  Wrinkling of an inextensible elastic lining of an inner-lined tube under
imposed pressure is considered. A simple equation modeling the elastic
properties of the lining, the pressure, and the soft-substrate forces is
derived. This equation aims to capture the wrinkling response of arterial
endothelium to blood pressure changes. Numerical continuation is used to
construct a bifurcation diagram as a function of the imposed pressure for
in-plane deformations, in excellent agreement with weakly nonlinear theory,
which we also develop. Our approach explains how the wavelength and amplitude
of the wrinkles are selected as a function of the parameters in compressed
wrinkling systems and shows how localized folds and mixed-mode states form in
secondary bifurcations from wrinkled states.
