title: The mathematical formulation of a generalized Hooke's law for blood vessels.
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.
authors.affiliation: Department of Biomedical Engineering, IUPUI, Indianapolis, IN 46202, USA.
authors.forename: Wei
authors.initials: W
authors.lastname: Zhang
authors.forename: Chong
authors.initials: C
authors.lastname: Wang
authors.forename: Ghassan S
authors.initials: GS
authors.lastname: Kassab
mesh_terms: D000818:Animals; D001808:Blood Vessels; D008962:Models, Theoretical; D011817:Rabbits