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On Weingarten-Volterra Defects

  • Amit Acharya
Article
  • 53 Downloads

Abstract

The kinematic theory of Weingarten-Volterra line defects is revisited, both at small and finite deformations. Existing results are clarified and corrected as needed, and new results are obtained. The primary focus is to understand the relationship between the disclination strength and Burgers vector of deformations containing a Weingarten-Volterra defect corresponding to different cut-surfaces.

Keywords

Line defects Disclinations Dislocations Incompatibility 

Mathematics Subject Classification

74A05 

Notes

Acknowledgements

I am very grateful to Reza Pakzad and Raz Kupferman for their valuable comments and discussion. I thank Reza for reading the whole paper and Raz for taking a look at the finite deformation part. I also thank Reza for showing me alternative proofs of the main results of this paper for bodies in two space dimensions with a single hole without involving any line or product integrals, but capitalizing only on appropriate statements of rigidity. I acknowledge the support of the Center for Nonlinear Analysis at Carnegie Mellon and grants ARO W911NF-15-1-0239 and NSF-CMMI-1435624.

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Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Dept. of Civil & Environmental Engineering, and Center for Nonlinear AnalysisCarnegie Mellon UniversityPittsburghUSA

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