  We study the behavior of thin elastic sheets that are bent and strained under
the influence of weak, smooth confinement. We show that the emerging shapes
exhibit the coexistence of two types of domains that differ in their
characteristic stress distributions and energies, and reflect different
constraints. A focused-stress patch is subject to a geometric,
piecewise-inextensibility constraint, whereas a diffuse-stress region is
characterized by a mechanical constraint - the dominance of a single component
of the stress tensor. We discuss the implications of our findings for the
analysis of elastic sheets that are subject to various types of forcing.
