Variational analysis of the coupling between a geometrically exact Cosserat rod and an elastic continuum

We formulate the static mechanical coupling of a geometrically exact Cosserat rod to a nonlinearly elastic continuum. In this setting, appropriate coupling conditions have to connect a one-dimensional model with director variables to a three-dimensional model without directors. Two alternative coupl...

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Published inZeitschrift für angewandte Mathematik und Physik Vol. 65; no. 6; pp. 1261 - 1288
Main Authors Sander, Oliver, Schiela, Anton
Format Journal Article
LanguageEnglish
Published Basel Springer Basel 01.12.2014
Subjects
Calculus of variations
Continuums
Engineering
Joining
Mathematical analysis
Mathematical Methods in Physics
Mathematical models
Optimization
Theoretical and Applied Mechanics
Three dimensional models
74K10
49K20
Hyperelastic material
Cosserat rod
Energy minimization
74B20
Coupling conditions
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ISSN0044-2275
1420-9039
DOI10.1007/s00033-013-0389-y

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Summary:We formulate the static mechanical coupling of a geometrically exact Cosserat rod to a nonlinearly elastic continuum. In this setting, appropriate coupling conditions have to connect a one-dimensional model with director variables to a three-dimensional model without directors. Two alternative coupling conditions are proposed, which correspond to two different configuration trace spaces. For both, we show existence of solutions of the coupled problems, using the direct method of the calculus of variations. From the first-order optimality conditions, we also derive the corresponding conditions for the dual variables. These are then interpreted in mechanical terms.
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ISSN:0044-2275
1420-9039
DOI:10.1007/s00033-013-0389-y