The Euklidian group in global modells of continuum mechanics and the existence of a symmetric stress tensor

Schwarz, Günter

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URN: urn:nbn:de:bsz:180-madoc-19972
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): Raumgruppe , Spannungstensor , Hodge-Theorie
Abstract: One of the foundations of continuum mechanies is the description of forces in terms of a symmetric tensor. The fundamental observation that the existence of a symmetric stress tensor is a consequence of the material frame indifference is due to Noll (No63,Tr]. This in turn means a local symmetry of the system under the action of the Euklidean group. In this paper we will show that the assumption of locality in the axiom of frame indifference is not necessary for a wide class of modells. We will prove the existence of a symmetric stress tensor, demanding only the invariance of the system under global rigid infintesimal Eukledian group action. The localization of that global symmetry will be done by means of Hodge theory on manifolds with boundary.
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