Stress analysis of blood vessels by a viscoplastic constitutive model based on the internal variable theory.

Abstract

Stress analysis of blood vessels is performed by means of a transversely isotropic viscoplastic constitutive model. This model is based on the concept that the hysteresis loops of stress-strain relationships under cyclic loading conditions are caused by loading path dependence and loading rate dependence. Then the method of analysis is discussed in detail on the basis of finite deformation theory for the case of axisymmetric deformation of a long circular cylindrical tube under the condition of constant axial stretch and repeated pressurization. Simulation results show that the model can describe the experimental results by Takamizawa et al. with a relatively high accuracy. The stress histories at some points in the wall and the stress distribution across the wall are also discussed with a special emphasis on the difference between viscoplastic and elastic predictions. The results show that the inelastic properties of blood vessels reduce the stress concentration at the inner wall.