Structure-property relation is hailed as one of the three pillars of materials science. However, such relation has remained largely empirical or qualitative, especially for polycrystalline materials. As compared with single crystals, microstructure of polycrystalline materials has far more microstructural variables. How to quantitatively describe them and then apply the microstructure information in establishing connection with material properties remains a grand challenge in materials science.
Microstructure in polycrystalline materials, either coarse-grained or nano-crystalline, is characterized by complex topological structure of grain boundary networks which are composed of an array of geometric entities with different dimensions. Collectively, they contribute to the materials’ properties. In this talk, I present recent developed algorithms and numerical methods in polycrystalline samples and how we can exploit the structure-property relations. Such quantitative methods enable detailed and rigorous treatment of microstructures in a wide range of modeling applications, including both atomistic simulation and continuum modeling.