Article

Zeitschrift für angewandte Mathematik und Physik

, Volume 58, Issue 5, pp 843-856

First online:

On the geometric character of stress in continuum mechanics

  • Eva KansoAffiliated withUniversity of Southern California
  • , Marino ArroyoAffiliated withUniversitat Politècnica de Catalunya
  • , Yiying TongAffiliated withCalifornia Institute of Technology
  • , Arash YavariAffiliated withGeorgia Institute of Technology
  • , Jerrold G. MarsdenAffiliated withCalifornia Institute of Technology
  • , Mathieu DesbrunAffiliated withCalifornia Institute of Technology

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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