Resumen
The aim of this study is to establish a new method for predicting the effective elastic and thermal behavior of heterogeneous materials through mathematical curve fitting. The research initiates with the collection of 3D microstructures comprising 200 spherical inclusions embedded within a linear elastic matrix. This database is acquired by varying the volume fraction of the inclusions (10%, 15%, 20%, or 25%) and the contrast between the two phases. The contrast is quantified in terms of the ratio of the Young?s modulus and thermal conductivity modulus, EiEm" role="presentation">????????EiEm
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, with values ranging from 10 to 200. These microstructures are then used to estimate the elastic and thermal properties by calculating the effective bulk, shear, and thermal conductivity moduli via the finite element method (FEM). The compiled database is a crucial asset for the development of mathematical equations that precisely fit the curves of various moduli based on changes to input parameters such as the volume fraction and the contrast. The process includes analyzing the data, identifying patterns, and establishing mathematical relationships that effectively reflect the moduli?s observed behavior. By integrating these individual equations and taking into account their interdependencies, the resultant comprehensive 3D model provides an extensive representation of the material?s behavior and takes into consideration the impacts of varying the volume fraction and contrast on the different moduli. This approach enables a better understanding of the material?s response under diverse conditions. Results exhibit the accuracy and reliability of the chosen mapping functions and parameters. Thereby, these proposed functions, with respect to boundary conditions and analytical limits, confirm the relevance of the proposed model to capture such information with a suitable level of precision.