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Description
A concept for the embedding of homogenized fibers into bulk materials is proposed and generalized from [1, 2, 3]. Each fiber family in the bulk material is implied by a set of two level-set functions: The intersecting level sets of these function pairs are the continuously embedded fiber geometries. A mechanical model for the simultaneous consideration of all fibers in a large displacement, hyper-elastic context is proposed. The fiber model is coupled to classical mechanical models of homogeneous and isotropic bulk materials. This enables a new concept for advanced, fibrous materials such as in biological tissues and textiles. For the numerical analysis, the bulk domain is meshed using classical, higher-order elements. It is noteworthy that these elements do by no means align to the embedded fibers which is characteristic for a fictious domain method (FDM). However, the present approach does not come with the usual challenges of FDMs and was called Bulk Trace FEM in [1]. Boundary conditions and numerical integration are done as in the classical FEM and there is no need for stabilization. Numerical results confirm the success of the proposed embedding of fibers in various contexts, even enabling optimal, higher-order accurate results when smooth solutions are expected.
REFERENCES
[1] T.P. Fries, M.W. Kaiser: On the Simultaneous Solution of Structural Membranes on all Level Sets within a Bulk Domain, Comp. Methods in Appl. Mech. Engrg., 415, 116223, 2023. DOI: 10.1016/j.cma.2023.116223
[2] M.W. Kaiser, T.P. Fries: Simultaneous analysis of continuously embedded Reissner-Mindlin shells in 3D bulk domains, Internat. J. Numer. Methods Engrg., 125, e7495, 2024. DOI: 10.1002/nme.7495
[3] T.P. Fries, J. Neumeyer, M.W. Kaiser: A new concept for embedding sub-structures via level-sets, Proceedings of the 16th World Congress on Computational Mechanics (WCCM 2024), Vancouver, Canada, 2024. DOI: 10.23967/wccm.2024.025
