A bilinear stress–strain relationship for arteries

A comprehensive understanding of the mechanical properties of blood vessels is essential for vascular physiology, pathophysiology and tissue engineering. A well-known approach to study the elasticity of blood vessels is to postulate a strain energy function such as the exponential or polynomial forms. It is typically difficult to fit experimental data to derive material parameters for blood vessels, however, due to the highly nonlinear nature of the stress–strain relation. In this work, we generalize the strain definition to absorb the elastic nonlinearity and then propose a two-dimensional bilinear stress–strain relation between second Piola-Kirchhoff stress and the new strain measure. The model is found to represent the Fung's exponential model very well. The novel linearized constitutive relation simplifies the determination of material constants by reducing the nonlinearity and provides a clearer physical interpretation of the model parameters. The limitations of the constitutive model and its implications for vascular mechanics are discussed.