Stress theory for classical fields

Raz Kupferman, Elihu Olami, Reuven Segev*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

Classical field theories, together with the Lagrangian and Eulerian approaches to continuum mechanics, are embraced under a geometric setting of a fiber bundle. The base manifold can be either the body manifold of continuum mechanics, the space manifold, or space–time. Differentiable sections of the fiber bundle represent configurations of the system and the configuration space containing them is given the structure of an infinite-dimensional manifold. Elements of the cotangent bundle of the configuration space are interpreted as generalized forces and a representation theorem implies that there exists a stress object representing forces, non-uniquely. The properties of stresses are studied, as well as the role of constitutive relations in this general setting.

Original languageAmerican English
Pages (from-to)1472-1503
Number of pages32
JournalMathematics and Mechanics of Solids
Volume25
Issue number7
DOIs
StatePublished - 1 Jul 2020

Bibliographical note

Publisher Copyright:
© The Author(s) 2017.

Keywords

  • Continuum mechanics
  • configuration space
  • fiber bundle
  • field theories
  • stress

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