  An elastic bilayer, consisting of an equibiaxially pre-stretched sheet bonded
to a stress-free one, spontaneously morphs into curved shapes in the absence of
external loads or constraints. Using experiments and numerical simulations, we
explore the role of geometry for square and rectangular samples in determining
the equilibrium shape of the system, for a fixed pre-stretch. We classify the
observed shapes over a wide range of aspect ratios according to their
curvatures and compare measured and computed values, which show good agreement.
In particular, as the bilayer becomes thinner, a bifurcation of the principal
curvatures occurs, which separates two scaling regimes for the energy of the
system. We characterize the transition between these two regimes and show the
peculiar features that distinguish square from rectangular samples. The results
for our model bilayer system may help explaining morphing in more complex
systems made of active materials.
