A novel concept for embedding fibers into geometrically nonlinear membranes is introduced and builds on previous works in [1, 2, 3, 4]. The fibers are defined by the intersection of the level sets of a scalar function defined in three-dimensional space, and the surface of a curved, two-dimensional membrane. This approach results in continuously embedded, homogenized fibers as sub-structures in two-dimensional membranes which enables a new concept for advanced, anisotropic materials such as composites, textiles, and biological tissues. A mechanical model is proposed which considers the physics of the individual fibers, including the generalization to the fiber family in the whole bulk domain. This is based on former approaches for ropes, membranes, and shells [1, 2]. The new model results from coupling the bulk model for the fibers with the membrane model [1, 3, 4]. The membrane surface is discretized for the numerical analysis using classical, higher-order surface finite elements [4]. These elements do by no means align to the embedded fibers, and similar discretization schemes have been called Bulk Trace FEM in [1]. The accuracy of the proposed sub-structure model for anisotropic, hyperelastic membranes is demonstrated by various numerical examples, even enabling optimal, higher-order accurate results when smooth solutions are available. REFERENCES [1] Fries T.P., Kaiser M.W., On the Simultaneous Solution of Structural Membranes on all Level Sets within a Bulk Domain, Comp. Methods in Appl. Mech. Engrg., 415, 116223, 2023. [2] Kaiser M.W., Fries T.P., Simultaneous analysis of continuously embedded Reissner-Mindlin shells in 3D bulk domains, Internat. J. Numer. Methods Engrg., 125, e7495, 2024. [3] Fries T.P., Neumeyer J., Kaiser M.W., A new concept for embedding sub-structures via level-sets, Proceedings of the 16thWorld Congress on Computational Mechanics (WCCM 2024), Vancouver, Canada, 2024. [4] Fries T.P., Schöllhammer D., A unified finite strain theory for membranes and ropes, Comp. Methods in Appl. Mech. Engrg., 365, 113031, 2020.