Mullins effect in an aorta and limiting extensibility evolution

Cyclic uni-axial tensile tests with samples of human aorta were performed with an aim to obtain data describing the Mullins effect of arterial tissue. Due to presumed anisotropy of an aorta, reported widely, both samples oriented longitudinally and circumferentially were tested in each case. Every tested sample underwent cyclic tension limited to a certain value of a stretch four times, consecutively the limit of sustained deformation was increased and subsequent four cycles were performed. Significant stress softening of aortic tissue and residual strains were confirmed. An idealization was made in such a way that reloading and unloading curves are coincident. It was hypothesized that the stress softening observed within reloading of previously loaded tissue may be described by an evolution of material parameters. These parameters should be related to an alternation of internal structure. The model based on changes in limiting fiber extensibility of fibrillar component of the aortic wall, primarily represented by a collagen, was proposed. The arterial wall was assumed to be hyperelastic transversely isotropic material with different response under primary loading and unloading. A stored energy function was additively split into isotropic and anisotropic part. Preferred direction in continuum, defined in referential configuration, was assumed to be unchanged with cyclic loading. Every straining level in the cyclic test had its own value of fiber extensibility. Explicit form of the relation between evolving limiting extensibility of fibers and maximum previously sustained deformation was proposed in such a way that limiting extensibility under primary loading is considered as the limit. The isotropic matrix response was modeled using Neo-Hooke term with shear modulus values different under primary loading and reloading, however all reloading values were held the same. The predictions of the model described above were in good agreement with observations.