Homological Characterization of Microstructure Response Fields

Within this project, quantitative characterizations for the thermal-elastic response of calcite-based polycrystals are developed. The characterization is based on topological measurements such as the number of components and the number of handles of a complex microstructure. These characterizations are then applied to characterize both the grain boundary misorientations in the polycrystal and the resulting elastic energy density and principal stress fields. It is demonstrated that the topological analysis can quantitatively distinguish between different types of grain boundary misorientations, as well as between the resulting differences in the response fields.