Validation of a numerical method based on Fast Fourier Transforms for heterogeneous thermoelastic materials by comparison with analytical solutions

A numerical method based on Fast Fourier Transforms to compute the thermoelastic response of heterogeneous materials is presented and validated by comparison with analytical solutions of the Eshelby inclusion problem. Spherical and cylindrical, homogeneous and inhomogeneous inclusion configurations are used to validate the results of the proposed spectral method. Dependencies of the numerical solutions on homogeneity, geometry and resolution are also explored, and the differences with respect to known analytical solutions are quantified and discussed. In the case of homogeneous inclusions, the proposed numerical method is direct, i.e. does not require iteration. Using enough resolution, the micromechanical fields predicted for these simple geometries are shown to be in good agreement with the analytical results. The specific way in which inclusions are voxelized is also explored, and its effect on local fields near interfaces is assessed.