Three-part passive constitutive laws for the aorta in simple elongation

A variety of uniaxial constitutive laws have been proposed for the characterization of the aorta's nonlinear passive response, but a detailed comparison of them appears to be lacking. In this study, a systematic presentation of all available phenomenological formulations is undertaken and explicit formulae of constitutive laws are provided for simple elongation tests performed on healthy aortic strips. Common to all derived laws is the use of three analytical functions to approximate the low, physiologic, and high-stress parts of the aortic response, and the very close and essentially equally accurate fits that they give to the experimental data over the full range of stresses. Another feature of the three-part laws is their compatibility with the biphasic nature of the aortic tissue under passive conditions, allowing direct microstructural interpretation of their parameters. Importantly, although it is found that the aorta displays strain softening, i.e. its passive response is dependent on the highest previously experienced stress, the three-part character of the laws seems to be unaffected by the preconditioning procedure.