The mathematical formulation of a generalized Hooke's law for blood vessels

Biomaterials. 2007 Aug;28(24):3569-78. doi: 10.1016/j.biomaterials.2007.04.030. Epub 2007 May 3.

Abstract

It is well known that the stress-strain relationship of blood vessels is highly nonlinear. To linearize the relationship, the Hencky strain tensor is generalized to a logarithmic-exponential (log-exp) strain tensor to absorb the nonlinearity. A quadratic nominal strain potential is proposed to derive the second Piola-Kirchhoff stresses by differentiating the potential with respect to the log-exp strains. The resulting constitutive equation is a generalized Hooke's law. Ten material constants are needed for the three-dimensional orthotropic model. The nondimensional constant used in the log-exp strain definition is interpreted as a nonlinearity parameter. The other nine constants are the elastic moduli with respect to the log-exp strains. In this paper, the proposed linear stress-strain relation is shown to represent the pseudoelastic Fung model very well.

Publication types

  • Research Support, N.I.H., Extramural

MeSH terms

  • Animals
  • Blood Vessels*
  • Models, Theoretical*
  • Rabbits