  This article proposes a mortar type finite element formulation for
consistently embedding curved, slender beams, i.e. 1D Cosserat continua, into
3D solid volumes. A consistent 1D-3D coupling scheme for this problem type is
proposed, which enforces both positional and rotational constraints. Since
Boltzmann continua exhibit no inherent rotational degrees of freedom, suitable
definitions of orthonormal triads are investigated that are representative for
the orientation of material directions in the 3D solid. The rotation tensor
defined by the polar decomposition of the deformation gradient is demonstrated
to represent these material directions in a L2-optimal manner. Subsequently,
objective rotational coupling constraints between beam and solid are formulated
and enforced in a variationally consistent framework. Eventually, finite
element discretization of all primary fields results in an embedded mortar
formulation for rotational and translational constraint enforcement. Based on
carefully chosen numerical test cases, the proposed scheme is demonstrated to
exhibit a consistent spatial convergence behavior and to offer the up-scaling
potential for studying real-life engineering applications such as
fiber-reinforced composite materials.
