The Existance of a Symmetric Stress Tensor in a Non-Local Description of Continuum Mechanics

Schwarz, Günter

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URL:	https://ub-madoc.bib.uni-mannheim.de/1673
URN:	urn:nbn:de:bsz:180-madoc-16739
Document Type:	Working paper
Year of publication:	1991
The title of a journal, publication series:	None
Publication language:	English
Institution:	School of Business Informatics and Mathematics > Sonstige - Fakultät für Wirtschaftsinformatik und Wirtschaftsmathematik
MADOC publication series:	Veröffentlichungen der Fakultät für Mathematik und Informatik > Institut für Mathematik > Mannheimer Manuskripte
Subject:	510 Mathematics
Subject headings (SWD):	Hodge-Theorie , Riemannscher Raum
Abstract:	Among the foundations of continuum mechanics is the description of constitutive forces in terms of a symmetric tensor. Noll showed that this is a consequence of the axiom of material frame indifference [Nol,Tru], what in turn means a local invariance of the system under the Euklidean group. Here we will prove that the assumption of locality in this axiom is redundant to obtain the same result. We model a non-local system by means of a virtual work [AnOs,EpSe]. Under the global demand that this functional does not respond on rigid infintesimal motions, we show the existance of a symmetric stress tensor as a local result. As the mathematical tool for the localization we use the Hodge theory on manifolds with boundary.