# Photoelasticity as a Tool for Stress Analysis of Re-Entrant Auxetic Structures
## 1 Introduction
The authors of [16] described auxetic structures with different configurations and found out that isotropic systems, like hexachiral or rotating places structures, have a limit on the maximum negative Poisson's ratio achievable in any direction. On the other hand, anisotropic systems, like re-entrant structures, can achieve a more negative Poisson's ratio in one direction and a lower negative Poisson's ratio in the other in-plane direction. A negative Poisson's ratio significantly influences the stress distribution within the material, which can be effectively analyzed using photostress methods. Photostress analysis, a subset of photoelasticity, enables the visualization of stress patterns through polarized light, allowing the observation of isochromatic lines that reveal paths of constant stress differences [17]. When a structure is subjected to mechanical stress, the resulting stress fields are complex due to the material's expansion in both longitudinal and transverse directions. This complexity is captured in the form of isochromatic lines, which represent the paths of constant difference in principal stresses [18]. In auxetic materials, the stress concentration areas, often highlighted by these isochromatic lines, behave differently compared to conventional materials [19]. The negative Poisson's ratio leads to a more uniform distribution of stress across the material, potentially reducing the likelihood of failure points [20], which is a critical insight provided by photostress analysis. Additionally, because auxetic structures often experience higher strains under the same load conditions compared to non-auxetic materials [21], the photoelastic response in these regions is more pronounced, allowing for a more detailed analysis of the stress-strain behavior [22]. In this article, we highlight the practical potential of using photoelasticity with standard measurement techniques that place lower demands on hardware and software equipment and personnel. However,advancements in digital photoelasticity have revolutionized the process, providing automated and more accurate stress analysis across the entire field of observation. Recent innovations in digital photoelasticity have significantly enhanced the clarity and resolution of fringe patterns, even in complex multicolored stress fields. For example, the Twelve Fringe Photoelasticity (TFP) method, developed to improve color accuracy in photoelastic images, enables the demodulation of highly intricate stress patterns. This method proves particularly effective in scenarios where multiple stress levels coexist, enhancing the interpretation of complex geometries and multicolored fringe patterns, and thereby improving the accuracy of stress quantification in materials with complex structures [23]. In recent years, the development of machine learning algorithms has added another layer of precision to digital photoelasticity. The introduction of deep learning models such as FringeNet, a U-Net model specifically designed for photoelastic applications, offers enhanced fringe demodulation. By applying advanced neural networks, FringeNet improves the resolution and continuity of fringe patterns, overcoming traditional limitations in digital photoelasticity such as fringe overlap or discontinuities. These advancements make it possible to analyze isochromatic fringe patterns with higher accuracy, particularly in complex stress fields common in auxetic materials [24]. Moreover, full-field automated techniques such as RGB photoelasticity have advanced the field further, allowing for the observation and analysis of stress distributions under white light conditions. Previously, such analyses were limited by the monochromatic light used in traditional photoelastic setups. RGB photoelasticity facilitates faster and more precise measurements of stress patterns, making it possible to automate the analysis of complex geometries [25], as is the case in auxetic structures.