Notes on metric independent analysis of classical fields

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27 Scopus citations

Abstract

A metric independent geometric framework for some fundamental objects of continuum mechanics is presented. In the geometric setting of general differentiable manifolds, balance principles for extensive properties are formulated and Cauchy's theorem for fluxes is proved. Fluxes in an n-dimensional space are represented as differential (n - 1)-forms. In an analogous formulation of stress theory, a distinction is made between the traction stress, enabling the evaluation of the traction on the boundaries of the various regions, and the variational stress, which acts on the derivative of a virtual velocity field to produce the virtual power density. The relation between the two stress fields is examined as well as the resulting differential balance law. As an application, metric-invariant aspects of electromagnetic theory are presented within the framework of the foregoing flux and stress theory.

Original languageEnglish
Pages (from-to)497-566
Number of pages70
JournalMathematical Methods in the Applied Sciences
Volume36
Issue number5
DOIs
StatePublished - 1 Mar 2013

Keywords

  • balance principles
  • continuum mechanics
  • differentiable manifolds
  • differential forms
  • flux
  • premetric electromagnetism
  • stress

ASJC Scopus subject areas

  • General Mathematics
  • General Engineering

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