Browsing by Subject "Homogenization"

From batteries to bones, rocks to concrete, porous materials are ubiquitous in the natural and engineered environment, yet remain elusive in their characterization. One of the fundamental challenges of studying porous materials comes down to a fundamental question of linking the microscale to the mesoscale. This work addresses two primary linkages for analysis--the chemical response and the mechanical response of the material. Minkowski functionals served as the primary vessel for understanding how material microstructural geometry ties to macroscale energetics. In the case of chemical systems, Minkowski functionals proved to be powerful predictive tools in both reaction steady states and reaction dynamics. These exponential linkage to morphometers serves as a basis for understanding how the interfacial geometry of system affects the non-mixed chemical behavior of said system over time.As a study on novel simulation frameworks for modeling discrete chemical behavior at the microstructural scale, this work also introduces a unique means for modeling interface chemistry--surface CRNs. Surface CRNs are asynchronous cellular automata models similar to Markov chain models. This class of simulator efficiently translates complex chemical behavior into relatively easy-to-follow reaction rules. This class of simulator has proven to be surprisingly accurate despite its simplicity, creating a strong basis for understanding chemical behavior at a discrete level. While one half of this work focused on the ability of Minkowski functionals to predict chemical behavior, the other half of this work focuses on their ability to link to the mechanics of a microstructure. To address the mechanics problem, Minkowski functionals were extracted from 3D x-ray tomographic scans and assessed mechanically via 3D printed and digitally modeled strength assessments. Ultimately, a deep learning model was trained that could accurately predict and recreate the mechanical response profile of a digitally simulated porous microstructure from just four Minkowski functionals. This extended further to 3D printed samples, allowing for the mechanical behavior of physical samples to be predicted just from its geometric descriptors.