  The wrinkle pattern exhibited upon stretching a rectangular sheet has
attracted considerable interest in the "extreme mechanics" community.
Nevertheless, key aspects of this notable phenomenon remain elusive.
Specifically -- what is the origin of the compressive stress underlying the
instability of the planar state? what is the nature of the ensuing bifurcation?
how does the shape evolve from a critical, near-threshold regime to a
fully-developed pattern of parallel wrinkles that permeate most of the sheet?
In this paper we address some of these questions through numerical simulations
and analytic study of the planar state in Hooekan sheets. We show that
transverse compression is a boundary effect, which originates from the relative
extension of the clamped edges with respect to the transversely-contracted,
compression-free bulk of the sheet, and draw analogy between this edge-induced
compression and Moffatt vortices in viscous, cavity-driven flow. Next we
address the instability of the planar state and show that it gives rise to a
buckling pattern, localized near the clamped edges, which evolves -- upon
increasing the tensile load -- to wrinkles that invade the uncompressed portion
of the sheet. Crucially, we show that the key aspects of the process -- from
the formation of transversely-compressed zones, to the consequent instability
of the planar state and the emergence of a wrinkle pattern -- can be understood
within a Hookean framework, where the only origin of nonlinear response is
geometric, rather than a non-Hookean stress-strain relation.
