4. Discussion / conclusion The current study was aimed at having a new experimental glance on the question of residual stresses in arteries. Only a few experiments have been carried out so far and no quantitative conclusion can be drawn for the moment, the experimental approach needing to be further validated. However, the new protocol proposed in this study, based on imaging and finite element analyses, has revealed important subjects of discussion that could be investigated in the future regarding residual stresses in arteries. More especially, the distribution of residual stresses through the thickness of an artery is not necessarily linear, even if the distribution of residual strains in the circumferential direction is linear (for instance in an open angle experiment). Two points that are generally not considered in the literature and may affect the distribution of residual stresses through the thickness of arteries are: 1. the constitutive behavior may be different in medial and adventitial layers, even at low strain. The rationale supporting this assumption relies on the nature of the composition of these layers [1]. The adventitia comprises mainly collagen fibers which are loose at the no-pressure state, whereas the media includes elastin sheets, smooth muscle cells and other components which provide an elastic stiffness even at low pressures. For this reason, different constitutive parameters may be affected to each of these layers, the adventitia being softer [9]. 2. Axial strain is never considered in opening angle experiments (plane strain is generally assumed i.e. the axial stretch remains constant during an opening angle experiment [1]). We show here first that the axial strain is not zero when the residual stresses are released and second that it strongly affects the circumferential stress response by Poisson effect (due to the quasi-incompressibility of the medium). Investigating these two points will require the development of a new theoretical background which is out of scope of this paper. It will also require applying the imaging and finite element approach developed in this study on a large number of specimens to generate sufficient database. To this aim, a certain number of points regarding tissue handling will be improved for rendering the approach more robust, in particular controlling better the fixing action of needles and also the foam influence that may induce some internal pressure and induce an offset on the residual stresses. Regarding the finite element model, it is envisaged to include more realistic constitutive equations based on local indentation tests for deriving the residual stresses in future experiments. 5. References [1] Humphrey JD. Cardiovascular Solid Mechanics: Cells, Tissues, and Organs, Springer, 2002. radial location. Figure 6. Cauchy stress (with a shift of -4 kPa corresponding to the action of the foam) distribution as a function of the 39
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