Bending-torsion moments in thin multi-structures in the context of nonlinear elasticity

Here, we address a dimension-reduction problem in the context of nonlinear elasticity where the applied external surface forces induce bending-torsion moments. The underlying body is a multi-structure in ${\mathbb{R}}^3$ consisting of a thin tube-shaped domain placed upon a thin plate-shaped domain. The problem involves two small parameters, the radius of the cross-section of the tube-shaped domain and the thickness of the plate-shaped domain. We characterize the different limit models, including the limit junction condition, in the membrane-string regime according to the ratio between these two parameters as they converge to zero.