  We present a hybrid Eulerian-Lagrangian method for the direct simulation of
three-dimensional, heterogeneous structures made of soft fibers and immersed in
incompressible viscous fluids. Fiber-based organization of matter is pervasive
in 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 or
energy harvesting, through mechanisms that are often not fully understood.
While simulations can support the analysis (and subsequent translational
engineering) of these systems, extreme fibers' aspect-ratios, large elastic
deformations and two-way coupling with three-dimensional flows, all render the
problem numerically challenging. To address this, we couple Cosserat rod
theory, which exploits fibers' slenderness to capture their dynamics in
one-dimensional, accurate fashion, with vortex methods via a penalty immersed
boundary technique. The favorable properties of the resultant hydroelastic
solver are demonstrated against a battery of benchmarks, and further showcased
in a range of multi-physics scenarios, involving magnetic actuation, viscous
streaming, biomechanics, multi-body interaction, and self-propulsion.
