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