  This paper presents an experimental investigation on pattern formation and
evolution in bilayered tubular organs using swelling deformation of
polydimethylsiloxane (PDMS) and aims at supplying a thorough comparison with
theoretical and finite element results. To create a twin model in modelling and
simulation, the shear modulus in the incompressible neo-Hookean material is
estimated via uni-axial tensile and pure shear tests. Five bilayered tubes with
different material or geometrical parameters are fabricated. Swelling
experiments are carried out for these samples in an individual experimental
setup where a plane-strain deformation is guaranteed, and several surface
patterns and the associated mode transformations are observed, namely, creases,
wrinkles, period-doubling profiles, wrinkle-to-crease transition, and
wrinkle-to-period-doubling transition. In particular, an interfacial wrinkling
pattern is also observed. To make comparisons, a buckling analysis is conducted
within the framework of finite elasticity by means of the Stroh formulation. In
addition, a finite element analysis is performed to trace the evolution of
surface instabilities. It turns out that the experimental findings agree well
with the theoretical predictions as well as the finite element results. From
our experiments, it is found that creasing mode may appear instead of wrinkling
mode when both layers share a similar mechanical property. It is expected that
the current work could provide novel experimental insight into pattern
formation in tubular structures, and the good agreement among experimental,
theoretical, and simulation consequences supplies strong evidence that a
phenomenological growth model is satisfactory to reveal mechanisms behind
intricate surface morphology in tubular tissues.
