  Cohesive assemblies of filaments are a common structural motif found in
diverse contexts, ranging from biological materials such as fibrous proteins,
to artificial materials such as carbon nanotube ropes and micropatterned
filament arrays. In this paper, we analyze the complex dependence of cohesive
energy on twist, a key structural parameter of both self-assembled and
fabricated filament bundles. Based on the analysis of simulated ground states
of cohesive bundles, we show that the non-linear influence of twist derives
from two distinct geometric features of twisted bundles: (i) the geometrical
frustration of inter-filament packing in the bundle cross-section; and (ii) the
evolution of the surface geometry of bundles with twist, which dictates the
cohesive cost of non-contacting filaments at the surface. Packing frustration
in the bundle core gives rise to the appearance of a universal sequence of
topological defects, excess 5-fold disclinations, with increasing twist, while
the evolution of filament contact at the surface of the bundle generically
favors twisted geometries for sufficiently long filaments. Our analysis of both
continuum and discrete models of filament bundles shows that, even in the
absence of external torque or intrinsic chirality, cohesive energy universally
favors twisted ground states above a critical (length/radius) aspect ratio and
below a critical filament stiffness threshold.
