Finite deformations of cylindrical membrane under internal pressure

Pamplona, Djenane; Gonçalves, Paulo B.; Lopes, Stefane

doi:10.1016/j.ijmecsci.2005.12.007

Cited by 101 publications

(62 citation statements)

References 13 publications

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“…We also observe that (2.22) 4 together with (2.22) 2 implies that (β 1 − β 0 ) > 0. Equation (2.20) shows that for the case of closed ends and fixed F , the first pressure turning point corresponds to the onset of localized bulging, as has been observed experimentally [10,11]. However, human arteries have the important property that pressure fluctuations can be accommodated by very little extra axial stretch.…”

Section: Problem Formulation and Constitutive Assumptionsmentioning

confidence: 75%

“…Alternatively, we may consider the exterior system [37,38] 10) and its adjoint system 11) where the components of the vector function y ∧ come from all the 3 × 3 minors of the 6 × 3 matrix (y 1 , y 2 , y 3 ), and the components of the 20 × 20 matrix M ∧ in terms of those of M have previously been derived by Il'ichev and Fu [8].…”

Section: Stability Of the Weakly Nonlinear Bulging Solutionsmentioning

confidence: 99%

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Localized standing waves in a hyperelastic membrane tube and their stabilization by a mean flow

Ильичев

2014

Mathematics and Mechanics of Solids

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We first give a complete analysis of the dispersion relation for traveling waves propagating in a pre-stressed hyperelastic membrane tube containing a uniform flow. We present an exact formula for the so-called pulse wave velocity, and demonstrate that as any pre-stress parameter is increased gradually, localized bulging would always occur before a superimposed small-amplitude traveling wave starts to grow exponentially. We then study the stability of weakly and fully nonlinear localized bulging solutions that may exist in such a fluid-filled hyperelastic membrane tube. Previous studies have shown that such localized standing waves are unstable under pressure control in the absence of a mean-flow, whether the fluid inertia is taken into account or not. Stability of such localized aneurysm-type solutions is desired when aneurysm formation in human arteries is modelled as a bifurcation phenomenon. It is shown that in the near-critical regime axisymmetric perturbations are governed by the Korteweg-de Vries equation, and so the associated (weakly nonlinear) aneurysm solutions are (orbitally) stable with respect to axisymmetric perturbations. Stability of the fully nonlinear aneurysm solutions are studied numerically using the Evans function method. It is found that for each wall-fluid density ratio there exists a critical mean-flow speed above which no axisymmetric unstable modes can be found, which implies that a fully nonlinear aneurysm solution may be completely stabilized by a mean flow.

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Section: Problem Formulation and Constitutive Assumptionsmentioning

confidence: 75%

Section: Stability Of the Weakly Nonlinear Bulging Solutionsmentioning

confidence: 99%

Localized standing waves in a hyperelastic membrane tube and their stabilization by a mean flow

Ильичев

2014

Mathematics and Mechanics of Solids

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“…Localized bulging in an inflated isotropic rubber tube was first documented by Mallock (1891), and later studied experimentally and numerically by Kyriakides & Chang (1990, Pamplona et al (2006), Goncalves et al (2008), and Shi & Moita (1996). The propagation stage was recognized by Yin (1977) and Chater & Hutchinson (1984) as a twophase deformation governed by Maxwell's equal area rule, but the character of the initiation stage, and its connection with the so-called limit-point instability (Alexander, 1971;Kanner & Horgan, 2007), was not fully understood until more recently.…”

Section: Introductionmentioning

confidence: 99%

Localized bulging in an inflated cylindrical tube of arbitrary thickness – the effect of bending stiffness

Liu

Francisco

2016

Journal of the Mechanics and Physics of Solids

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We study localized bulging of a cylindrical hyperelastic tube of arbitrary thickness when it is subjected to the combined action of inflation and axial extension. It is shown that with the internal pressure P and resultant axial force F viewed as functions of the azimuthal stretch on the inner surface and the axial stretch, the bifurcation condition for the initiation of a localized bulge is that the Jacobian of the vector function (P, F ) should vanish. This is established using the dynamical systems theory by first computing the eigenvalues of a certain eigenvalue problem governing incremental deformations, and then deriving the bifurcation condition explicitly. The bifurcation condition is valid for all loading conditions, and in the special case of fixed resultant axial force it gives the expected result that the initiation pressure for localized bulging is precisely the maximum pressure in uniform inflation. It is shown that even if localized bulging cannot take place when the axial force is fixed, it is still possible if the axial stretch is fixed instead. The explicit bifurcation condition also provides a means to quantify precisely the effect of bending stiffness on the initiation pressure. It is shown that the (approximate) membrane theory gives good predictions for the initiation pressure, with a relative error less than 5%, for thickness/radius ratios up to 0.67. A two-term asymptotic bifurcation condition for localized bulging that incorporates the effect of bending stiffness is proposed, and is shown to be capable of giving extremely accurate predictions for the initiation pressure for thickness/radius ratios up to as large as 1.2.

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“…Several theoretical and numerical studies have been published in this field, but the total number of studies that have used this approach is rather low compared to theoretical and numerical approaches [Alexander 1971;Pamplona et al 2006;2001;Pamplona and Bevilacqua 1992;Gonçalves et al 2009;.…”

Section: Introductionmentioning

confidence: 99%

Characterization of human skin through skin expansion

Pamplona

Carvalho

2012

J. Mech. Mater. Struct.

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This study characterized human skin of the lower leg and scalp during the surgical process of skin expansion. To our knowledge, this is the first study in this field, which has provided results that considerably improve our understanding of human skin. A detailed in vivo analysis was carried out involving four different patients that allowed for observation during the relaxation process. A comparison between the in vivo and numerical finite elements model of the expansion was used to identify the material elastic parameters of the skin. After a comprehensive search of constitutive equations for describing skin, Delfino's constitutive equation was chosen to model the in vivo results. We considered skin as an isotropic, homogeneous, hyperelastic, and incompressible membrane. The parameters of Delfino's exponential function obtained for the first skin stretch process were a = 40.0 KPa and b = 20.2. As skin is extended, such as with expanders or in other procedures that tighten the skin, the collagen fibers are also extended and cause stiffening in the skin, which results in it being more and more resistant to expansion or further stretching. We observed this phenomenon as an increase in parameters a and b as subsequent expansions continued. The results of this study allow for the quantification of stiffening of the skin after several stretches, when the skin becomes more and more inelastic. These results are very encouraging and provide insight into our understanding of the behavior of stretched skin and maybe other biological tissues, as swollen artery and veins.A list of symbols can be found on page 653.

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Finite deformations of cylindrical membrane under internal pressure

Cited by 101 publications

References 13 publications

Localized standing waves in a hyperelastic membrane tube and their stabilization by a mean flow

Localized standing waves in a hyperelastic membrane tube and their stabilization by a mean flow

Localized bulging in an inflated cylindrical tube of arbitrary thickness – the effect of bending stiffness

Characterization of human skin through skin expansion

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