## 1 Introduction
Figure 1: Plot (replicated from [12; 13; 14]) of the DIC evaluated strain for a plate with hole loaded in tension for various values of the DIC step. The non-local peridynamics (PD) theory of continuum mechanics based on integral formulation of the equations of motion was developed by [PERSON] in 2000 [26]. Due to not including local spatial derivatives into the formulation, the PD theory is very promising for applications to discontinuous fields [27; 28]. Although the PD theory is defined in terms of the stretch between material points and the conventional continuum mechanics quantities of strain and stress are not PD theory conventional parameters, strains can still be retrieved in PD by the use of the PD integro-differentiation. The peridynamic differential operator (PDDO) was created for this purpose [29]. PDDO is always valid, even in the case of discontinuity. [PERSON] et al. [29; 30; 31] demonstrated other possible applications of the PDDO, for example, signal and images processing, data smoothing and noise reduction, data compression and recovery, interpolation and other mathematical operations. Coupling between the two aforementioned methods, namely the experimental DIC and the computational PD, has also been of recent interest. [PERSON] et al. [32] used PD for tracking crack propagation paths. In their study displacements are imported from DIC measurements and used to calculate crack path using the PD simulation and PD damage parameters. [PERSON] [33] and [PERSON] et al. [34] coupled DIC with PD simulation by reading the displacement field from DIC measurements and using it in PD simulations to circumvent the DIC difficulties when measuring full field deformations in discontinuous displacement field. The method was also applied to potential damage regions determined according to the low DIC correlation coefficients. According to their results, the authors claim that their coupled DIC and PD strategy can be used to predict both macro damage evolution and invisible micro-crack initiation and propagation before macro-crack forms. Despite the work mentioned before related to DIC-PD coupling, the topic is still a very new one and of high potential to contribute to and enhance the capabilities of both experimental DIC and computational PD methods. Moreover, applying PDDO directly to DIC displacement field rather than coupling DIC displacement with PD simulations (this was done in studies [32; 33; 34]) brings new approach to be investigated. The aim of this study is to investigate into the possible applications of the PDDO to full field DIC in order to find possible improvements of the DIC differentiation algorithm and thus the DIC strain calculation accuracy. The problem of the plate with circular hole under tension is analyzed here, as means of introduction (Figure 1) the displacement and strain field gradients which pose a challenge for the conventional DIC calculation algorithm. The PDDO is used as a mathematical tool in order to differentiate the DIC discrete displacement field, for the cases of high gradients and oscillatory/noisy DIC data. Moreover, the proposed DIC-PDDO method performance against conventional DIC algorithms is evaluated based on the benchmark data from DIC Challenge 2.0 [11] and Metrological Efficiency Indicator (MEI) [35; 36] which combines both spatial and measurement resolutions. Finally, the PDDO applications for faulty DIC data to recover the correct strain field are also analyzed. The manuscript is organized as follows: brief review of the theoretical background related to the conventional DIC strain calculation and PD-PDDO theory is presented in Section 2; methods related to the experimental setup and computational models are presented in Section 3; results including a benchmark analysis of strains as calculated by conventional DIC, PDDO applied to DIC displacement data, and FE simulation are presented in Section 4. The results presented here can help to better understand the DIC method capabilities and the PDDO differentiation method potential to improve the DIC results.