This thesis reports a rare combination of experiment and theory on the role of geometry in materials science. It is built on two significant findings: that curvature can be used to guide crack paths in a predictive way, and that protected topological order can exist in amorphous materials. In each, the underlying geometry controls the elastic behavior of quasi-2D materials, enabling the control of crack propagation in elastic sheets and the control of unidirectional waves traveling at the boundary of metamaterials. The thesis examines the consequences of this geometric control in a range of materials spanning many orders of magnitude in length scale, from amorphous macroscopic networks and elastic continua to nanoscale lattices.

Autorentext
Noah Mitchell is a postdoctoral fellow at the Kavli Institute for Theoretical Physics at the University of California, Santa Barbara. He received his PhD from the University of Chicago in 2018.

Inhalt
Chapter1: Introduction.- PartI: Gaussian Curvature as a Guide for Material Failure.- Chapter2: Fracture in sheets draped on curved surfaces.- Chapter3: Conforming nanoparticle sheets to surfaces with gaussian curvature.- PartII: Topological mechanics in gyroscopic metamaterials.- Chapter4: Realization of a topological phase transition in a gyroscopic lattice.- Chapter5: Tunable band topology in gyroscopic lattices.- Chapter6: Topological insulators constructed from random point sets.- Chapter7: Conclusions and outlook.