  Networks of flexible filaments often involve regions of tight contact.
Predictively understanding the equilibrium configurations of these systems is
challenging due to intricate couplings between topology, geometry, large
nonlinear deformations, and friction. Here, we perform an in-depth study of a
simple yet canonical problem that captures the essence of contact between
filaments. In the orthogonal clasp, two filaments are brought into contact,
with each centerline lying in one of a pair of orthogonal planes. Our data from
X-ray tomography (micro-CT) and mechanical testing experiments are in excellent
agreement with the finite element method (FEM) simulations. Despite the
apparent simplicity of the physical system, the data exhibits strikingly
unintuitive behavior, even when the contact is frictionless. Specifically, we
observe a curvilinear diamond-shaped ridge in the contact pressure field
between the two filaments, sometimes with an inner gap. When a relative
displacement is imposed between the filaments, friction is activated, and a
highly asymmetric pressure field develops. These findings contrast to the
classic capstan analysis of a single filament wrapped around a rigid body. Both
the micro-CT and the FEM data indicate that the cross-sections of the filaments
can deform significantly. Nonetheless, an idealized geometrical theory assuming
undeformable tube cross-sections and neglecting elasticity rationalizes our
observations qualitatively and highlights the central role of the small but
finite tube radius of the filaments. We believe that our orthogonal clasp
analysis provides a building block for future modeling efforts in frictional
contact mechanics of more complex filamentary structures.
