Faithin Omaha eBook Collection

Download or read book Stochastic Multiscale Modeling of Complex Materials written by Joseph Bakarji and published by . This book was released on 2020 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Multiscale modeling and simulation of complex materials is still a formidable task. The challenge arises due to the lack of scale separation in systems that exhibit nonlinear and chaotic dynamics. In this dissertation, we develop stochastic, multiscale and data-driven methods for modeling complex systems, with a focus on the dynamic compaction of heterogeneous granular materials. We first devise an energy-conserving multiscale hybrid model that explicitly accounts for macropore compaction dynamics at the mesoscale. Subsequently, we develop a probabilistic generalization that models the heterogeneous initial microstructure as a random field to explain thermal localization. The results motivate a data-driven sparse regression method to discover analytical expressions for PDF equations from Monte Carlo simulation data. This method has shown to be a promising direction for data-driven coarse-graining in a wide range of physics and engineering applications. In addition, we introduce model uncertainty and subscale fluctuations that arise due chaotic intergranular stresses through the formalism of stochastic differential equations (SDE). Finally, a hybrid algorithm that couples SDEs with PDEs is developed to combine fine- and coarse-grained probabilistic models in the same domain.