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Preprint 32-2012

Variational Analysis of the Coupling Between a Geometrically Exact Cosserat Rod and an Elastic Continuum

Source file is available as :   Portable Document Format (PDF)

Author(s) : Oliver Sander , Anton Schiela

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 32-2012

MSC 2000

74K10 Rods
74B20 Nonlinear elasticity

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.

Keywords : coupling conditions, energy minimization, Cosserat rod, hyperelastic material

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