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Influence of atherosclerosis on anisotropy and incompressibility of the human thoracic aortic wall

Kozun Marta, Chwilkowska Agnieszka, Pezowicz Celina, Kobielarz Magdalena

Biocybernetics and Biomedical Engineering

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2021

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Vol. 41, no. 1

15--27

EN

In this study, we analysed the influence of atherosclerosis on the anisotropic and incompressible behaviour of the human thoracic aortic wall under mechanical loads. The mechanical tests involved preparations of the human thoracic aortic wall, which were evaluated based on the six-stage histological classification of atherosclerosis proposed by Stary. Anisotropy was evaluated on the basis of directional tests of mechanical properties, which were determined based on a uniaxial tensile test conducted in two directions, i.e. longitudinal and circumferential. The evaluation of incompressibility was carried out based on the product of the stretch ratios obtained in the x–y and y–z planes and on the basis of Poisson's ratio. The results presented in this study indicate that the blood vessel wall is an anisotropic material only in the case of normal vessels and in early atherosclerotic lesions. Atherosclerosis progression causes a gradual loss of the anisotropic character of the work of the thoracic aortic wall in moderate and very advanced stages of atherosclerosis under mechanical loads. The results show that the wall of the thoracic aorta is an incompressible material. Development of atherosclerosis does not cause a loss of incompressibility of the thoracic aorta. This study is the only one so far that presents changes in the mechanical properties at all stages of atherosclerotic development. A large number of preparations were included in the study, which is important for the results obtained due to the multi-factorial etiology of atherosclerosis development.

2

Volumetric locking suppression method for nearly incompressible nonlinear elastic multi-layer beams using ANCF elements

Orzechowski G., Frączek J.

Journal of Theoretical and Applied Mechanics

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2017

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Vol. 55 nr 3

977--990

EN

The analysis and solution of many modern flexible multibody dynamic problems require formulations that are able to effectively model bodies with nonlinear materials undergoing large displacements and deformations. The absolute nodal coordinate formulation (ANCF) in connection with a continuum-based approach is one way to deal with these systems. The main objective of this work is to extend an existent approach for the modelling of slender structures within the ANCF framework with nonlinear, nearly incompressible materials using the volumetric energy penalty technique. The main part of the study is devoted to the evaluation of multi-layer beam models and simplifications in the locking suppression method based on F-bar projection. The results present significantly better agreement with the reference solution for multi-layer structures built with the standard ANCF beam element as compared with the earlier implementation.

3

Experimental characterization of the mechanical properties of the abdominal aortic aneurysm wall under uniaxial tension

Kobielarz M., Jankowski L. J.

Journal of Theoretical and Applied Mechanics

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2013

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Vol. 51 nr 4

949--958

EN

Although many researchers have made the assumption that the abdominal aortic aneurysym (AAA) wall behaves as an incompressible and isotropic material, the experimental evidence for it is insufficient. Hence, the assumptions about the incompressibility and isotropy of the AAA wall were verified through analysis of stretch ratios of samples excised from the aneurysms walls. The stretch ratios were calculated on the basis of a real-time analysis of geometric dimensions of samples subjected to uniaxial tension. It was proved that the walls of abdominal aortic aneurysms can be modelled as an incompressible and isotropic material. Using histological techniques, the assumption concerning the negligence of shear stress in the analysis of AAA wall stresses was indirectly validated. The results were incorporated into a hyperelastic constitutive equation.

4

Incompressible limit for a magnetostrictive energy functional

Gambin B., Bielski W.

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2013

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Vol. 61, nr 4

1025--1030

EN

The modern materials undergoing large elastic deformations and exhibiting strong magnetostrictive effect are modelled here by free energy functionals for nonlinear and non-local magnetoelastic behaviour. The aim of this work is to prove a new theorem which claims that a sequence of free energy functionals of slightly compressible magnetostrictive materials with a non-local elastic behaviour, converges to an energy functional of a nearly incompressible magnetostrictive material. This convergence is referred to as a Γ -convergence. The non-locality is limited to non-local elastic behaviour which is modelled by a term containing the second gradient of deformation in the energy functional.

5

SPH computation of incompressible viscous flows

Pozorski J., Wawreńczuk A.

Journal of Theoretical and Applied Mechanics

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2002

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Vol. 40 nr 4

917-937

EN

The paper is concerned with the numerical flow computation using the method of Smoothed Particle Hydrodynamics (SPH). Fundamental concepts of the method are briefly recalled. Physical aspects of the incompressibility and its mathematical formulation are described. A new proposal for the incompressibility constraint is put forward in the SPH context. Numerical implementation of the method is described and main parts of the algorithm are presented, including the issue of boundary conditions. Some validation cases and examples of results for viscous flows are presented.

PL

Praca dotyczy numerycznych obliczeń przepływów z wykorzystaniem metody cząstek rozmytych (ang. SPH - Smoothed Particle Hydrodynamics). Przypomniano pokrótce podstawy metody, a także fizyczne i matematyczne aspekty nieściśliwości. Przedstawiono nową propzycję spełnienia warunku nieściśliwości w podejściu SPH. Opisano numeryczną implementację metody i podstawowe elementy algorytmu, w tym sposób stawiania warunków brzegowych. przedstawiono wyniki testów metody oraz przykłady obliczeń przepływów lepkich.