Ultra-efficient reconstruction of 3D microstructure and distribution of properties of random heterogeneous materials containing multiple phases

Ultra-fast 3D material microstructure reconstruction and quantitative structure-property mapping are crucial components of integrated computational material engineering (ICME). It is particularly challenging for modeling random heterogeneous materials such as alloys, composites, polymers, porous media, and granular matters, which exhibit strong randomness and variations of their material properties due to the hierarchical uncertainties associated with their complex microstructure at different length scales. An explicit mixture random field (MRF) model is proposed to characterize and reconstruct multi-phase stochastic material property and microstructure simultaneously. The proposed method is shown to have ultra-high computational efficiency and only requires minimal imaging and property input data. The material property field is modeled by this strongly non-Gaussian random field, which is generated by a nonlinear mapping from the underlying Gaussian random field explicitly. The corresponding microstructure is represented by discrete phase indicators obtained from the material property field. A decomposed Karhunen–Loève (K-L) expansion method is used to dramatically reduce the computational costs and memory requirement for high-dimensional and high-resolution generations. The feasibility and superior efficiency are demonstrated by reconstructing various materials, from 2D to 3D, bi-phase to multi-phase, isotropic to anisotropic materials. The results show that it only takes approximately seconds to reconstruct a 3D material with the resolution of $500\times 500\times 500$ pixels. The elegant expression for explicit microstructure-property mapping with uncertainty quantification capability can be directly incorporated into the ICME framework for material design and optimization.