Simulace zbytkových napětí (přetvoření) v tepnách

Simulation of residual stresses (strains) in arteries

conference paper

en

Residual stresses and strains contribute substan-tially to stress-strain states in arteries. They manifest them-selves by opening of the artery after having been cut longitudi-nally and can be quantified by means of the opening angle of a ring cut out of the artery and cut longitudinally afterwards. The magnitude of the opening angle changes with species, age of the individual, artery location, etc. Although the magnitude of these stresses appears slight, they can influence the stress (and strain) distribution in the arterial wall substantially by reducing the extreme values throughout the wall. Their surpri-singly high influence on the resulting stresses is given by the non-linear stress-strain characteristics of vascular wall. When applied to the blood pressure, the uniform stress and uniform strain hypotheses have been formulated to explain this pheno-menon. The usual way of their modeling is based on using a model with the geometry of the opened arterial ring; the resi-dual stresses are then induced in the model by closing it into the original approximately circular shape. This method, how-ever, is not applicable for more complex non-symmetric ar-terial geometries, because the induced strains depend on local bending stiffness. Therefore another approach is used in the paper, based on introducing an interference between two lay-ers of aorta represented in the model. The method is demon-strated with a circular ring used typically in experimental assessment of residual strains and results of both methods are compared. In addition, the proposed interference method is numerically more stable, because of the two orders lower dis-placements, and it is able to induce constant strains through-out all the wall thickness by using more than two layers in the arterial wall model.

V příspěvku je prezentována nová metoda pro určování zbytkových napětí v tepnách pomocí MKP, založená na vyvolání zbytkových napětí v jednotlivých vrstvách předepsáním jejich přesahu. Výhodou oproti klasickému přístupu je lepší konvergence a použitelnost u nepravidelných geometrických tvarů, např. aneurysmat.

Residual stresses and strains contribute substan-tially to stress-strain states in arteries. They manifest them-selves by opening of the artery after having been cut longitudi-nally and can be quantified by means of the opening angle of a ring cut out of the artery and cut longitudinally afterwards. The magnitude of the opening angle changes with species, age of the individual, artery location, etc. Although the magnitude of these stresses appears slight, they can influence the stress (and strain) distribution in the arterial wall substantially by reducing the extreme values throughout the wall. Their surpri-singly high influence on the resulting stresses is given by the non-linear stress-strain characteristics of vascular wall. When applied to the blood pressure, the uniform stress and uniform strain hypotheses have been formulated to explain this pheno-menon. The usual way of their modeling is based on using a model with the geometry of the opened arterial ring; the resi-dual stresses are then induced in the model by closing it into the original approximately circular shape. This method, how-ever, is not applicable for more complex non-symmetric ar-terial geometries, because the induced strains depend on local bending stiffness. Therefore another approach is used in the paper, based on introducing an interference between two lay-ers of aorta represented in the model. The method is demon-strated with a circular ring used typically in experimental assessment of residual strains and results of both methods are compared. In addition, the proposed interference method is numerically more stable, because of the two orders lower dis-placements, and it is able to induce constant strains through-out all the wall thickness by using more than two layers in the arterial wall model.

Zbytková napětí, metoda přesahu, dvouvrstvý model, úhel rozevření

Residual stress, interference method, two-layer model, opening angle

2012

15.02.2012

Springer

Budapest

978-3-642-23507-8

IFMBE Proceedings, Volume 37

454–457

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