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.
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