  We address the fully-developed wrinkle pattern formed upon stretching a
Hookean, rectangular-shaped sheet, when the longitudinal tensile load induces
transverse compression that far exceeds the stability threshold of a purely
planar deformation. At this "far from threshold" parameter regime, which has
been the subject of the celebrated Cerda-Mahadevan (CM) model, the wrinkle
pattern expands throughout the length of the sheet and the characteristic
wavelength of undulations is much smaller than its width. Employing Surface
Evolver simulations over a range of sheet thicknesses and tensile loads we
elucidate the theoretical underpinnings of the far-from-threshold framework in
this set-up. We show that the evolution of wrinkles comes in tandem with
collapse of transverse compressive stress, rather than vanishing transverse
strain, such that the stress field approaches asymptotically a compression-free
limit, describable by tension field theory. We compute the compression-free
stress field by simulating a Hookean sheet that has finite stretching modulus
but no bending rigidity, and show that this singular limit encapsulates the
geometrical nonlinearity underlying the amplitude-wavelength ratio of wrinkle
patterns in physical, highly bendable sheets, even though the actual strains
may be so small that the local mechanics is perfectly Hookean. Finally, we
revisit the balance of bending and stretching energies that gives rise to a
favorable wrinkle wavelength, and study the consequent dependence of the
wavelength on the tensile load as well as the thickness and length of the
sheet.
