© 2020

Geometric Control of Fracture and Topological Metamaterials


Part of the Springer Theses book series (Springer Theses)

Table of contents

  1. Front Matter
    Pages i-xix
  2. Noah Mitchell
    Pages 1-14
  3. Gaussian Curvature as a Guide for Material Failure

    1. Front Matter
      Pages 15-15
  4. Topological Mechanics in Gyroscopic Metamaterials

    1. Front Matter
      Pages 53-53
    2. Noah Mitchell
      Pages 93-95
  5. Back Matter
    Pages 97-121

About this book


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.


gyroscopic metamaterials topological order in amorphous materials crack kinking Berry curvature topological mechanics Gaussian curvature of metamaterials elastic quasi-2D materials crack propagation

Authors and affiliations

  1. 1.Kavli Institute for Theoretical PhysicsUniversity of California at Santa BarbaraSanta BarbaraUSA

About the authors

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.

Bibliographic information

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