Geometric theory of smooth and singular defects

Marcelo Epstein, Reuven Segev

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

A unified theory of material defects, incorporating both the smooth and the singular descriptions, is presented based upon the theory of currents of Georges de Rham. The fundamental geometric entity of discourse is assumed to be represented by a single differential form or current, whose boundary is identified with the defect itself. The possibility of defining a less restrictive dislocation structure is explored in terms of a plausible weak formulation of the theorem of Frobenius. Several examples are presented and discussed.

Original languageEnglish
Pages (from-to)105-110
Number of pages6
JournalInternational Journal of Non-Linear Mechanics
Volume66
DOIs
StatePublished - 1 Jan 2014

Keywords

  • De Rham currents
  • Differential geometry
  • Dislocations
  • Frank's rules
  • Frobenius theorem
  • Integrability

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