One-Forms on Spaces of Embeddings : A Frame Work for Constitutive Laws in Elasticity

Binz, Ernst ; Fischer, Hans-Rudolf

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URN: urn:nbn:de:bsz:180-madoc-16687
Document Type: Working paper
Year of publication: 1990
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
Subject headings (SWD): Nichtlineare Funktionalanalysis , Elastizitätstheorie
Abstract: The contribution to this volume comes from non-linear functional analysis and is motivated by a traditional part of physics. More precisely, the motivation arises from elasticity theory : Given a body, thought of as a smooth compact manifold M', possibly with boundary, moving and deforming in IRn,the latter equipped with a fixed scalar product. The deformations shall be such that the diffeomorphism type does not change. Hence M' is the image under a smooth embedding of a smooth compact manifold M, possibly with boundary ∂M. Therefore the collection E(M,IRn) of all smooth embeddings of M into IRn is the collection of all the configuration under considerations. It is a Fréchet manifold if endowed with the C∞-topology.
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