Zeitschrift für angewandte Mathematik und Physik

, Volume 58, Issue 5, pp 843–856

On the geometric character of stress in continuum mechanics

  • Eva Kanso
  • Marino Arroyo
  • Yiying Tong
  • Arash Yavari
  • Jerrold G. Marsden
  • Mathieu Desbrun
Article

DOI: 10.1007/s00033-007-6141-8

Cite this article as:
Kanso, E., Arroyo, M., Tong, Y. et al. Z. angew. Math. Phys. (2007) 58: 843. doi:10.1007/s00033-007-6141-8

Abstract.

This paper shows that the stress field in the classical theory of continuum mechanics may be taken to be a covector-valued differential two-form. The balance laws and other fundamental laws of continuum mechanics may be neatly rewritten in terms of this geometric stress. A geometrically attractive and covariant derivation of the balance laws from the principle of energy balance in terms of this stress is presented.

Keywords.

Continuum mechanicselasticitystress tensordifferential forms

Copyright information

© Birkhäuser Verlag, Basel 2007

Authors and Affiliations

  • Eva Kanso
    • 1
  • Marino Arroyo
    • 2
  • Yiying Tong
    • 3
  • Arash Yavari
    • 4
  • Jerrold G. Marsden
    • 3
  • Mathieu Desbrun
    • 3
  1. 1.University of Southern CaliforniaLos AngelesUSA
  2. 2.Universitat Politècnica de CatalunyaBarcelonaSpain
  3. 3.California Institute of TechnologyPasadenaUSA
  4. 4.Georgia Institute of TechnologyAtlantaUSA