Effect of torsion on the initiation of localized bulging in a hyperelastic tube of arbitrary thickness

Althobaiti, Ali

doi:10.1007/s00033-022-01743-7

Cited by 7 publications

(2 citation statements)

References 46 publications

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“…Fu et al (2016) showed that the associated bifurcation condition for localized bulging corresponds to the vanishing of the Jacobian determinant of the internal pressure and resultant axial force as functions of the azimuthal stretch and the axial stretch; see also Yu & Fu (2022) for an alternative derivation. This provides a framework under which additional effects such as rotation (Wang et al, 2017), double-fiber-reinforcement (Wang & Fu, 2018), bi-laying (Liu et al, 2019;Ye et al, 2019), torsion (Althobaiti, 2022), and surface tension (Emery & Fu, 2021a,b,c;Emery, 2023) can be assessed in a systematic manner. Ye et al (2020) conducted a weakly non-linear analysis and derived the bulging solution explicitly.…”

Section: Introductionmentioning

confidence: 99%

A one-dimensional model for axisymmetric deformations of an inflated hyperelastic tube of finite wall thickness

Fu¹

2023

Preprint

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We derive a one-dimensional (1d) model for the analysis of bulging or necking in an inflated hyperelastic tube of finite wall thickness from the three-dimensional finite elasticity theory by applying the dimension reduction methodology proposed by Audoly and Hutchinson (J. Mech. Phys. Solids, 97, 2016). The 1d model makes it much easier to characterize fully nonlinear axisymmetric deformations of a thick-walled tube using simple numerical schemes such as the finite difference method. The new model recovers the diffuse interface model for analyzing bulging in a membrane tube and the 1d model for investigating necking in a stretched solid cylinder as two limiting cases. It is consistent with, but significantly refines, the exact linear and weakly nonlinear bifurcation analyses. Comparisons with finite element simulations show that for the bulging problem, the 1d model is capable of describing the entire bulging process accurately, from initiation, growth, to propagation. The 1d model provides a stepping stone from which similar 1d models can be derived and used to study other effects such as anisotropy and electric loading, and other phenomena such as rupture.

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Section: Introductionmentioning

confidence: 99%

A one-dimensional model for axisymmetric deformations of an inflated hyperelastic tube of finite wall thickness

Fu¹

2023

Preprint

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“…Previous linear bifurcation analyses (Haughton and Ogden, 1979a,b) had focussed on periodic axi-symmetric modes, and the zero wavenumber mode was incorrectly thought to correspond to an alternate uniformally inflated state. Since the revelation of Fu et al (2016), many additional effects such as rotation (Wang et al, 2017), double fibre-reinforcement (Wang and Fu, 2018), bi-layering (Liu et al, 2019) and torsion (Althobaiti, 2022) have been incorporated into the analysis.…”

Section: Introductionmentioning

confidence: 99%

Elasto-capillary necking, bulging and Maxwell states in soft compressible cylinders

Emery¹

2022

Preprint

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Localized pattern formations and "two-phase" deformations are studied theoretically in soft compressible cylinders subject to surface tension and axial loading through several forcecontrolled loading scenarios. By drawing upon known results for separate yet mathematically similar elastic localization problems, a concise family of analytical bifurcation conditions for localized bulging or necking are derived in terms of a general compressible strain energy function. The effect of material compressibility and strain-stiffening behaviour on the bifurcation point is analysed, and comparisons between our theoretical bifurcation conditions and the corresponding numerical simulation results of Dortdivanlioglu and Javili (Extreme Mech. Lett. 55, 2022) are made. It is then explained how the fully developed "two-phase" (Maxwell) state which evolves from the initial localized bifurcation solution can be comprehensively understood using the simple analytical expressions for the force parameters corresponding to the primary axial tension deformation. The power of this simple analytical approach in validating numerical simulation results for elastic localization and phase-separation-like problems of this nature is highlighted.

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Sensitivity analysis of fibrous thick-walled tubes with mechano-sensitive remodeling fibers in homeostasis

Asghari,

Topol,

Lacalle

et al. 2024

Acta Mech

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In this article, we apply the sensitivity analysis method to capture the influence of various parameters on the inflation pressure, axial force, and the deformation for an inflated and axially stretched cylinder. The material consists of an isotropic ground substance material reinforced with fibers that undergo a continuous and mechano-sensitive remodeling process. The input parameters of the mechanical system are assumed to be distributed according to the uniform probability distribution function. In the sensitivity analysis, we apply the Sobol method to determine how the variations of input parameters affect the inflation as well as the axial force in the cylinder. Special attention is given to the fiber remodeling process associated with a homeostatic balance between the constant fiber creation process and the strain-stabilized fiber dissolution. The results may help to understand the importance of the effect of material parameter changes, for example, due to remodeling processes in the context of diseases or recovering processes, on the overall tissue behavior.

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Effect of torsion on the initiation of localized bulging in a hyperelastic tube of arbitrary thickness

Cited by 7 publications

References 46 publications

A one-dimensional model for axisymmetric deformations of an inflated hyperelastic tube of finite wall thickness

A one-dimensional model for axisymmetric deformations of an inflated hyperelastic tube of finite wall thickness

Elasto-capillary necking, bulging and Maxwell states in soft compressible cylinders

Sensitivity analysis of fibrous thick-walled tubes with mechano-sensitive remodeling fibers in homeostasis

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