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We present a hybrid Eulerian-Lagrangian method for the direct simulation ofthree-dimensional, heterogeneous structures made of soft fibers and immersed inincompressible viscous fluids. Fiber-based organization of matter is pervasivein nature and engineering, from biological architectures made of cilia, hair,muscles or bones to polymers, composite materials or soft robots. In nature,many such structures are adapted to manipulate flows for feeding, locomotion orenergy harvesting, through mechanisms that are often not fully understood.While simulations can support the analysis (and subsequent translationalengineering) of these systems, extreme fibers' aspect-ratios, large elasticdeformations and two-way coupling with three-dimensional flows, all render theproblem numerically challenging. To address this, we couple Cosserat rodtheory, which exploits fibers' slenderness to capture their dynamics inone-dimensional, accurate fashion, with vortex methods via a penalty immersedboundary technique. The favorable properties of the resultant hydroelasticsolver are demonstrated against a battery of benchmarks, and further showcasedin a range of multi-physics scenarios, involving magnetic actuation, viscousstreaming, biomechanics, multi-body interaction, and self-propulsion.

Soft, slender and active structures in fluids: embedding Cosserat rods in vortex methods