## 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

Review: |

## Related URLs

## Project information

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