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Emilio Silva Homogenization Method Applied to the Development of Composite Materials Homogenization method allows us to calculate the effective properties of a periodic composite material knowing its unit cell topology, which can have any complex shape if the method implementation is based on FEM. Thus, this method has been extensively applied to characterize composite materials. An emerging field that can take advantage of applying homogenization method is the FGM (Functionally Graded Materials) composite materials. These composite materials are made to take advantage of desirable features of its constituent phases and they possess continuously graded properties with gradual change in microstructure. This makes difficult to calculate their effective properties by using analytical and self-consistent methods. In this sense, the homogenization method is a powerful tool that allows us to characterize FGM materials effective properties. By changing the composite material unit cell topology, its effective properties can be changed. Based on this idea, homogenization method can be combined with synthesis methods, such as, topology optimization, allowing the design of composite material unit cell topology considering desired properties or performance improvement. Topology optimization is a general structural optimization method that combines optimization algorithm with finite element method to find an optimal material distribution inside a given domain that extremizes a specified objective function. In the last few years, material synthesis methods have been successfully applied to design negative poisson´s ratio materials, zero expansion coefficient thermoelastic materials, high performance piezocomposite materials, among others. In this lecture, an overview of the concept and implementation of homogenization theory and material design method will be given, as well as the current state and future trends of these topics will be discussed.
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