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

Paper ID Volume ID Publish Year Pages File Format Full-Text
10640 695 2007 10 PDF Available
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.

Keywords
Hooke's law; Constitutive relation; Strain measure; Nonlinearity
First Page Preview
The mathematical formulation of a generalized Hooke's law for blood vessels
Publisher
Database: Elsevier - ScienceDirect
Journal: Biomaterials - Volume 28, Issue 24, August 2007, Pages 3569–3578
Authors
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Subjects
Physical Sciences and Engineering Chemical Engineering Bioengineering