Mechanical Response of a Metallic Aortic Stent—Part II: A Beam-on-Elastic Foundation Model

The main objective of the paper is to develop the mathematical analysis of the response of a metallic stent subject to axisymmetric loads over its length and to different boundary conditions. These situations introduce bending stresses in the stent and cannot be captured by a model of the stent that can be used to characterize the pressure-diameter relationship under axially uniform loading. The analysis presented here is based on an analogy between a thin-walled pressure vessel and a beam on elastic foundation; in the present application, we derive an equivalent beam model for the bending response of a stent. Using this model, we evaluate the shape of the stent exiting the catheter as well as the variation of the diameter along the length of the stent constrained by stiff end supports. This approach can be used to evaluate the coupled response of the stent and the blood vessel, if the mechanical properties of the blood vessel are known. The coupled problem and its implications in the design of stents are discussed.