Elastic instability of cylindrical vessels immersed in fluid.

We develop a numerical model to study the deformation of growing neo-Hookean elastic cylindrical vessels immersed in an incompressible fluid. The vessel is treated as a two-dimensional shell embedded in a three-dimensional space and the fluid-structure interaction is described using the Immersed-Boundary formulation. In our simulation, the shell grows in a confined space, that is, its surface area increases over time while the vessel itself is restricted from lengthening due to the periodic boundary condition. To accommodate for the new surface area, the shell is under axial compression and must alter its original geometry; hence, it buckles. We recover the two well-known modes of buckling: bending and barreling. We also observed other buckling modes such as kinking, twisting, or lumen collapsing. As an outlook for our project, we will add flow to our model and study how buckling affects the fluid flow within the shell. To strike for a more realistic model of a biological vessel, we also consider using a different non-linear elastic model such as the exponential Fung model.