Modelling of residually stressed, extended and inflated cylinders with application to aneurysms

Font, Alejandro; Jha, Niraj Kumar; Dehghani, Hamidreza; Reinoso, J.; Merodio, J.

doi:10.1016/j.mechrescom.2020.103643

Cited by 24 publications

(21 citation statements)

References 16 publications

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“…Besides bent buckling, twist buckling and helical buckling may occur in arteries and veins (Selvaggi et al, 2006;Wong et al, 2007;Garcia et al, 2013Garcia et al, , 2017Rodriguez and Merodio, 2016;Sharzehee et al, 2019). Barrel shape bulging buckling and crosssectional collapse and "beads" -like or "aneurysmal" buckling may also occur as shown in recent reports (Alhayani et al, 2013;Emery and Fu, 2021;Font et al, 2021;Fu et al, 2021). It could be FIGURE 9 | Effect of eccentricity on the AR of the (A) lumen and (B) the outer wall of elliptic arteries with initial lumen AR = 0.8 during the axial stretch and lumen pressure loading process.…”

Section: Limitationsmentioning

confidence: 84%

Buckling of Arteries With Noncircular Cross Sections: Theory and Finite Element Simulations

Seddighi

Han

2021

Front. Physiol.

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The stability of blood vessels is essential for maintaining the normal arterial function, and loss of stability may result in blood vessel tortuosity. The previous theoretical models of artery buckling were developed for circular vessel models, but arteries often demonstrate geometric variations such as elliptic and eccentric cross-sections. The objective of this study was to establish the theoretical foundation for noncircular blood vessel bent (i.e., lateral) buckling and simulate the buckling behavior of arteries with elliptic and eccentric cross-sections using finite element analysis. A generalized buckling equation for noncircular vessels was derived and finite element analysis was conducted to simulate the artery buckling behavior under lumen pressure and axial tension. The arterial wall was modeled as a thick-walled cylinder with hyper-elastic anisotropic and homogeneous material. The results demonstrated that oval or eccentric cross-section increases the critical buckling pressure of arteries and having both ovalness and eccentricity would further enhance the effect. We conclude that variations of the cross-sectional shape affect the critical pressure of arteries. These results improve the understanding of the mechanical stability of arteries.

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Section: Limitationsmentioning

confidence: 84%

Buckling of Arteries With Noncircular Cross Sections: Theory and Finite Element Simulations

Seddighi

Han

2021

Front. Physiol.

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“…The specific additive form W = W o + W τ that is used in this study is motivated by, and in keeping with, prototypical forms that are utilized in previous works. These additive forms are now beginning to see usage in computational treatments (e.g., [8,22]) that address fundamental questions of bifurcation, imperfection sensitivity and symmetry breaking deformations, all of which are issues that are beyond the scope of this article. In the context of W = W o + W τ we have made use of W τ given by the first of (2.13).…”

Section: Discussionmentioning

confidence: 99%

On the Inflation of Residually Stressed Spherical Shells

Yücesoy

Pence

2021

J Elast

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A well known result from the non-linear theory of elasticity applied to spherical shells is that the classical Mooney-Rivlin constitutive law may give either a monotonic or a nonmonotonic pressure-inflation response for finite deformation. Specifically, this is determined by two factors: the relative shell thickness, and the relative I 1 to I 2 contribution in the M-R constitutive law. Here we consider how a residual stress field may affect this behavior. Using a constitutive framework for hyperelastic materials with residual stress that has been especially applied to tubes, this paper focuses on finite thickness spherical shells while using a similar prototypical energy response. In this context we examine different residual stress states, and show how certain of these lead to more workable analytical results than others. All of them enable Taylor and asymptotic expansions in the small and large inflation limit. On this basis it is shown how particular residual stress fields can cause a monotonic inflation graph to become non-monotonic, and vice versa.

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“…Bulging of a pressurized cylinder has been studied in different works such as Fu et al [1,2] and Merodio and collaborators [3][4][5][6][7] in the context of volume-preserving material behavior. While Kyriakides and Chang [8] and Kyriakides [9] show that bulging can be the result of a limit load instability, Fu et al [2] illustrate that localized bulging can occur even when there is no maximum pressure.…”

Section: Introductionmentioning

confidence: 99%

Bulging initiation and propagation in fiber-reinforced swellable Mooney–Rivlin membranes

et al. 2021

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This article considers a thin-walled hollow cylinder, which is composed of a fibrous and swellable hyperelastic material. The fibers are arranged in two families and they are taken to be parallel within each fiber family. The two fiber families are also assumed to be mechanically equivalent and symmetrically disposed in the ground substance material. At each instant of the homogeneous swelling, the material is taken to be incompressible. This article studies the interplay of swelling, fiber orientation, and the mechanical properties of the constituents on the initiation as well as on the axial propagation of bulging.

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Modelling of residually stressed, extended and inflated cylinders with application to aneurysms

Cited by 24 publications

References 16 publications

Buckling of Arteries With Noncircular Cross Sections: Theory and Finite Element Simulations

Buckling of Arteries With Noncircular Cross Sections: Theory and Finite Element Simulations

On the Inflation of Residually Stressed Spherical Shells

Bulging initiation and propagation in fiber-reinforced swellable Mooney–Rivlin membranes

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