Pseudoelasticity of arteries and the choice of its mathematical expression

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Abstract
Arteries are not elastic bodies in the usual sense. But when subjected to cyclic loading and unloading, the stress-strain relationship is well defined after preconditioning. For the loading branch or the unloading branch, a pseudo strain energy function can be used to express the stress-strain relationship. The following expression is the most practical approximation for an artery subjected to internal pressure and longitudinal stretching within the physiologic range .**GRAPHIC**. where C, a1, a2, a4 are material constants and .**GRAPHIC**. are strains corresponding to a standard pair of stresses .**GRAPHIC**. Differentiation of .rho.oW(2) with respect to E.theta..theta. and EZZ yields the stresses S.theta..theta. and SZZ, respectively. The radial stress is ignored in comparison with S.theta..theta., SZZ. This formula is applied to the variation of the mechanical properties of rabbit arteries along the arterial tree.