# Strain Transfer Analysis of a Clamped Fiber Bragg Grating Sensor
## 1 Introduction  
Fiber Bragg grating (FBG) sensors have attracted wide attention from the civil and mechanical research community because of its many merits such as small size, high sensitivity, and immunity to electromagnetic interference [1]. In common practice, a bare optical fiber is encapsulated into a capillary tube with adhesives for real structural monitoring applications. Due to the interaction effect between different materials with different mechanical properties, the strain measured by FBG sensors is smaller than that of the strain of the host material. The error caused by the strain transfer rate between the host material and the FBG sensor cannot be ignored, especially in real applications. Recently, some research has concentrated on analyzing the strain transfer rate of FBG sensors and the accuracy of strain measurements from FBG sensors has been continually improved. [PERSON] et al. [2] considered that when the elastic modulus of the interlayer was equal to the optical fiber, the maximum strain of the host material was transferred by the interlayer. [PERSON] et al. [3] proposed a theoretical model for the coated optical fiber embedded in composite materials. Results revealed that when the elastic modulus of the coated layer was equal to the average elastic modulus of the host material and optical fiber, the maximum strain can be sensed by the FBG sensor. [PERSON] et al. [4] acquired a theoretical expression describing strain transfer rate (\(\alpha\)) based on the shear-lag theory, which was suitable for short fiber composites. Moreover, the theoretical results were verified through a series of experiments involving white light interferometry. On the other hand, [PERSON] et al. [5] assumed the same strain change rate between the gauge length center and the host material, amending [PERSON]'s results to obtain theactual strain with better accuracy [4]. It also revealed that the maximum strain transfer ratio occurred in the middle of the optical fiber sensor. Moreover, [PERSON] et al. [6] discussed the influencing parameters on strain transfer rate. [PERSON] et al. [7] made an improvement on [PERSON]'s study by taking into account temperature variations and nonaxial stresses. [PERSON] et al. [8] evaluated the interaction between the matrix and optical fiber, giving the distributions of interfacial shearing stress. To achieve the accurate surface strain monitoring of the host material, [PERSON] et al. [9] established the mechanical model of the surface FBG sensor and derived a general expression of the relation between the FBG sensor strain and the host material strain. [PERSON] et al. [10] presented the strain transfer mechanism and the error modification theory of an embedded FBG sensor. [PERSON] et al. [11] also studied the long-term service performance of FBG strain sensors embedded in concrete structures. The creep constitutive relation of concrete was introduced to analyze the strain transfer and the finite element method was used to verify the theoretical analysis results. [PERSON] et al. [12] studied the transfer efficiency of substrate package FBG sensors, established the strain transfer model and compared it with experimental tests. A package mode of beryllium bronze was put forward and analyzed by using finite element analysis software ANSYS (ANSYS 16.0, ANSYS Inc., Pittsburgh, PA, USA). Calculation results show that characteristics of strain transfer of beryllium bronze package is normal, but it has a good protection performance for FBG sensors. [PERSON] et al. [13] investigated the strain transfer factors of a pasted FBG under bending parts, establishing a pasted FBG strain transfer model by theoretical analysis. The strain transfer parameters were analyzed by a simulated analysis method. Experimental and simulation results show that the length and the middle layer thickness have the dominating effect on the strain transfer rate of FBG sensors. [PERSON] et al.