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

Title data

Sander, Oliver ; Schiela, Anton:
Variational analysis of the coupling between a geometrically exact Cosserat rod and an elastic continuum.
In: Zeitschrift für angewandte Mathematik und Physik. Vol. 65 (2014) Issue 6 . - pp. 1261-1288.
ISSN 0044-2275
DOI: https://doi.org/10.1007/s00033-013-0389-y

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Official URL: Volltext

Project information

Project title:
Project's official titleProject's id
DFG Research Center Matheon "Mathematics for key technologies"FZT 86

Project financing: Deutsche Forschungsgemeinschaft

Abstract in another language

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.

Further data

Item Type: Article in a journal
Refereed: Yes
Additional notes: A preliminary version is published at the Preprint series of the Institute of Mathematics, Technische Universität Berlin, Preprint 32-2012.
Keywords: Coupling conditions; Energy minimization; Cosserat rod; Hyperelastic material
Subject classification: MSC classification: 74K10 (49K20 74B20)
Institutions of the University: Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics)
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Professorship Applied Mathematics (Applied Mathematics) > Professorship Applied Mathematics (Applied Mathematics) - Univ.-Prof. Dr. Anton Schiela
Profile Fields > Advanced Fields > Nonlinear Dynamics
Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Profile Fields
Profile Fields > Advanced Fields
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Professorship Applied Mathematics (Applied Mathematics)
Result of work at the UBT: No
DDC Subjects: 500 Science > 510 Mathematics
Date Deposited: 29 Jan 2015 07:05
Last Modified: 17 Aug 2017 08:28
URI: https://eref.uni-bayreuth.de/id/eprint/6016