Computational Design of Three-Dimensional Multi-Constituent Material Microstructure Sets with Prescribed Statistical Constituent and Geometric Attributes

The generation of three-dimensional (3D) microstructures with multiple constituents is an important part of multiscale computational simulation and design for a wide range of materials including heterogeneous polycrystalline metals, ceramics, composites, and energetics. Realistic 3D microstructures for multiphase materials are difficult to obtain experimentally or computationally. Challenges include generation and representation of complex constituent morphologies, topological arrangement and distribution, defect description, and statistical conformity. Here, we present a novel technique for systematically composing complex 3D statistically equivalent microstructure sample sets (SEMSS) with prescribed statistical constituents and morphological attributes. Based on large libraries of varying representations of individual constituents, the technique can be used with experimental micro computerized tomography (CT) scans to establish SEMSS that track the attributes of existing materials as well as to design SEMSS for new materials not yet in existence for computational exploration. Heterogeneous systems involving different combinations of molecular crystallites, metallic particles, oxidizer granules, and a polymeric matrix are designed and generated to track the properties of an existing material. The corresponding SEMSS are used in multiphysics simulations accounting for coupled thermal–mechanical processes or thermal–mechanical-chemically reactive processes. The results are used to quantify microstructure-induced response variations and point out the limitations of two-dimensional (2D) microstructures that are direct sections of the full 3D microstructures. The use of the SEMSS has also enabled uncertainty quantification (UQ) and the development of probabilistic characterizations for variations in macroscopic responses due to intrinsic material microstructural heterogeneities.