Denoising diffusion-based synthetic generation of three-dimensional (3D) anisotropic microstructures from two-dimensional (2D) micrographs

For instance, multiscale computational analysis that employ the concept of the representative volume element (RVE) have been widely utilized to analyze the representative material response under specific boundary conditions [2, 7]. In particular, computational homogenization methods accompanying with finite element analysis (FEA) based on the asymptotic homogenization theory [8, 9], have been used to analyze the macroscopic properties of representative microstructures (i.e., RVEs) for various types of microstructural materials including particulate or fibrous composites [10-14], multi-phase polycrystalline metals [15, 16], metal matrix composites [17, 18], and lattice materials [19-21]. In general, these methods assume that the behavior of a heterogeneous material can be described by an RVE that is periodic throughout the material of interest. If an RVE is properly modeled for the subsequent computational homogenization analysis with periodic boundary conditions (PBC), and the macro-structure is sufficiently large, accurate solutions for the homogenized material properties (i.e., effective material properties) can be obtained. The homogenized properties of heterogenous materials can also be acquired based on the fast Fourier transform (FFT) [22, 23], which avoids the time-consuming FEA for computing the material response under macroscopic loading. Meanwhile, the recently proposed deep learning (DL) models [24-28] that link microstructure to material properties are gaining significant attention, due to their remarkably lower computational cost compared to conventional computational homogenization methods. For instance, Rao and Liu developed a three-dimensional convolutional neural network (3D-CNN) for homogenization of heterogeneous materials with random spherical inclusions [24]. Their results showed that after training the 3D-CNN using the training data pairs (i.e., microstructure RVEs and anisotropic material properties), the model could accurately estimate the anisotropic elastic material properties with a maximum prediction error of up to 0.5%.