The results of measuring gradient strain fields by embedded or mounted point fiber-optic sensors based on Bragg gratings and distributed fiber-optic sensors based on Rayleigh scattering are discussed. Along with the experiment, the results of numerical modeling of strain measurement errors associated with the assumption of uniaxial stress state in the area of the embedded Bragg grating and measurement errors by distributed fiber-optic sensors associated with gage length are presented. Experimental results are presented for 3D printed samples and samples made of polymer composite material. The geometry of the samples was chosen based on the results of numerical simulations, and provides different variants of non-uniform strain distribution under uniaxial tension, including the variant in which the derivative of the strain distribution function changes its sign. A good agreement of numerical results and experimental data obtained by distributed and point fiber-optic sensors in areas where the derivative of the strain distribution function keeps a sign and an increase in the error of strain measurement results by distributed fiber-optic sensors in areas where this derivative changes sign are demonstrated.

The results of strain measuring experiments, with the help of rosettes consisting of fiber Bragg grating sensors (FBG) embedded at the manufacturing stage in a polymer composite material are considered in this paper. The samples were made by the direct pressing method from fiberglass prepregs. A cross-shaped sample was tested under loading conditions corresponding to a complex stress state. A variant of strain calculations based on experimental data is discussed. The calculations were performed under the assumption of a uniaxial stress state in an optical fiber embedded in the material. The obtained results provide a reasonable explanation of the absence in the conducted experiment of two peaks in the reflected optical spectrum, the presence of which follows from the known theoretical principles. The experimental result with two peaks in the reflected optical spectrum was obtained for the same sample under a different loading scheme. The proposed variant of the numerical model of the experiment and the results of numerical simulation made for FBG rosettes embedded in the material allowed to estimate error in the strain values calculated on the assumption of the uniaxial stress state in the optical fiber and in the presence of two peaks in the reflected optical spectrum.

This paper presents the results of analytical and numerical investigations into stress behavior in the vicinity of different types of singular points on two-dimensional (2D) elastic bodies made of functionally graded materials (FGMs). A variant of constructing eigensolutions for plane FGM wedges, where the elastic properties are represented as a series expansion with respect to the radial coordinates, was considered. It was shown that, in the vicinity of singular points, the stress behavior is determined by solving the problem for the corresponding homogeneous wedge, where the elastic characteristics coincide with the characteristics of FGMs at the wedge vertex. Numerical investigations were carried out to evaluate the stress state of elastic bodies containing FGM elements at singular points, where the type of boundary conditions changes or where dissimilar materials come into contact. The results of the calculations showed that the behavior of stresses in FGMs in the vicinity of singular points can also be determined from an analysis of the eigensolutions for the corresponding homogeneous wedges, where the elastic properties coincide with the elastic constants of FGMs at singular points and that the functionally graded properties are dependent on one or two polar coordinates.

An algorithm for the numerical analysis of singular solutions of two-dimensional problems of asymmetric elasticity is considered. The algorithm is based on separation of a power-law dependence from the finite-element solution in a neighborhood of singular points in the domain under study, where singular solutions are possible. The obtained power-law dependencies allow one to conclude whether the stresses have singularities and what the character of these singularities is. The algorithm was tested for problems of classical elasticity by comparing the stress singularity exponents obtained by the proposed method and from known analytic solutions. Problems with various cases of singular points, namely, body surface points at which either the smoothness of the surface is violated, or the type of boundary conditions is changed, or distinct materials are in contact, are considered as applications. The stress singularity exponents obtained by using the models of classical and asymmetric elasticity are compared. It is shown that, in the case of cracks, the stress singularity exponents are the same for the elasticity models under study, but for other cases of singular points, the stress singularity exponents obtained on the basis of asymmetric elasticity have insignificant quantitative distinctions from the solutions of the classical elasticity.

One of the issues in the strain measurement with the help of fiber-optic sensors based on Bragg gratings is the calculation of the strain based on the information from the sensor and its correspondence to the material strain. Relationships between the data measured by the sensor and the strain in the Bragg grating have a unique solution under the condition of uniaxial stress state of the fiber, which are not fulfilled when the fiber is embedded in the material. The paper presents the results of numerical experiments with an example of a model problem for a polymer composite material with an embedded optical fiber, which can be surrounded by a resin pocket. The presented results allow to estimate the error of the strain values calculated on the basis of uniaxial stress state assumption of the optical fiber. Based on numerical calculations, parameters of a capillary on an optical fiber in the Bragg grating zone are estimated, ensuring uniaxial stress state of the fiber in the Bragg grating zone. To ensure these conditions, the cross section of the capillary in an isotropic material is a circle, and in an anisotropic material, good results can be obtained with an elliptical cross section.