On Cauchy's stress theorem

Miroslav Šilhavŷ

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (1990)

  • Volume: 1, Issue: 3, page 259-263
  • ISSN: 1120-6330

Abstract

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In this work a new proof of the theorem of Cauchy on the existence of the stress tensor is given which does not use the tetrahedron argument.

How to cite

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Šilhavŷ, Miroslav. "On Cauchy's stress theorem." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 1.3 (1990): 259-263. <http://eudml.org/doc/244201>.

@article{Šilhavŷ1990,
abstract = {In this work a new proof of the theorem of Cauchy on the existence of the stress tensor is given which does not use the tetrahedron argument.},
author = {Šilhavŷ, Miroslav},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Stress tensor; Continuous body; Balance equations; balance equations; contact forces in continuous body; explicit, coordinate-free formula for stress tensor in terms of surface tractions; existence of the stress tensor},
language = {eng},
month = {9},
number = {3},
pages = {259-263},
publisher = {Accademia Nazionale dei Lincei},
title = {On Cauchy's stress theorem},
url = {http://eudml.org/doc/244201},
volume = {1},
year = {1990},
}

TY - JOUR
AU - Šilhavŷ, Miroslav
TI - On Cauchy's stress theorem
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1990/9//
PB - Accademia Nazionale dei Lincei
VL - 1
IS - 3
SP - 259
EP - 263
AB - In this work a new proof of the theorem of Cauchy on the existence of the stress tensor is given which does not use the tetrahedron argument.
LA - eng
KW - Stress tensor; Continuous body; Balance equations; balance equations; contact forces in continuous body; explicit, coordinate-free formula for stress tensor in terms of surface tractions; existence of the stress tensor
UR - http://eudml.org/doc/244201
ER -

References

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  1. NOLL, W., The foundations of classical mechanics in the light of recent advances in continuum mechanics. In: P. SUPPES (ed.), The Axiomatic Method, with Special References to Geometry and Physics. North Holland, Amsterdam1959, 266-281. Zbl0087.39401MR108036
  2. GURTIN, M. E. - WILLIAMS, W. O., An axiomatic foundation for continuum thermodynamics. Arch. Rational Mech. Anal., 26, 1967, 83-117. Zbl0144.48302MR214335
  3. GURTIN, M. E. - MIZEL, V. J. - WILLIAMS, W. O., A note on Cauchy's stress theorem. J. Math. Anal. Appl., 22, 1968, 398-401. Zbl0179.53902MR225517
  4. GURTIN, M. E. - MARTINS, L. C., Cauchy's theorem in classical physics. Arch. Rational Mech. Anal., 60, 1976, 305-324. Zbl0347.73001MR408377
  5. SILHAVY, M., The existence of the flux vector and the divergence theorem for general Cauchy fluxes. Arch. Rational Mech. Anal., 90, 1985, 195-212. Zbl0593.73007MR803773DOI10.1007/BF00251730
  6. SILHAVY, M., The Cauchy stress theorem and tensor fields with divergences in L p . Forthcoming. Zbl0776.73003

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