The three-dimensional shapes of thin lamina, such
as leaves, flowers, feathers, wings, etc., are driven
by the differential strain induced by the relative
growth. The growth takes place through variations
in the Riemannian metric given on the thin sheet as
a function of location in the central plane and also
across its thickness. The shape is then a consequence
of elastic energy minimization on the frustrated
geometrical object. Here, we provide a rigorous
derivation of the asymptotic theories for shapes
of residually strained thin lamina with non-trivial
curvatures, i.e. growing elastic shells in both the
weakly and strongly curved regimes, generalizing
earlier results for the growth of nominally flat plates.
The different theories are distinguished by the scaling
of the mid-surface curvature relative to the inverse
thickness and growth strain, and also allow us to
generalize the classical Föppl–von Kármán energy to
theories of prestrained shallow shells.