  An important class of fluid-structure problems involve the dynamics of
ordered arrays of immersed, flexible fibers. While specialized numerical
methods have been developed to study fluid-fiber systems, they become
infeasible when there are many, rather than a few, fibers present, nor do these
methods lend themselves to analytical calculation. Here, we introduce a
coarse-grained continuum model, based on local-slender body theory, for elastic
fibers immersed in a viscous Newtonian fluid. It takes the form of an
anisotropic Brinkman equation whose skeletal drag is coupled to elastic forces.
This model has two significant benefits: (1) the density effects of the fibers
in a suspension become analytically manifest, and (2) it allows for the rapid
simulation of dense suspensions of fibers in regimes inaccessible to standard
methods. As a first validation, without fitting parameters, we achieve very
reasonable agreement with 3D Immersed Boundary simulations of a bed of anchored
fibers bent by a shear flow. Secondly, we characterize the effect of density on
the relaxation time of fiber beds under oscillatory shear, and find close
agreement to results from full numerical simulations. We then study buckling
instabilities in beds of fibers, using our model both numerically and
analytically to understand the role of fiber density and the structure of
buckling transitions. We next apply our model to study the flow-induced bending
of inclined fibers in a channel, as has been recently studied as a flow
rectifier, examining the nature of the internal flows within the bed, and the
emergence of inhomogeneous permeability. Finally, we extend the method to study
a simple model of metachronal waves on beds of actuated fibers, as a model for
ciliary beds. Our simulations reproduce qualitatively the pumping action of
coordinated waves of compression through the bed.
