On the irredundant part of the first Piola-Kirchhoff stress tensor

Binz, Ernst

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URL: https://ub-madoc.bib.uni-mannheim.de/1677
URN: urn:nbn:de:bsz:180-madoc-16770
Document Type: Working paper
Year of publication: 1992
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): Riemannscher Raum , Spannungstensor , Differentialgeometrie
Abstract: Let us assume a given medium moves and deforms in an ambient smooth and oriented Riemannian manifold N with metric (, ). This medium at hand is supposed to maintain the shape of a compact smooth orientable and connected manifold M with boundary. Clearly dim M ≤ dim N. By a configuration j of the medium we mean a smooth embedding of M into N. The configuration space is E(M, N), the collection of all smooth embeddings of M into N endowed with the C∞-topology. [...] The main purpose of this notes is to exhibit (in absence of exterior force densities) the irredundant part of a(j) that determines the force densities mentioned and the virtual work caused by any infinitesimal distortion at j.[...]
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