Estudo e desenvolvimento de software para homogeneização das propriedades elásticas de materiais heterogêneos bifásicos através da micromecânica dos campos médios

Abstract

Initially, a bibliographic study was carried out on the micromechanics of the mean fields for heterogeneous materials and on the Dilute suspension, Self-consistent, Mori-Tanaka and Differential Scheme homogenization methods. Based on this, an algorithm was developed to determine the effective elastic properties of a two-phase material through the main techniques for the following inclusion geometries: spherical, aligned and misaligned fibers, the last two being able to have a prolate or oblate shape, all arranged randomly in the space. This algorithm was transformed in the Calc-Composite software, using the MATLAB language. Through the literature and DIGIMAT, the code validation was carried out. The results obtained with Calc-Composite for the main homogenization methods were compared with experimental results and with the finite element technique, where the Differential Scheme presented the best results for high volumetric fractions. With the help of Calc-Composite, a study was carried out on the influence of geometry on the Young's modulus of a composite material, noting that aligned fibers present greater stiffness when compared to misaligned fibers and spherical inclusion. It was also observed that the stiffness of a heterogeneous material with spheroid-shaped inclusions increases as the aspect ratio moves away from 1 on the left or right, reaching a limit value, where the increase or decrease of the aspect ratio does not more will have a significant influence on the stiffness of the material.