On the notion of the stress tensor associated with Rn-invariant constitutive laws admitting integral representations

Binz, Ernst

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URL: http://ub-madoc.bib.uni-mannheim.de/1967
URN: urn:nbn:de:bsz:180-madoc-19673
Document Type: Working paper
Year of publication: 1988
Publication language: English
Institution: School of Business Informatics and Mathematics > Sonstige - Fakultät für Mathematik und Informatik
MADOC publication series: Veröffentlichungen der Fakultät für Mathematik und Informatik > Institut für Mathematik > Mannheimer Manuskripte
Subject: 510 Mathematics
Classification: MSC: 58D10 ,
Subject headings (SWD): Einbettung <Mathematik> , Fréchet-Mannigfaltigkeit
Keywords (English): space of embeddings , smooth R-valued one forms , Fréchet manifold , smooth embeddings , integral representation
Abstract: By an Rn-invariant constitutive law F we mean a smooth Rn-invariant one form on the Fréchet manifold E(M,Rn) of all Euclidean smooth embeddings of a compact manifold M. Associated with it are a natural integrable Rn-valued one form and a natural two tensor, both embedding dependent, provided F is induced by a one form ~F on E(M,Rn)/Rn and ~F admits an integral representation. This two tensor plays the role of the stress tensor in elasticity theory.
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