Stress theory for classical fields

Raz Kupferman, Elihu Olami, Reuven Segev

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


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 languageEnglish
Pages (from-to)1472-1503
Number of pages32
JournalMathematics and Mechanics of Solids
Issue number7
StatePublished - 1 Jul 2020


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

ASJC Scopus subject areas

  • General Mathematics
  • General Materials Science
  • Mechanics of Materials


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