Computational Homogenization of Precipitated Shape Memory Alloys: A Comparative Study of FFT Versus FEA

Aging heat treatments in Shape Memory Alloys (SMAs) often lead to formation of precipitates, which affect phase transformation. In order to analyze the effects of volume fraction, shape, and spatial distribution of precipitates in a non-linear setting, computational homogenization is required. In this work, a comparative study on the performance of a fast Fourier transform (FFT) method and that of a more established finite element analysis (FEA) is undertaken toward predicting the behavior of precipitated SMAs. To this end, both conforming and non-conforming meshes are used in the finite element analyses. It is found that FEA homogenization may be more accurate when using conforming meshes. However, FFT-based homogenization, which utilizes voxel based, hence non-conforming discretization, provides the same order of convergence as FEA with conforming discretization and a significant improvement in computation time.