Three-Dimensional Steady Flow in Non-Linear Elastic Collapsible Tubes

Abstract

Three-dimensional fluid-structure interaction problem arising from steady flow in non-linear elastic tube is studied numerically by using a finite element software, ADINA. Strain-energy density function is used for non-linear elastic analysis of solid material. Navier-Stokes equation coupled with elastic wall condition is solved for the fluid flow. To simulate interactions between the fluid and the solid domains, arbitrary Lagrangian-Eulerian (ALE) formulation is utilized. For validation, thin-walled linear elastic collapsible tubes is computed and compared with previous numerical results. The tube collapses into the buckling mode N = 2 and the results are in excellent agreement with a previous study. Then, the results for linear elastic tube are compared with those for non-linear elastic tube to show the effects of non-linear elasticity of the wall. The wall material is considered to be non-linear hyperelastic and isotropic. The non-linear elastic wall shows the tendency to preserve its shape more than the linear material. The deformation patterns, pressure distributions of the tube with non-linear elastic material are significantly different from those with linear elastic material.