Bundle architecture of twisted elastic filaments with migration

We will discuss an investigation of the assembly of filaments bundles starting from linear elements which are located uniformly in a circle and then brought together to form a tight bundle with twist. Using x-ray tomography, we examine the bundle cross sections and show that the filaments come together in a tight circle initially before a radial instability occurs as the hoop stress builds up. This instability leads to an order-disorder packing transition of the filaments in the bundle for sufficiently large number of filaments in contrast with twisted bundle architecture starting with a stack of hexagonal-closed-packed filaments. Our measurements further show filament migration during the twisting process which is known to be important to the structural mechanics of yarns and fabrics. Nonetheless, we find that the inclination of the filaments in the resulting architecture can be described by an angle which depends on the distance from the axis of rotation and average twist angle imposed per unit bundle length. We use these findings to develop an elasto-geometric model of the energy stored in the system as a function of applied loading. The contributions of stretching, bending, twist, and contact to the total energy and torque required to twist the bundle will be discussed.