Hodge duality and continuum theory of defects

Kazuhito Yamasaki, Hiroyuki Nagahama

Research output: Contribution to journalArticlepeer-review

17 Citations (Scopus)

Abstract

Dual material space-time with defect field is presented in the language of differential forms: one is the strain space-time whose basic equation is the continuity equation for the dislocation 2-form; the other is the stress space-time whose basic equation is the continuity equation for the couple-stress and angular momentum 2-form. Continuity and kinematic equations in each space can be derived by the transformation from p-form to (p + 1)-form. Moreover, several constitutive equations can be recognized as the transformation between the p-form of the strain space-time and the (4 - p)-form of the stress space-time. These kinematic, continuity and constitutive equations can be interpreted geometrically as Cartan structure equations, Bianchi identities and Hodge duality transformations, respectively.

Original languageEnglish
Pages (from-to)L475-L481
JournalJournal of Physics A: Mathematical and General
Volume32
Issue number44
DOIs
Publication statusPublished - 1999 Nov 5

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)

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