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

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