Zeitschrift für angewandte Mathematik und Physik

, Volume 65, Issue 6, pp 1261–1288

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

Article

## Abstract

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.

### Mathematics Subject Classification (2000)

74K10 74B20 49K20

### Keywords

Coupling conditions Energy minimization Cosserat rod Hyperelastic material

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