Despite the phenomenological approach presents excellent results in material behavior analysis, real-world materials are inherently heterogeneous. A material is considered heterogeneous when, at a particular observation scale, it becomes feasible to discern multiple mixture phases within it. This level of observation is commonly referred to as the microscale, where interactions between constituents occur, ultimately leading to the emergence of cracks.Modeling a material at the microscale begins with defining a Representative Volume Element (RVE), which is the smallest part of the material that is large enough to statistically represent the entire mixture. This ensures that other samples of the same size exhibit similar properties with minor variations. The analysis of the RVE leads to obtaining the effective properties of a portion of the material. That process is called homogenization.Modeling a RVE can be a challenging task, as it requires the use of highly refined meshes to accurately capture the geometric representation of all mixture components. Therefore, phase-field models present themselves as a suitable choice for this type of modeling, once due to the intrinsic features of its variational formulation, they already need refined meshes and do not present localization effects.Thus, the objective of this work is to model a heterogeneous RVE and obtain its homogenized properties. This homogenization of the material parameters is fundamental for the upscaling operation of multiscale analyses.All implementation were done in INSANE, an opensource software developed by the Engineering Structures Department (DEES) of Federal University of Minas Gerais (UFMG).
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