  Cilia are motile biological appendages that are driven to bend by internal
shear stresses between tubulin filaments. A continuum model of ciliary material
is constructed that incorporates the essential ciliary constraints: (1)
one-dimensional inextensibility of filaments, (2) three-dimensional
incompressibility, and (3) shear strain only along filaments. This hypothetical
ciliary material combines one- and three-dimensional properties in a way that
makes it a natural and flexible model for how real cilia convert nanoscopic
shear stress into motility on a much larger scale. Without reference to the
evolving shape of the cilium, conventional continuum mechanics applied to this
hypothetical material leads to the standard model of ciliary dynamics, but with
one additional term, required by constraints (2) and (3) above, a
model-independent coupling of shear and twist in general ciliary motion.
