Effective mechanical properties of composite materials depend on the material properties of the constituents, the shape and volume fraction of the reinforcement as well as the interactions between the reinforcement and the matrix. The strain field at the microscopic level is inhomogeneous due to the contrast between the matrix and reinforcement material properties. The strain field heterogeneity can be analyzed by using various analytical, numerical and experimental methods. Analytical micromechanical models based on Eshelby’s solution [
1] such as Mori–Tanaka [
2,
3] or self-consistent [
4,
5] methods allow the estimation of the strain partitioning between the matrix and reinforcement by referring to the per phase average strains. On the other hand, when analytical methods are used, it is difficult to consider strain concentrations which are effects of fibers clustering and nonuniform spatial distribution. The other way is to use numerical methods which can take into consideration complex geometrical models describing the material microstructure. The most versatile and widely used numerical method for analysis of the deformation behavior of composites at the microstructural level is the finite element method (FEM) [
6,
7,
8,
9]. The other numerical methods which can be used for this purpose are the boundary element method (BEM) [
10,
11] and meshless methods [
12,
13]. Recently also experimental optical methods have been applied for measuring the deformation behavior at the microstructural level. In this case the most popular method is digital image correlation (DIC) which is a computer-based procedure that allows full-field displacement information to be obtained by recording the motion of a speckle pattern on a specimen surface during the deformation [
14,
15,
16,
17]. The numerical procedures of the DIC are based on pseudo-affine transformation where series of pictures collected during the deformation of the specimen are correlated and results are presented in the form of full field color maps of the displacements or strains [
18]. The DIC can be applied for different length scales since the method has no inherent length scale [
14]. However, the accuracy of the DIC method depends on the quality of the speckle pattern which must be placed on the specimen surface [
19,
20]. Literature discusses several different approaches to the preparation of the speckle pattern for DIC testing at the microscale. The feasibility of the DIC technique for the measurement on micro- and nanoscale was demonstrated by Berfield et al. [
14], the random speckle pattern was created by a fine point airbrush (for microscale measurement) and by solution deposition of fluorescent silica nanoparticles (for nanoscale measurement). Ghadbeigi et al. measured the strain field at the microstructure level of dual-phase steel [
21] and interstitial-free steel [
22], the authors used the natural pattern of the microstructure in order to carry out the DIC analysis. Anzelotti et al. [
23] studied the behavior of a twill-weave carbon fiber reinforced epoxy lamina, the surface was prepared for the DIC measurement by using a white ink spray. Canal et al. [
24] and Mehdikhani et al. [
25] analyzed the behavior of fiber-reinforced composites, the speckle patterns were created by depositing submicron alumina particles. Joo et al. [
26] measured local strain in a dual phase steel by DIC by basing on the nanodot patterns.
The present paper is devoted to theoretical study on the influence of the speckle size on the accuracy of the strain field measurement at the microstructural scale by means of DIC. This is a very important issue from the practical point view because before capturing the images of undeformed and deformed specimen a speckle pattern that guarantees exposing the strain field heterogeneity due to the underlying microstructure is required. Theoretical estimation of the required speckle size can provide information on how the speckle pattern should be prepared, or which preparation method should be used. On the other hand, the error of measurement caused by the non-optimal speckle pattern can be quantified. The paper presents a numerical procedure of the generation of artificial speckle patterns and the technique of mapping of these patterns on a virtually deformed specimen. This work concentrates on unidirectional long fiber reinforced composites. The accuracy of DIC analysis with respect to different sizes of the speckles is investigated by analyzing microgeometries containing several fibers. Moreover, the paper presents a novel approach of inverse identification of the properties of the composite constituents. The idea is to perform an inverse identification of the elastic constants of the composite constituents by basing on the full strain field measurement. This way of indirect estimation of material properties may be very useful for quantification of the properties of individual phases of composites which are difficult to capture during standard experimental testing, for instance in the case of in situ composites. There are several works which are devoted to usage of full field measurement for the purpose of inverse identification of elastic properties of materials at the macroscopic level (constituents are not distinguished in this case) [
27,
28,
29,
30,
31]. One of the most widely used identification approaches is the finite element model updating method which is based on minimizing the discrepancy between the displacements measured experimentally and the displacements computed by the FEM depending on the material constants (variables). Rahmani et al. [
32] used the full field measurement data for identification of the elastic constants of composite constituents, the authors improved the finite element model updating method by adding a regularization term which assumes that besides the displacements, the results provided by the micromechanical model are also fitted to the experimental data. The present paper introduces a novel approach of inverse identification which is based on minimizing the discrepancy between the per phase average strains measured experimentally and computed by using FEM. The inverse problem is solved in a framework of new two-step optimization procedure, which reduces the problem complexity. The feasibility and accuracy of the proposed approach are presented by analysis of two exemplary microgeometries representing the microstructures of fiber reinforced composites.