Necking, beading, and bulging in soft elastic cylinders

Fu, Yibin; Jin, Lishuai; Goriely, Alain

doi:10.1016/j.jmps.2020.104250

Cited by 47 publications

(67 citation statements)

References 49 publications

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“…It follows that the bifurcation is sub-critical since the term γ1 κ1 in the solitary wave solution forces γ1 to be negative. Based on the findings for a solid cylinder [37], we expect that the relation κ2 = λ 2 κ1 dγ cr /dλ holds true, and…”

Section: (A)mentioning

confidence: 99%

“…Theoretically, it has been evidenced in the case of a solid cylinder that the beading instability culminates in a 'two-phase' state, or a 'kink-wave' solution, characterized by two sections with distinct but uniform axial stretch connected by a smooth transition zone [35,36]. Moreover, it was determined in [37] that a localized bulging or necking solution will initially occur depending on the loading path.…”

Section: Introductionmentioning

confidence: 99%

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Post-bifurcation behaviour of elasto-capillary necking and bulging in soft tubes

Emery

2021

Proc. R. Soc. A.

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Previous linear bifurcation analyses have evidenced that an axially stretched soft cylindrical tube may develop an infinite-wavelength (localized) instability when one or both of its lateral surfaces are under sufficient surface tension. Phase transition interpretations have also highlighted that the tube admits a final evolved ‘two-phase’ state. How the localized instability initiates and evolves into the final ‘two-phase’ state is still a matter of contention, and this is the focus of the current study. Through a weakly nonlinear analysis conducted for a general material model, the initial sub-critical bifurcation solution is found to be localized bulging or necking depending on whether the axial stretch is greater or less than a certain threshold value. At this threshold value, an exceptionally super-critical kink-wave solution arises in place of localization. A thorough interpretation of the anticipated post-bifurcation behaviour based on our theoretical results is also given, and this is supported by finite-element method simulations.

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Section: (A)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Post-bifurcation behaviour of elasto-capillary necking and bulging in soft tubes

Emery

2021

Proc. R. Soc. A.

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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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“…The inflation of cylindrical elastic balloons is often accompanied by different types of instabilities, such as bulging and necking. These phenomena have been analyzed theoretically for hyperelastic balloons, [125][126][127] In (c) and (d), the dashed black lines correspond to the deterministic solutions based only on the mean values of the parameters, whereas the red versions show the arithmetic mean value solutions. In all cases, when the parameter ratio is sufficiently small, the required dead load changes from increasing to decreasing, and the material displays necking instability.…”

Section: Instabilities In Liquid Crystal Elastomersmentioning

confidence: 99%

Instabilities in liquid crystal elastomers

Mihai

Goriely

2021

MRS Bulletin

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Stability is an important and fruitful avenue of research for liquid crystal elastomers. At constant temperature, upon stretching, the homogeneous state of a nematic body becomes unstable, and alternating shear stripes develop at very low stress. Moreover, these materials can experience classical mechanical effects, such as necking, void nucleation and cavitation, and inflation instability, which are inherited from their polymeric network. We investigate the following two problems: First, how do instabilities in nematic bodies change from those found in purely elastic solids? Second, how are these phenomena modified if the material constants fluctuate? To answer these questions, we present a systematic study of instabilities occurring in nematic liquid crystal elastomers, and examine the contribution of the nematic component and of fluctuating model parameters that follow probability laws. This combined analysis may lead to more realistic estimations of subsequent mechanical damage in nematic solid materials. Because of their complex material responses in the presence of external stimuli, liquid crystal elastomers have many potential applications in science, manufacturing, and medical research. The modeling of these materials requires a multiphysics approach, linking traditional continuum mechanics with liquid crystal theory, and has led to the discovery of intriguing mechanical effects. An important problem for both applications and our fundamental understanding of nematic elastomers is their instability under large strains, as this can be harnessed for actuation, sensing, or patterning. The goal is then to identify parameter values at which a bifurcation emerges, and how these values change with external stimuli, such as temperature or loads. However, constitutive parameters of real manufactured materials have an inherent variation that should also be taken into account, thus the need to quantify uncertainties in physical responses, which can be done by combining the classical field theories with stochastic methods that enable the propagation of uncertainties from input data to output quantities of interest. The present study demonstrates how to characterize instabilities found in nematic liquid crystal elastomers with probabilistic material parameters at the macroscopic scale, and paves the way for a systematic theoretical and experimental study of these fascinating materials.

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Necking, beading, and bulging in soft elastic cylinders

Cited by 47 publications

References 49 publications

Post-bifurcation behaviour of elasto-capillary necking and bulging in soft tubes

Post-bifurcation behaviour of elasto-capillary necking and bulging in soft tubes

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

Instabilities in liquid crystal elastomers

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