Stochastic Multiscale Modeling of Polycrystalline Materials.

摘要

Mechanical properties of engineering materials are sensitive to the underlying random microstructure. Quantification of mechanical property variability induced by microstructure variation is essential for the prediction of extreme properties and microstructure-sensitive design of materials. Recent advances in high throughput characterization of polycrystalline microstructures have resulted in huge data sets of microstructural descriptors and image snapshots. To utilize these large scale experimental data for computing the resulting variability of macroscopic properties, appropriate mathematical representation of microstructures is needed. By exploring the space containing all admissible microstructures that are statistically similar to the available data, one can estimate the distribution/envelope of possible properties by employing efficient stochastic simulation methodologies along with robust physics-based deterministic simulators. The focus of this thesis is on the construction of lowdimensional representations of random microstructures and the development of efficient physics-based simulators for polycrystalline materials. By adopting appropriate stochastic methods, such as Monte Carlo and Adaptive Sparse Grid Collocation methods, the variability of microstructure-sensitive properties of polycrystalline materials is investigated.