Numerical evaluation of the thermomechanical effective properties of a functionally graded material using the homogenization method

When the stresses of the functionally graded materials (FGMs) are discussed under thermal and/or mechanical loading conditions, the different thermomechanical effective properties are needed. For the steady state thermal analyses, these properties include the Young’s modulus, Poisson’s ratio, thermal expansion coefficient and thermal conductivity. For the transient analyses of the heat conduction problem, on the other hand, the density and heat capacity should be added to the aforementioned properties. The homogenization method (HM) based on the finite element method (FEM) is used as it has advantages, such as it is appropriate for estimating the effective properties of composites with a given periodic fiber distribution and complicated geometries. For a periodic composite structure, it is not necessary to study the whole structure but only a representative volume element (RVE) or a unit cell (UC). As the overall behavior of composites depends on the arrangement of the reinforcements, the corresponding UCs of two different arrangements of the fibers are analyzed; namely the square and hexagonal arrangements. It is found that the square arrangement predicts higher values of the Young’s modulus than the hexagonal one but with small difference. In order to verify the computed values of the properties, the results are compared with previous experimental measurements and results of analytical and numerical methods, and good agreement is achieved.