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ARTICLE
On the Onset of Cracks in Arteries1
P. Mythravaruni, K.Y. Volokh*
Faculty of Civil and Environmental Engineering, Technion - IIT, Haifa, 3200003, Israel
* Corresponding Author: K.Y. Volokh. Email:
Molecular & Cellular Biomechanics 2020, 17(1), 1-17. https://doi.org/10.32604/mcb.2019.07606
Abstract
We present a theoretical approach to study the onset of failure localization into cracks in arterial wall. The arterial wall is a soft composite comprising
hydrated ground matrix of proteoglycans reinforced by spatially dispersed elastin
and collagen fibers. As any material, the arterial tissue cannot accumulate and dissipate strain energy beyond a critical value. This critical value is enforced in the
constitutive theory via energy limiters. The limiters automatically bound reachable
stresses and allow examining the mathematical condition of strong ellipticity. Loss
of the strong ellipticity physically means inability of material to propagate superimposed waves. The waves cannot propagate because material failure localizes into
cracks perpendicular to a possible wave direction. Thus, not only the onset of a
crack can be analyzed but also its direction. We use the recently developed constitutive theories of the arterial wall including 8 and 16 structure tensors to account for
the fiber dispersion. We enhance these theories with energy limiters. We examine
the loss of strong ellipticity in uniaxial tension and pure shear in circumferential
and axial directions of the arterial wall. We find that the vanishing longitudinal
wave speed predicts the appearance of cracks in the direction perpendicular to tension. We also find that the vanishing transverse wave speed predicts the appearance
of cracks in the the direction inclined (non-perpendicular) to tension. The latter
result is counter-intuitive yet it is supported by recent experimental observations.
Keywords
Cite This Article
Mythravaruni,, P. (2020). On the Onset of Cracks in Arteries
1.
Molecular & Cellular Biomechanics, 17(1), 1–17.