Topological Defects in Twisted Bundles of Two-Dimensionally Ordered Filaments

Twisted assemblies of filaments in ropes, cables, and bundles are essential structural elements in both macroscopic materials and living organisms. We develop the unique, nonlinear elastic properties of twisted filament bundles that derive from generic properties of two-dimensional line-ordered materials. Continuum elasticity reveals a formal equivalence between the elastic stresses induced by bundle twist and those induced by the positive curvature in thin, elastic sheets. These geometrically induced stresses are screened by fivefold disclination defects in the lattice packing, and we predict a discrete spectrum of elastic-energy ground states associated with integer numbers of disclinations in cylindrical bundles. Finally, we show that elastic-energy ground states are extremely sensitive to the defect position in the cross section, with off-center disclinations driving the entire bundle to buckle and writhe.