Sander, OliverOliverSanderSchiela, AntonAntonSchiela2020-08-142020-08-142013-12-19Zeitschrift fur Angewandte Mathematik und Physik 6 (65): 1261-1288 (2013)http://hdl.handle.net/11420/7049© 2013, Springer Basel. 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.en1420-90392013612611288Springer International Publishing AGMathematikJournal Article10.1007/s00033-013-0389-yOther