SIM-AM 2023

Stretch and Stress Distributions in Arterial Wall with Residual Stress Based on Riemannian Stress-Free Configuration

  • Takamizawa, Keiichi (Private Researcher)

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It is well known that the arteries have residual stresses. The residual stresses are shown deformations of arterial parts by cut. The earlier studies noted the opening angle of the sliced ring by a radial cut. However, it has also been noted that the axial strips of the straight blood vessels curled. In the case of both of opened ring by a radial cut and curled axial strip sectioned from artery, the global stress-free configuration becomes a 3D non-Euclidean manifold, i.e., the Riemannian geometry should be used to describe the stress-free configuration of the straight tube of artery. An artery consists of three layers, i.e., intima, media, and adventitia. It is difficult to separate an intact wall into three layers in small animals although it is possible in large animals, especially in high aged human donors. Sommer et al. [1] have separated human arterial walls into two layers which are cylindrical tubes, i.e., adventitia and media-intima tubes. The author has analysed the human common carotid artery using the above kinematical theory and a strain energy function at the physiological pressures and the supraphysiological pressures (0-100 kPa) based on two-layer model with the data of Sommer et al. [1], and Sommer and Holzapfel [2]. The calculated results have shown that the stresses increase from the inner surface to the outer surface. This is opposite to the results without considering residual stresses. The mechanical loads are mainly supported by the adventitia at physiological and supraphysiological pressures. The flattest circumferential stress distribution in the adventitia has been obtained at the intraluminal pressure of 100 kPa in the present study. On the other hand, the magnitude of circumferential and axial stresses in the media-intima was low and the values were negative at the inner surface at all pressures calculated. REFERENCES [1] G. Sommer, P. Regitnig, L. Kӧltringer, G. A. Holzapfel, Biaxial mechanical properties of intact and layer dissected human carotid arteries at physiological and supraphysiological loadings. American Journal of Physiology Heart and Circulatory Physiology (2010) 298, H898-H912. [2] G. Sommer, G. A. Holzapfel, 3D constitutive modeling of the biaxial mechanical response of intact and layer-dissected human arteries. Journal of the Mechanical Behavior of Biomedical Materials (2012) 5, 116-128.