  We investigate the stability of the deformation modeled by the opening angle
method, often used to give a measure of residual stresses in arteries and other
biological soft tubular structures. Specifically, we study the influence of
stiffness contrast, dimensions and inner pressure on the onset of wrinkles when
an open sector of a soft tube, coated with a stiffer film, is bent into a full
cylinder. The tube and its coating are made of isotropic, incompressible,
hyperelastic materials. We provide a full analytical exposition of the
governing equations and the associated boundary value problem for the large
deformation and for the superimposed small-amplitude wrinkles. For
illustration, we solve them numerically with a robust algorithm in the case of
Mooney-Rivlin materials. We confront the results to experimental data that we
collected for soft silicone sectors. We study the influence of axial stretch
and inner pressure on the stability of closed-up coated tubes with material
parameters comparable with those of soft biological tubes such as arteries and
veins, although we do not account for anisotropy. We find that the large
deformation described in the opening angle method does not always exist, as it
can become unstable for certain combinations of dimensions and material
parameters.
