## 1 Introduction  
Heterogeneous and composite materials [1; 2; 3] are increasingly used in various industrial sectors, notably in the aerospace and automotive industries. Despite their growing popularity, the full potential of these materials is yet to be fully realized, mostly due to their inherent variability and complex microstructural morphologies. Accurate prediction of composite performance and heterogeneous materials, which exhibit a wide range of arrangements and morphologies of heterogeneities, is a challenging task. Solely relying on experimental and analytical homogenization approaches [4; 5; 6], based on either real [7] or virtual [8; 9] microstructures, proves to be excessively time-consuming and resource-intensive. However, a viable approach is to utilize experimental data to create a multitude of random yet statistically equivalent virtual microstructures. The primary goal of this approach is to methodically predict the macroscopic behavior of these materials, taking into account the complexities and variations inherent in their structures. Given the broad spectrum of materials requiring analysis, the use of curve fitting [10] and mathematical modeling [11] is indispensable for constructing homogenized behavioral models. These models, when efficiently optimized, can accurately determine critical parameters such as shape, volume fraction, and contrast. Applying curve-fitting techniques enables us to efficiently exploit a massive database of materials to develop refined and optimized macroscopic behavioral models. Over the last few years, several experimental studies have leveraged curve fitting to predict mechanical and thermal properties of heterogeneous materials. [PERSON] and [PERSON] [12] employed this methodology to estimate the effective thermal conductivity of Lotus-type porous materials (LTPM) by delineating the characteristics of each phase according to its unique porous morphology. The model's efficiency was thoroughly investigated in light of results obtained using finite element homogenization methods. This methodological precision not only facilitated the accurate prediction of LTPM thermal conductivity but also proved its reliability and applicability through a rigorous validation process in relation to standard computational methods. As an extension of this method, [PERSON] and [PERSON] [13] have taken advantage of the capabilities of curve fitting to develop a sophisticated mathematical model specifically designed for estimating thermal conductivity in two-phase heterogeneous two-dimensional materials. Their study stood out for its comprehensive approach, in which model predictions were rigorously evaluated against established analytical benchmarks, including series, parallel, and Maxwell models. This meticulous comparative analysis not only highlighted the efficiency and accuracy of their curve-fitted model but also showed its potential in capturing the complex thermal behavior of these materials. [PERSON] [14] made a significant contribution by developing four distinct mathematical models for estimating the relative Young's moduli of materials. The first two models incorporated three essential variables: the contrast between the two phases and the Poisson's coefficient. Relying on this foundation, the latter two models introduced an additional parameter--the volume fraction of particle packing--with the aim of enhancing the precision of predictions. What sets these models apart is not only their mathematical sophistication but also their practical utility, as [PERSON] meticulously validated the models' efficiency through a comprehensive comparison with experimental data. In their pioneering work, [PERSON] and [PERSON] [15] introduced a sophisticated mathematical method designed to ascertain the elastic properties of composite materials featuring multiple phases. Their innovative approach relied on advanced numerical techniques to analyze stress-strain relationships, with a particular emphasis on unraveling the intricate influence of pores (voids) on the material's behavior.