# Strain Transfer Model Assessment for Steel-Reinforced and Polymer-Coated Optical Fiber Cables Used as Distributed Strain Sensors

Mira Kabbara, Xavier Chapeleau, Qinghua Zhang, Frédéric Bourquin

► To cite this version:

Mira Kabbara, Xavier Chapeleau, Qinghua Zhang, Frédéric Bourquin. Strain Transfer Model Assessment for Steel-Reinforced and Polymer-Coated Optical Fiber Cables Used as Distributed Strain Sensors. IEEE Sensors Letters, 2025, 9 (8), pp.1-4. 10.1109/LSENS.2025.3589372. hal-05367567

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# Strain transfer model assessment for steel-reinforced and polymer-coated optical fiber cables used as distributed strain sensors

Mira Kabbara<fnref n="1" />, Xavier Chapeleau<fnref n="1" />, Qinghua Zhang<fnref n="2" />, and Frédéric Bourquin<fnref n="3" />

Manuscript received June 7, 2017; revised June 21, 2017; accepted July 6, 2017. Date of publication July 12, 2017; date of current version July 12, 2017.

**Abstract**—Strain transfer in distributed optical fiber sensors is typically represented by a simplified one-dimensional model that incorporates a strain lag parameter dependent on cable characteristics and installation conditions. Initially developed for thin cables with polymer coatings, this study extends the evaluation of the model's applicability to robust four-layered cables—one with polymer coatings only and the other including a steel layer—designed for use in harsh environments and complex installation scenarios. Finite element simulations are conducted to assess the model's performance for both steel-reinforced and polymer-coated cables subjected to strain gradients, using strain lag parameters specific to each cable. The results demonstrate that the model accurately predicts strain transfer in steel-reinforced cables but shows reduced accuracy for polymer-coated cables. Furthermore, the influence of the precision of the strain lag parameter and variations in interlayer stiffness, governing the interfacial behavior and affected by installation practices, on the model's validity is critically examined.

**Index Terms**—Distributed optical fiber sensors, mechanical strain transfer, structural health monitoring.

## I. INTRODUCTION

In recent years, optical fiber sensors have attracted growing interest for structural health monitoring, especially for distributed strain and temperature measurements using Rayleigh backscattering [1]–[3]. OFDR technology, based on Rayleigh scattering, is particularly effective for detecting strain gradients and crack openings due to its millimeter-scale resolution [4]–[6]. A typical optical fiber cable includes a silica glass core and cladding, surrounded by protective coatings that prevent damage in stress-concentrated scenarios. However, these coatings can hinder strain transfer from the structure to the fiber core, leading to discrepancies between measured and actual strain. Whether embedded or bonded at the surface, optical fiber cables are subjected to complex stress fields. Consequently, mechanical strain transfer requires a 3D model, which is inherently complex, while fiber sensors measure a one-dimensional strain profile along their length. To address this, Ansari and Libo proposed a 1D analytical model in 1998 based on the strain-lag approach [7]. This model was later extended to other cable types and installation configurations [8], [9], including cases with adhesive bonding that can produce non-concentric geometries [10], [11]. These models reduce the 3D problem to a 1D second-order differential equation relating strain in the host material to that at the fiber core, governed by the strain-lag parameter. This parameter depends on the cable’s mechanical and geometric properties of the constitutive layers and its installation in the structure. A wide range of commercially available cables features multiple protective coatings made from various materials, including polymer-coated and steel-reinforced designs. While multilayer polymer-coated cables offer good performance, steel-reinforced ones are often more advantageous due to their resilience in harsh environments and better

suitability for complex installations [12], [13]. However, they tend to smooth out localized strain variations in the measured profiles.

Most existing studies rely on simplified scenarios, such as idealized host strain profiles (e.g., linear, bilinear, or parabolic) [14], [15], which often fail to capture the complexity of real structural conditions. While some experimental investigations have addressed polymer-coated cables under strain gradients [16], fewer have examined steel-reinforced cables in the presence of displacement discontinuities, as in [17]. Even fewer studies have performed numerical evaluations under realistic conditions with detailed cable geometries [18]. The present study is the first comparative case study that numerically analyzes the strain transfer response of two fundamentally different, yet commercially relevant, cable designs: a polymer-coated cable and a steel-reinforced cable, subjected to a significant strain gradient. In doing so, it calls for a reassessment of the applicability of the simplified 1D model in complex scenarios such as the one considered here, helping to refine its limitations and its relevance for structural health monitoring. First, a finite element simulation (FES) of a cylindrical concrete beam with a soft inclusion, instrumented with different cables, is conducted. Then, an approach based on strain profile outputs at both the core and host material levels is proposed to validate the 1D model. The strain-lag parameter is generally unknown due to its dependence on cable properties not disclosed by manufacturers and on installation processes. A key variable is the inter-layer stiffness coefficient, which describes bonding between consecutive layers and between the cable and the host material. These values are difficult to measure but significantly influence the strain-lag parameter. Therefore, their impact on model accuracy is investigated.

## II. MODEL VALIDATION APPROACH APPLIED TO A FOUR-LAYERED OPTICAL FIBER SENSOR

In this paper, the representative model used for the optical fiber sensor is a four-layered one. It consists of an optical fiber (core +

Corresponding author: M. Kabbara (e-mail: mira.kabbara@univ-eiffel.fr).

Associate Editor: Alan Smithee.

Digital Object Identifier 10.1109/LSENS.2023.0000000

<footnote n="1">¹COSYS-SII/14S, Université Gustave Eiffel, Inria, 44340 Bouguenais, France</footnote>

<footnote n="2">²COSYS-SII/14S, Université Gustave Eiffel, Inria, 35042 Rennes, France</footnote>

<footnote n="3">³ Université Gustave Eiffel, 77420 Champs-sur-Marne, France</footnote>
optical cladding) with a diameter of about 125 µm made of pure silica glass. Three protective layers made of different materials are added to enhance the cable's durability. In the four-layered model, proposed in [16] and given in (1), $\hat{\varepsilon}_f$ and $\varepsilon_m$ represent the longitudinal strain at the optical fiber and the host material, respectively. These profiles vary as a function of $z$, which represents the coordinate along the length of the cable. This model includes the strain-lag parameter, $\beta$, which is determined by various mechanical and geometric properties of the cables, such as the radius $r_i$, Young's modulus $E_i$, shear modulus $G_i$, and Poisson's ratio $\nu_i$ for each layer $i = 1, \dots, 4$, where 1 corresponds to the core, 2 to the first coating, 3 to the second coating, and 4 to the third coating. Additionally, the stiffness coefficients between consecutive layers, $k_{f/(i+1)}$, are considered. Note that $k_{4/m}$ represents the bonding between the third coating and the host material, thereby reflecting the installation conditions within the structure.

$$ \begin{cases} \hat{\varepsilon}_f''(z) - \beta^2 \hat{\varepsilon}_f(z) = -\beta^2 \varepsilon_m(z) \\ \hat{\varepsilon}_f(0) = \varepsilon_0, \quad \hat{\varepsilon}_f(L) = \varepsilon_L \end{cases} \quad (1) $$

$$ \text{where } \beta = \left[ \frac{1}{k_{1/2}} \left( \frac{r_1}{2} E_1 \right) + \frac{1}{k_{2/3}} \left( \frac{r_1^2}{2r_2} E_1 + \frac{r_2^2 - r_1^2}{2r_2} E_2 \right) + \frac{1}{k_{3/4}} \left( \frac{r_1^2}{2r_3} E_1 \right. \right. \\ + \frac{r_2^2 - r_1^2}{2r_3} E_2 + \frac{r_3^2 - r_2^2}{2r_3} E_3 \left. \right) + \frac{1}{k_{4/m}} \left( \frac{r_1^2}{2r_4} E_1 + \frac{r_2^2 - r_1^2}{2r_4} E_2 \right. \\ + \frac{r_3^2 - r_2^2}{2r_4} E_3 + \frac{r_4^2 - r_3^2}{2r_4} E_4 \left. \right) + \frac{1}{G_2} \left( \left( \frac{r_1^2}{2} E_1 - \frac{r_1^2}{2} E_2 \right) \ln\left(\frac{r_2}{r_1}\right) \right. \\ + \frac{r_2^2 - r_1^2}{4} E_2 \left. \right) + \frac{1}{G_3} \left( \left( E_1 \frac{r_1^2}{2} + E_2 \frac{r_2^2 - r_1^2}{2} - E_3 \frac{r_2^2}{2} \right) \ln\left(\frac{r_3}{r_2}\right) \right. \\ + E_3 \frac{r_3^2 - r_2^2}{4} \left. \right) + \frac{1}{G_4} \left( \left( E_1 \frac{r_1^2}{2} + E_2 \frac{r_2^2 - r_1^2}{2} + E_3 \frac{r_3^2 - r_2^2}{2} \right. \right. \\ \left. \left. - E_4 \frac{r_3^2}{2} \right) \ln\left(\frac{r_4}{r_3}\right) + E_4 \frac{r_4^2 - r_3^2}{4} \right) \right]^{-1/2} \quad (2) $$

To validate this model, a FES is conducted, incorporating a structure with an optical fiber cable. The outputs at discrete points $z$ for $\varepsilon_m(z)$ and $\varepsilon_f(z)$ are extracted. Using the strain-lag parameter expression in equation (2) along with the properties of the introduced cable in the FES, the value of $\beta$ is calculated. Subsequently, the solution of the equation (1) is computed at these discrete points $z$, utilizing $\varepsilon_m(z)$, the computed value of $\beta$, and the strain at both ends of the fiber $\varepsilon_0$, $\varepsilon_L$ from the FES. The resulting profile is then compared to the FES output at the optical fiber level of the cable ($\hat{\varepsilon}_f$ vs. $\varepsilon_f$). An error criterion is applied to assess the validity of the model at each point $z$.

### III. DESCRIPTION OF THE THREE-DIMENSIONAL FES OF A CYLINDRICAL BEAM INCLUDING AN INCLUSION

The 3D simulation involves a cylindrical beam made of concrete with a radius of 10 cm and a length of 60 cm, subjected to a tensile force of 125 kN. At the center of the beam, an inclusion (with a radius of 2 cm) made of soft material is introduced (Fig.1), resulting in a strain gradient. Two systems are simulated, each with the same structure but differing in the type of cable placed in the center: Cable 1 and Cable 2. According to Table 1, the unique difference between these two cables is the material composing Coating 2. Specifically,

Coating 2 is composed of polymer with a Young modulus of $E_1 = 4$ GPa for Cable 1 and steel with a Young modulus of $E_2 = 200$ GPa for Cable 2. Considering the various characteristics of the cables and the expression in equation (2), the strain-lag parameter is calculated as $\beta_1 = 45.2 \text{ m}^{-1}$ for Cable 1 and $\beta_2 = 8.6 \text{ m}^{-1}$ for Cable 2. The cylindrical symmetry of the model (symmetry of revolution around the longitudinal axis of the cable) allows for simplification of the calculations through two-dimensional axisymmetric modeling. The mesh consists of quadrilateral elements. Several meshes were tested to ensure the results were not influenced by mesh selection. A mesh with elements in the z-direction was chosen with a length close to the resolution of the optical interrogator (1 mm), ensuring mesh-independent results.

<figure><img src="image_2.png" /><figcaption>Fig. 1. Cylindrical concrete beam with a soft material inclusion and centered Cable i subjected to tensile loading.</figcaption></figure>

<table><caption>TABLE 1. Geometric and mechanical properties of Cable 1 (polymer-coated cable) and Cable 2 (steel-reinforced cable)</caption><thead><tr><th></th><th>Layer</th><th>Radius (mm)</th><th>Material (Young Modulus in GPa, Poisson's ratio)</th><th>Stiffness coefficient (GPa/m)</th></tr></thead><tbody><tr><td rowspan="3">Cable 1</td><td>Core</td><td>0.06</td><td>Silica (70, 0.3)</td><td>10<sup>4</sup></td></tr><tr><td>Coating 1</td><td>0.12</td><td>Soft polymer (1, 0.4)</td><td>10</td></tr><tr><td>Coating 2</td><td>0.77</td><td>Hard polymer (E<sub>1</sub> = 4, 0.3)</td><td>10</td></tr><tr><td>Coating 3</td><td>I</td><td></td><td>Hard polymer (4, 0.4)</td><td>10</td></tr><tr><td rowspan="3">Cable 2</td><td>Core</td><td>0.06</td><td>Silica (70, 0.3)</td><td>10<sup>4</sup></td></tr><tr><td>Coating 1</td><td>0.12</td><td>Soft polymer (1, 0.4)</td><td>10</td></tr><tr><td>Coating 2</td><td>0.77</td><td>Steel (E<sub>2</sub> = 200, 0.3)</td><td>10</td></tr><tr><td>Coating 3</td><td>I</td><td></td><td>Hard polymer (4, 0.4)</td><td>10</td></tr></tbody></table>

### IV. COMPARISON BETWEEN THE 3D AND 1D MODEL FOR CABLE 1 AND 2

The results of the FES described in the previous section are used to validate the 1D model. The extracted strain profile in the host
material, ε<sub>m</sub>, is identical for both cables (see the blue curves in Fig. 2), indicating that the steel-reinforced cable Cable 2 does not contribute to structural reinforcement, even locally. However, the strain profiles at the optical fiber level, ε<sub>f</sub><sup>i</sup>, differ between the two cables (i=1 for Cable 1 and 2 for Cable 2). The strain profiles for each cable i are shown in Fig. 2, with the upper plot corresponding to Cable 1 and the lower plot to Cable 2. In both cases, the blue and orange curves represent the longitudinal strain (FES's output) in the host material, ε<sub>m</sub>, and in the optical fiber, ε<sub>f</sub><sup>i</sup>, respectively. The 1D model solution, ε&#770;<sub>f</sub><sup>i</sup>(z), is computed using ε<sub>m</sub>(z), the strain-lag parameter β<sub>i</sub> (β<sub>1</sub> = 45.2 m<sup>-1</sup> for Cable 1, β<sub>2</sub> = 8.6 m<sup>-1</sup> for Cable 2), and boundary conditions of 18.3 µm/m for Cable 1 and 5.7 µm/m for Cable 2, which are extracted from ε<sub>f</sub><sup>i</sup> at the ends of Cable i. The solutions, ε&#770;<sub>f</sub><sup>i</sup>(z), are represented by the black curves in Fig. 2. The absolute error between the calculated ε&#770;<sub>f</sub><sup>i</sup> and the measured ε<sub>f</sub><sup>i</sup> is shown as the purple curves in Fig. 2. For Cable 1, the error reaches a maximum of 29 µm/m at the center, where the deformation gradient is most pronounced. This corresponds to a 43% relative error compared to the FES strain value, ε<sub>f</sub><sup>i</sup>, at the same location, highlighting the limitations of the 1D model for this configuration. In contrast, for Cable 2, the error remains below 3 µm/m (less than 4% of relative error) along the entire length, validating the accuracy of the 1D model for steel-reinforced cables. For both the simulation and the 1D model, we used the same input data, which consists of the cable characteristics, and assumed a purely linear elastic behavior for both cables. Viscoelastic effects, which may be present and significant in reality, were not considered. Therefore, we suggest that the assumptions used to simplify the 3D model hold for steel-reinforced cables but not for polymer-coated ones in this case study. This highlights the need for further investigation by examining each assumption individually.

<figure><img src="image_3.png" /><figcaption>Fig. 2. Comparison between FES strain outputs (ε̂<sub>f</sub><sup>i</sup> in orange and ε<sub>m</sub> in blue) and 1D model predictions (ε&#770;<sub>f</sub><sup>i</sup> in black) for Cable i (i = 1, 2), with the corresponding absolute error shown in purple.</figcaption></figure>

# V. EVALUATION OF THE INFLUENCE OF THE PRECISION OF $\beta$ ON THE VALIDITY OF THE 1D MODEL FOR THE STEEL-REINFORCED CABLE

This section examines the importance of the strain-lag parameter, $\beta$, and its impact on the strain transfer model. It is crucial to note

that $\beta$ depends not only on the mechanical and geometric properties of the sensor, which are typically not disclosed by manufacturers, but also on its installation within the structure, which is challenging to calibrate. As a result, the value of $\beta$ must be estimated, making it highly susceptible to inaccuracies in the application of the strain transfer model. Therefore, it becomes essential to study the sensitivity of the 1D model to the precision of the strain-lag parameter value and to find out the allowable margin of error needed to obtain accurate results using the 1D model. In this context, equation (1) is solved for various $\beta$ values, using the strain profile at the concrete level and ensuring appropriate boundary conditions, obtained from the FES, are applied. Subsequently, for each $\beta$ value, the error between the calculated profile and the simulation's strain profile in the core is evaluated at each point. An error below 5 µm/m indicates acceptable results, this threshold being set based on typical OFDR noise levels (5–10 µm/m) to ensure strain differences stay within the system's detection limit. Figure 3 shows the zones of validity of the 1D model for the different values of $\beta$. Values of $\beta$ between 7.7 and 8.8 m<sup>-1</sup>, marked as the green zone in Fig. 3 ensure the model's validity throughout the entire length of the cable. However, values outside this range begin to produce inaccurate results, particularly in the center of the cable.

<figure><img src="image_4.png" /><figcaption>Fig. 3. Zones of validity of the 1D model along half the length of the steel-reinforced cable for different values of $\beta$ (in green).</figcaption></figure>

# VI. SENSITIVITY OF $\beta$ TO THE STIFFNESS COEFFICIENT VALUES VARIATION

As discussed in the previous section, the precision of the strain-lag parameter significantly affects the applicability of the 1D model. However, calculating this parameter presents a considerable challenge, as it depends on various mechanical and geometrical properties of the cable, including Young's modulus, Poisson's ratio, inter-layer stiffness coefficient, and radius. Among these properties, the inter-layer stiffness coefficient, which describes the bonding behavior at the interface (ranging from 10 GPa/m for imperfect bonding to 10<sup>4</sup> GPa/m for perfect bonding [19]), is the most difficult to measure. Assuming all other properties are known, the strain-lag parameter's sensitivity to variations in the stiffness coefficient is evaluated. A range of values for k<sub>1/2</sub>, k<sub>2/3</sub>, k<sub>3/4</sub>, and k<sub>4/m</sub>, varying from 10 to 10<sup>4</sup> in powers of 10, was tested, resulting in a total of 256 different possibilities. The $\beta$ values presented in this section were rounded to the first decimal place; however, each cable and installation corresponds to a specific, unique value of $\beta$ based on its mechanical and geometrical configuration. Among the 256 combinations of inter-layer stiffness
coefficient values, the combinations that yield acceptable $\beta$ values, within the range from 7.7 to 8.8 m⁻¹ as shown previously, are those with $k_{2/3}$ and $k_{3/m}$ fixed at 10, while $k_{f/1}$ and $k_{1/2}$ vary over multiple orders of magnitude, as shown in Tab.2. Additionally, Fig.4 shows the calculated values of $\beta$ with $k_{f/1} = k_{1/2} = 10$ GPa/m fixed, while $k_{2/3}$ and $k_{3/m}$ vary. The differences in the calculated $\beta$ values highlight the significant impact of $k_{2/3}$ and $k_{3/m}$ on the value of $\beta$. Since $k_{2/3}$ is typically calibrated by manufacturers, a precise installation protocol would be highly beneficial for minimizing the impact of $k_{3/m}$ on the value of $\beta$, ensuring more consistent results.

<table><caption>TABLE 2. Combination of stiffness coefficient values giving acceptable values of $\beta$</caption><thead><tr><th>k<sub>f/1</sub><br>(GPa/m)</th><th>k<sub>1/2</sub><br>(GPa/m)</th><th>k<sub>2/3</sub><br>(GPa/m)</th><th>k<sub>3/m</sub><br>(GPa/m)</th><th>β<br>(m<sup>-1</sup>)</th></tr></thead><tbody><tr><td>10, 10<sup>2</sup>, 10<sup>3</sup> or 10<sup>4</sup></td><td>10, 10<sup>2</sup>, 10<sup>3</sup> or 10<sup>4</sup></td><td>10</td><td>10</td><td>8.5 or 8.6</td></tr></tbody></table>

<figure><img src="image_5.png" /><figcaption>Fig. 4. Variation of strain-lag parameter ($\beta$) with $k_{2/3}$ and $k_{3/m}$, with fixed values of $k_{f/1}$ and $k_{1/2}$ at 10 GPa/m</figcaption></figure>

## VII. CONCLUSION

This paper evaluates the effectiveness of a 1D strain transfer model for two different four-layered cables using finite element simulation. The results show that the model is suitable for the steel-reinforced cable but less accurate for the polymer-coated one, highlighting the need for further studies to assess the model's assumptions in order to understand the model's limitations and delimit its validity. When the simplified one-dimensional model proves inadequate, more advanced methods become necessary; however, their development requires a comprehensive understanding of the existing model's limitations to effectively propose new approaches. Additionally, this study highlights the potential of using reinforced cables effectively through proper data processing with the 1D model, enabling full exploitation of their benefits. It also shows that even a small error in the estimated strain-lag parameter, $\beta$, leads to inaccurate results in the 1D model, particularly within the strain gradient zone, which is the primary area of interest. The study further revealed the sensitivity of $\beta$ to variations in inter-layer stiffness, especially between Coating 2 and Coating 3, and between the cable and the host material. Since the stiffness coefficient between Coating 2 and Coating 3 cannot be controlled by the user, establishing a precise installation protocol is crucial. This is because the installation process directly affects the

stiffness coefficient between the cable and the host material, which is challenging to calibrate, and influences the strain-lag parameter, thereby impacting strain transfer in the sensor.

## REFERENCES

[1] P. Ferdinand, "The evolution of optical fiber sensors technologies during the last 35 years and their applications in structural health monitoring," in *Proceedings of the SPIE*, vol. 9157, Jul. 2014.

[2] K. Feng, J. Cui, D. Jiang, H. Dang, Y. Jin, X. Sun, Y. Niu, and J. Tan, "Improvement of the strain measurable range of an OFDR based on local similar characteristics of a Rayleigh scattering spectrum," *Optics Letters*, vol. 43, no. 13, p. 3293-3296, 2018.

[3] G.-M. Ma et al., "High-resolution temperature distribution measurement of GIL spacer based on OFDR and ultrawean FBGs," *IEEE Trans. Instrum. Meas.*, vol. 69, no. 6, p. 3866-3873, Jun. 2020.

[4] M. Froggatt and J. Moore, "High-spatial-resolution distributed strain measurement in optical fiber with Rayleigh scatter," *Appl. Opt.*, vol. 37, no. 10, p. 1735-1740, Apr. 1998.

[5] M. Herbers, B. Richter, et al., "Rayleigh-based crack monitoring with distributed fiber optic sensors: Experimental study on the interaction of spatial resolution and sensor," *J. Civ. Struct. Health Monit.*, vol. 15, no. 5, p. 6, 2024.

[6] Y. Meng, C. Fu, L. Chen, C. Du, H. Zhong, Y. Wang, J. He, and W. Bao, "Submillimeter-spatial-resolution $\phi$-OFDR strain sensor using femtosecond laser induced permanent scatters," *Optics Letters*, vol. 47, no. 23, p. 6289-6292, Dec. 2022.

[7] F. Ansari and Y. Libo, "Mechanics of bond and interface shear transfer in optical fiber sensors," *J. Eng. Mech.*, vol. 124, no. 4, p. 385-394, 1998.

[8] A. Bassil, "Distributed fiber optics sensing for crack monitoring of concrete structures," Ph.D. dissertation, Univ. de Nantes, Nantes, France, Nov. 2019.

[9] H. Wang and Z. Zhou, "Advances of strain transfer analysis of optical fiber sensors," *Pac. Sci. Rev.*, vol. 76-77, p. 8-18, Sep. 2014.

[10] F. Falcetelli, L. Rossi, R. Di Sante, and G. Bolognini, "Strain transfer in surface-bonded optical fiber sensors," *Sensors*, vol. 20, no. 9, p. 1-13, 2020.

[11] S. C. Her and C. Y. Huang, "Effect of coating on the strain transfer of optical fiber sensors," *Sensors*, vol. 11, no. 7, p. 6926-6941, Jul. 2011.

[12] Liang J, Yu Y, Bian Q, Xu W, Wang Z, Zhang S, Weng J, Zhu J, Chen Y, Hu X, Yang J, Zhang Z. Metal-coated high-temperature strain optical fiber sensor based on cascaded air-bubble FPI-FBG structure, *Opt Express*, 2023 May 8;31(10):16795-16811.

[13] A. Piccolo et al., "Mechanical properties of optical fiber strain sensing cables under gamma-ray irradiation and large strain influence," *Sensors*, vol. 20, no. 3, p. 696, Jan. 2020.

[14] X. Zheng, B. Shi, C.-C. Zhang, Y. Sun, L. Zhang, and H. Han, "Strain transfer mechanism in surface-bonded distributed fiber-optic sensors subjected to linear strain gradients: Theoretical modeling and experimental validation," *Measurement*, vol. 179, 2021.

[15] Du W, Zheng X, Shi B, Sun M, Wu H, Ni W, Zheng Z, Niu M. Strain Transfer Mechanism in Surface-Bonded Distributed Fiber Optic Sensors under Different Strain Fields, *Sensors (Basel)*, 2023 Aug 23(15):6863.

[16] X. Chapeleau and A. Bassil, "A general solution to determine strain profile in the core of distributed fiber optic sensors under any arbitrary strain fields," *Sensors*, vol. 21, no. 16, p. 1-33, 2021.

[17] Zhang, Shenghan, Han Liu, Sanjay Govindjee, and Matthew J. DeJong. 2022. "Strain Transfer Mechanisms and Mechanical Properties of Optical Fiber Cables" *Sensors* 22, no. 24: 9966.

[18] M. Kabbara, X. Chapeleau, Q. Zhang, and F. Bourquin, "Numerical evaluation of strain transfer model for steel-reinforced optical fiber cable embedded in a cylindrical concrete beam with two void inclusions," *EPJ Web Conf.*, vol. 305, 2024.

[19] J.-M. Hénault, "Approche méthodologique pour l'évaluation des performances et de la durabilité des systèmes de mesure répartie de déformation: application à un câble à fibre optique noyé dans le béton," Ph.D. dissertation, Univ. Paris-Est, Paris, France, 2013.