A Two Dimensional Model of the Thin Laminar Wall of a Curvilinear Flexible Pipe

We present a two dimensional model describing the elastic behaviour of the wall of a curved pipe to model blood vessels in particular. The wall has a laminate structure consisting of several anisotropic layers of varying thickness and is assumed to be much smaller in thickness than the radius of the vessel which itself is allowed to vary. Our two-dimensional model takes the interaction of the wall with the surrounding material and the fluid flowing inside into account and is obtained via a dimension reduction procedure. The curvature and twist of the vessel axis as well as the anisotropy of the laminate wallpresent the main challenges in applying the dimension reduction procedure so plenty of examples of canonical shapes of vessels and their walls are supplied with explicit systems of dierential equations at the end