  Many biological materials such as cervical mucus and collagen gel possess a
fibrous micro-structure. This micro-structure affects the emergent mechanical
properties of the material, and hence the functional behaviour of the system.
We consider the canonical problem of stretching a thin sheet of
transversely-isotropic viscous fluid as a simplified version of the
spinnbarkeit test for cervical mucus. We propose a novel solution to the model
constructed by Green & Friedman by manipulating the model to a form amenable to
arbitrary Lagrangian-Eulerian techniques. The system of equations, reduced by
exploiting the slender nature of the sheet, are solved numerically and we
discover that the bulk properties of the sheet are controlled by an effective
viscosity dependent on the evolving angle of the fibres. In addition, we
confirm a previous conjecture by demonstrating that the centre-line of the
sheet need not be flat, and perform a short timescale analysis to capture the
full behaviour of the centre-line.
