  A novel mathematical model for fiber-reinforced materials is proposed. It is
based on a 1-dimensional beam model for the thin fiber structures, a flexible
and general 3-dimensional elasticity model for the matrix and an overlapping
domain decomposition approach. From a computational point of view, this is
motivated by the fact that matrix and fibers can easily meshed independently.
Our main interest is in fiber reinforce polymers where the Young's modulus are
quite different. Thus the modeling error from the overlapping approach is of no
significance. The coupling conditions acknowledge both, the forces and the
moments of the beam model and transfer them to the background material. A
suitable static condensation procedure is applied to remove the beam balance
equations. The condensed system then forms our starting point for a numerical
approximation in terms of isogeometric analysis. The choice of our discrete
basis functions of higher regularity is motivated by the fact, that as a result
of the static condensation, we obtain second gradient terms in fiber direction.
Eventually, a series of benchmark tests demonstrate the flexibility and
robustness of the proposed methodology. As a proof-of-concept, we show that our
new model is able to capture bending, torsion and shear dominated situations.
