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
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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 mechanics elasticity stress tensor differential 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

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