The present article proposes a novel computational method for coupling arbitrarily curved 1D fibers with a 2D surface as defined, e.g., by the 2D surfaces of a 3D solid body or by 2D shell formulations. The fibers are modeled as 1D Cosserat continua (beams) with six local degrees of freedom, three positional and three rotational ones. A kinematically consistent 1D-2D coupling scheme for this problem type is proposed considering the positional and rotational degrees of freedom along the beams. The positional degrees of freedom are coupled by enforcing a constant normal distance between a point on the beam centerline and a corresponding point on the surface. This strategy requires a consistent description of the surface normal vector field to guarantee fundamental mechanical properties such as conservation of angular momentum. Coupling of the rotational degrees of freedom of the beams and a suitable rotation tensor representing the local orientation within a solid volume has been considered in a previous contribution. In the present work, this coupling approach will be extended by constructing rotation tensors that are representative of local surface orientations. Several numerical examples demonstrate the consistency, robustness and accuracy of the proposed method. To showcase its applicability to multi-physics systems of practical relevance, the fluid-structure interaction example of a vascular stent is presented.

翻译：本文提出了一种新颖的计算方法，用于将任意弯曲的一维纤维与二维曲面进行耦合，例如由三维实体边界曲面或二维壳单元定义的曲面。纤维被建模为具有六个局部自由度（三个位置自由度和三个旋转自由度）的一维Cosserat连续体（梁）。针对此类问题，本文提出了一种考虑梁上位置与旋转自由度的运动学一致性一维-二维耦合方案。位置自由度的耦合通过强制梁中心线上点与曲面上对应点之间保持恒定法向距离来实现。该策略要求对曲面法向量场进行一致性描述，以保证角动量守恒等基本力学特性。梁的旋转自由度与代表实体内部局部方向的旋转张量之间的耦合已在先前研究中得到探讨。本工作将通过构建代表曲面局部方向的旋转张量来扩展该耦合方法。多个数值算例验证了所提方法的一致性、鲁棒性与精确性。为展示其在具有实际意义的多物理场系统中的应用，本文展示了血管支架流固耦合的数值实例。