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Journal of Elasticity
Erschienen in: Journal of Elasticity 1/2015

01.10.2015 | Classroom Note

Existence Theorem for Geometrically Nonlinear Cosserat Micropolar Model Under Uniform Convexity Requirements

verfasst von: Patrizio Neff, Mircea Bîrsan, Frank Osterbrink

Erschienen in: Journal of Elasticity | Ausgabe 1/2015

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Abstract

We reconsider the geometrically nonlinear Cosserat model for a uniformly convex elastic energy and write the equilibrium system as a minimization problem. Applying the direct methods of the calculus of variations we show the existence of minimizers. We present a clear proof based on the coercivity of the elastically stored energy density and on the weak lower semi-continuity of the total energy functional. Use is made of the dislocation density tensor \(\overline{\boldsymbol{K}}= \overline{\boldsymbol{R}}^{T}\operatorname{Curl}\overline{\boldsymbol{R}}\) as a suitable Cosserat curvature measure.
Vorheriger Artikel Spatial Behaviour in Thermoelastostatic Cylinders of Indefinitely Increasing Cross-Section

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Metadaten
Titel
Existence Theorem for Geometrically Nonlinear Cosserat Micropolar Model Under Uniform Convexity Requirements
verfasst von
Patrizio Neff
Mircea Bîrsan
Frank Osterbrink
Publikationsdatum
01.10.2015
Verlag
Springer Netherlands
Erschienen in
Journal of Elasticity / Ausgabe 1/2015
Print ISSN: 0374-3535
Elektronische ISSN: 1573-2681
DOI
https://doi.org/10.1007/s10659-015-9517-6

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