogoji delovanja. V diplomskem delu smo prikazali nosilnost valjev papirniškega stroja pod novimi obremenitvami in opisali tehnologije izdelave papirja, ki jih uporabljajo v papirnici Količevo. S pomočjo računalniškega programa Solidworks smo naredili geometrijske modele po načrtih, ki jih je posredovalo podjetje. Simulacije valjev smo izdelali pod novimi obremenitvami, ki jih je posredoval naročnik. Simulacije valjev so narejene s pomočjo programske opreme Abaqus in so izdelane po metodi končnih elementov (MKE). Naredili smo tudi analitični preračun valja. Na koncu je prikazana še primerjava rezultatov, podani pa so tudi faktorji varnosti za posamezen valj papirniškega stroja. Paper Mill Količevo Karton d.o.o. would like to increase the production capacity of their paper machines. The machines and their components will be experiencing more load with these new conditions. In this diploma we showed the paper machine rollers' capacity with new load and described the technologies which are used for paper making in the paper mill Količevo. With help of the application Solidworks we made geometric models in accordance with the plans we acquired at the company. The simulation of rollers was done with new load. The roller simulation were carried out with the finite element method, with help of the Abaqus application. We also did an analytical conversion of the roller. At the end we presented the comparison of results. We also presented safety factors for individual paper machine rollers.

Eco-friendly products have gained importance in recent years. The paper bottle is a sustainable packaging solution for carbonated beverages. The moulding process is a two-stage process. At first, pulp is poured in the forming mould and fibers are formed in the desired shape. Wet bottle is then transferred to the drying mould to remove bound water. The drying process makes use of an inflatable core, which not only prevents the shrinkage of fibers but also helps in attaining good fiber compaction. Preliminary investigations reported uneven fiber compaction in changing curvatures and sharp corners. A cause of uneven thickness distribution in the geometry is uneven compaction pressure during core expansion. A FEM approach is developed to predict the occurrence of non-conformities in the bottle. Hyperelastic core material is modelled using Mooney-Rivlin material model from the elastic strain density function. The model can be used to optimize the core shape, thus developing a robust tooling solution.

Paper materials have a long history of use as a packaging material, although traditional paper-based packaging is limited in its shape, complexity, and design. In order to better understand the deformation and failure mechanisms during 3-D forming, two experimental studies of paper materials have been conducted. Furthermore, constitutive modeling combined with explicit finite element modeling have been validated against numerous experimental setups and utilized to develop further understanding of 3-D forming processes. Two experimental studies were necessary to further investigate and model the 3-D formability of paper materials. The combined effect of moisture and temperature on the uniaxial mechanical properties of paper was investigated, providing new insights into how moisture and temperature affect both the elastic and plastic properties of paper materials. Furthermore, the in-plane, biaxial yield and failure surfaces were experimentally investigated in both stress and strain space, which gave an operating window for 3-D forming processes as well as input parameters for the constitutive models. The constitutive modeling of paper materials and explicit finite element modeling were directed towards two 3-D forming processes: deep drawing and hydroforming. The constitutive models were calibrated and validated against simple (typically uniaxial) mechanical tests, and the explicit finite element models (which utilize the developed constitutive models) were validated against 3-D forming experiments. Hand-made papers with fibers partially oxidized to dialcohol cellulose, which has greater extensibility than typical paper materials, was furthermore characterized, modeled, and 3-D formed as a demonstration of the potential of modified paper fiber products for 3-D forming applications. Papper har länge framgångsrikt använts som förpackningsmaterial, men traditionella pappers- och kartongförpackningar är begränsade i form och design. Två experimentella studier har utförts för att få bättre förståelse för deformations- och brottmekanismer under 3D formning. Resultat från konstitutivmodellering i kombination med explicit finit element modellering har validerats mot ett flertal experimentella uppställningar och använts för att utveckla bättre förståelse för 3D formningsprocesser. Två experimentella studier var nödvändiga för att ytterligare undersöka och modellera pappersmaterials 3D formbarhet. I den första undersöktes den kombinerade effekten av fukt och temperatur på pappers enaxliga mekaniska egenskaper, vilket gav nya insikter om hur fukt och temperatur påverkar både de elastiska och de plastiska egenskaperna hos papper. I den andra har biaxiella (i planet) flyt- och brottytor undersökts experimentellt i både spännings- samt töjningsrymden, vilket gav ett processfönster för 3D formningsmetoder samt ingångsparametrar för de konstitutiva ekvationerna. Konstitutiv modellering av pappersmateriel samt explicit finit element modellering riktades mot två 3D formningsprocesser: djupdragning och hydroformning. De konstitutiva modellerna kalibrerades och validerades mot enkla (oftast enaxliga) mekaniska experiment, och explicita finita elementmodeller (som utnyttjar de utvecklade konstitutiva modellerna) validerades mot 3D formningsexperiment. Handark med fibrer delvis oxiderade-reducerade till dialkohol cellulosa, som har större töjbarhet än andra pappersmateriel, har dessutom karakteriserats, modellerats, samt 3D formats som en demonstation av potentialen hos modifierade pappersfiberprodukter i 3D formning. QC 20170104

Esta tese objetiva apresentar um método inovador concebido para estudar como ocorre o fenômeno de migração de umidade no interior de sistemas isolantes papel-óleo de transformadores de potência. A ferramenta é composta por: a) um modelo matemático bidimensional, que representa a dinâmica da umidade no conjunto papel-óleo contemplando variações no carregamento elétrico, e que foi desenvolvido utilizando ferramental matemático, estudos existentes e a experiência de especialistas/analistas; e b) um método de classificação desenvolvido para estudar alguns dos efeitos nocivos da umidade em transformadores de potência, considerando a possibilidade de formação de bolhas e de água livre. O ineditismo da tese é composto por um método numérico, consistido em uma metodologia de cálculo que contempla a utilização do método dos elementos finitos - em duas dimensões - aplicado aos conceitos de transferência de massa e modelagem térmica do carregamento do transformador, considerando as diferenças de temperatura entre dois enrolamentos. Além disso, a novidade da metodologia de classificação consiste na criação de: a) um sistema de classificação para o conjunto transformador – carregamento elétrico em cinco níveis, de “A” a “E”, com as respectivas ações recomendadas; e b) uma análise que envolve a variação dos diferentes níveis de carregamento aplicados ao equipamento. Esta tese contribui com a literatura ao fornecer uma ferramenta eficaz, implementada em software, que fornece subsídios para a tomada de decisão da equipe de manutenção, quando da ocorrência de fenômenos e condições desfavoráveis ​​que podem afetar criticamente a vida útil dos equipamentos, em especial o seu isolamento. Esta tese apresenta ainda alguns estudos de caso de transformadores em operação, em condições reais de carga, em que a validação dos dados é realizada através da comparação dos resultados obtidos com a coleta e análise de amostras de óleo, tanto por métodos laboratoriais quanto por uso de dispositivo de monitoramento. Portanto, este trabalho é útil ao apoiar na classificação e diagnóstico em transformadores de potência, através da predição dos níveis de umidade no sistema isolante papel-óleo, auxiliando a evitar falhas nestes equipamentos e prejuízos aos proprietários dos transformadores e consumidores de energia supridos por estes. This thesis aims to present an innovative tool designed to study how the phenomenon of moisture migration occurs inside insulating paper-oil systems of power transformers. The tool consists of a two-dimensional mathematical model, representing the dynamics of humidity in the oil-paper set and including the variations in electrical charging, which was developed using mathematical tools, existing studies, and the experience of specialists/analysts. Furthermore, this study includes a classification method developed to investigate some of the harmful effects of moisture in power transformers, considering the possibility of bubbles and free water formation. The novelty of this numerical method consists of a calculation methodology that contemplates the use of the finite element method - in two dimensions - applied to the concepts of mass transfer and thermal modeling of the transformer loading, considering the temperature differences between two windings. Additionally, the classification method includes the creation of: a) a categorization system for the coupling of a transformer and electric charging in five levels, from “A” to “E”, with the respective recommended actions; and b) an analysis that involves varying the different levels of loading applied to the equipment. The contribution of this work is an efficient method, implemented via a computational algorithm, which provides support for the maintenance team's decision making when unfavorable phenomena and conditions occur that can critically affect the useful life of the equipment, especially its insulation. This thesis presents some case studies of transformers in operation, under real load conditions, in which the data validation is performed through the comparation of obtained data with experimental collection and analysis of oil samples and the results of monitoring device. Therefore, this work is useful in supporting the classification and diagnosis of power transformers, through the prediction of humidity levels in the oil-paper isolating system, assisting on failure prevention in this equipment and capital loss to the owners of the transformers and consumers supplied by these.

As a basic mechanical component, the sealing ring is widely used in industrial, aerospatial, and other fields. In this study, an elastic metal C-shaped sealing ring with a wave structure was taken as an example, and its performance was analyzed theoretically and measured experimentally. First, an experimental study was performed on the C-ring seal. The proposed method for experimental measurement of the contact stress of the C-ring seal involved innovative use of a universal electronic testing machine and pressure sensitive paper, in conjunction with the hue&ndash, saturation&ndash, brightness (HSB) method. Based on the discoloration of the pressure sensitive paper after contact stress, computer software was used for analysis, the discoloration was digitized, and the contact stress was established. Second, a theoretical calculation model of the C-ring seal was established using ANSYS software, and a finite element theoretical calculation of the mechanical properties of the sealing ring was established. Finally, the contact stress results were compared with the model calculation results of the C-ring seal. The error between the two was small (4.8%), which proved the validity of the calculation model and the scientificity of the experimental method.

The research hypothesis states that the impregnation of the honeycomb paper core of lightweight sandwich panels with modified starch, sodium silicate and epoxy resin (LiquidWood&reg, ) resin has a significant effect on its elastic properties. In this study, a recycled paper was used in three thicknesses, seven types of cell shapes, including two after numerical optimization and three types of impregnating agents. The method of digital image analysis determined the elastic constants of manufactured paper cores, which were subjected to axial compression in two directions. Based on the experimental results, elastic constants of the cores were calculated and compared with the results of numerical calculations. It has been shown that each of the impregnating solutions used improved the stiffness of the paper core. The best results were obtained for LiquidWood&reg, epoxy resin and modified starch. An important parameter of cell geometry affecting their rigidity is the angle of the cell wall &phi, as well as the arrangement of the common cell wall in relation to the direction of load. The numerical models developed were positively verified.

Paper-like electronics with thin multi-layer structures, which can be repeatedly bent and twisted like paper, are promising for diverse innovation application. Employing surface-mounted flexible strain sensors is a general way to monitor the bending characteristics of each layer inside paper-like electronics, however, the deviation of measured strain will reach up to 15% on account of the layer-to-layer interface sliding, neutral axes offset resulted from the extra effect of the flexible strain sensor. Here, we proposed a precise measurement method to evaluate the surface bending strain of paper-like electronics by using flexible sensors. In combination with the effects of the thickness, length, etc, a strain compensation model has been established to compensate the measurement deviation. Meanwhile, a slip failure model has been developed to guide the design of the sensitivity unit within the non-sliding area of the flexible sensor. Validated by finite element analysis and experiment, the bending strain of paper-like electronics (eg., ∼50 μm) can be evaluated much more accurate compared to the frequent access one. The newly-proposed method provides a powerful basis for further research of paper-like electronics.