Multidimensional coupling: A variationally consistent approach to fiber-reinforced materials

A novel coupling algorithm for the coupling of 1-dimensional fibers considered as beam models to the surrounding 3-dimensional matrix material is presented. An overlapping domain decomposition is used to embed the fibers within the matrix material. 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 in the continuum setting and afterwards in the coupling constraints in the discrete setting, reducing drastically the computational cost. Eventually, a series of benchmark tests demonstrate the flexibility and robustness of the proposed methodology.