Abstract2018-05-24T12:52:58+00:00

On the geometric character of stress in continuum mechanics

Author (s): Kanso E., Arroyo M., Tong Y., Yavari A., Marsden J.E. and Desbrun M
Journal: Zeitschrift für Angewandte Mathematik und Physik (ZAMP)

Volume: 58, Issue 5
Pages: 843 – 856
Date: 2007

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.

  
  

Bibtex:

@Article{Kanso2007,
author="Kanso, E.; Arroyo, M.; Tong, Y.; Yavari, A.; Marsden, J. G. and Desbrun, M.",
title="On the geometric character of stress in continuum mechanics",
journal="Zeitschrift f{\"u}r angewandte Mathematik und Physik",
year="2007",
volume="58",
number="5",
pages="843--856",
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.",
issn="1420-9039",
doi="10.1007/s00033-007-6141-8",
url="http://dx.doi.org/10.1007/s00033-007-6141-8"
}