A quasi-linear constitutive relation for arterial wall materials

Demiray, Hilmi

doi:10.1016/0021-9290(96)00004-8

Cited by 10 publications

(5 citation statements)

References 9 publications

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“…Here the explicit expressions of the coefficients β i (i = 1, 2, ... 19) and other details of the derivation are given in reference [19], for the constitutive relation proposed by Demiray [20] for soft biological tissues. Noting the relation between r f and r 0 , i.e., r f = r 0 + u * , the equation (4) can be written as follows:…”

Section: Equations Of Tubementioning

confidence: 99%

“…As is seen from the dispersion relation (20), the wave is dispersive and dissipative. The dissipative character of the wave is affected by viscosity of fluid and viscoelastic properties of the tube.…”

Section: Longwave Approximationmentioning

confidence: 99%

“…Thus, in order to have a real wave for longwave limit, the order of the viscosity should be less than or equal to k 2 , i.e., ν = O(k 2 ). The form of dispersion relation (20) suggests us to introduce the following coordinate stretching…”

Section: Longwave Approximationmentioning

confidence: 99%

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Nonlinear waves in a viscous fluid contained in a viscoelastic tube

Demiray

2001

Z. angew. Math. Phys.

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In the present work the propagation of weakly nonlinear waves in a prestressed viscoelastic thin tube filled with a viscous fluid is studied. Using the reductive perturbation technique in analyzing the nonlinear equations of a viscoelastic tube and the approximate equations of a viscous fluid, the propagation of weakly nonlinear waves in the longwave approximation is studied. Depending on the order of viscous effects, various evolution equations like, Burgers', Korteweg-de Vries, Korteweg-de Vries-Burgers' equations and their perturbed forms are obtained. Travelling wave type of solutions to some of these evolution equations are sought. Finally, utilizing the finite difference scheme, a numerical solution is presentede for the perturbed KdVB equation and the result is discussed.

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Section: Equations Of Tubementioning

confidence: 99%

Section: Longwave Approximationmentioning

confidence: 99%

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Nonlinear waves in a viscous fluid contained in a viscoelastic tube

Demiray

2001

Z. angew. Math. Phys.

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“…In order to complete the fluid equations one must know the constitutive relation for tube material. In the present work we shall adopt the following type of constitutive relation proposed by Demiray [16] for soft biological tissues…”

Section: Nonlinear Waves In An Inviscid Fluid 329mentioning

confidence: 99%

Nonlinear waves in an inviscid fluid contained in a prestressed viscoelastic thin tube

Demiray¹,

Antar²

1997

Z. angew. Math. Phys.

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In the present work, we examine the propagation of weakly nonlinear waves in a prestressed thin viscoelastic tube filled with an incompressible inviscid fluid. Considering that the arteries are initially subjected to a large static transmural pressure P 0 and an axial stretch λz and, in the course of blood flow, a finite time dependent displacement is added to this initial field, the nonlinear equation governing the motion in the radial direction is obtained. Using the reductive perturbation technique, the propagation of weakly nonlinear waves in the long-wave approximation is studied. After obtaining the general equation in the long-wave approximation, by a proper scaling, it is shown that this general equation reduces to the well-know nonlinear evolution equations. Intensifying the effect of nonlinearity in the perturbation process, the modified forms of these evolution equations are also obtained.Mathematics Subject Classification (1991). 76B25, 73D35, 73G25.

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“…In the present work, the latter value was used. Other researchers such as Demiray (1996), Kyriacou and Humphrey (1996), Shah and Humphrey (1999), Hademenos et al (1994), Thubrikar et al (1999), and Vorp et al (2003) used a nonlinear constitutive equation. Many of the users of the linear and nonlinear models applied a kind of thin-shell or membrane theories.…”

Section: Introductionmentioning

confidence: 98%