, Volume 58, Issue 5, pp 843-856
Date: 06 Jun 2007

On the geometric character of stress in continuum mechanics

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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.

Jerrold G. Marsden: Research partially supported by the California Institute of Technology and NSF-ITR Grant ACI-0204932.