On the geometric character of stress in continuum mechanics

Kanso, E., M. Arroyo, Y. Tong, A. Yavari, J. E. Marsden, and M. Desbrun

Z. Angew. Math. Phys., 58, (2007), 1-14

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.