Gradient-based microstructure reconstructions from distributions using fast Fourier transforms

Reconstructions are an important step in analyzing the statistics of local state distributions in the internal structure of heterogeneous material systems and in estimating their effective properties using deterministic models. In this paper, we demonstrate the use of fast Fourier transforms (FFTs) and gradient-based algorithms for the reconstruction of microstructure realizations from 2-point statistics. The FFT method greatly improves the computational efficiency of the algorithm, facilitating use of the full set of 2-point statistics in the reconstruction. This approach introduces periodic boundary conditions naturally into the model. The reconstruction of several two-phase 2D structures is demonstrated, resulting in exact replicas of the original microstructures. The limitations of the technique, especially for more complex structures, are also discussed.