Helical buckling of thick-walled, pre-stressed, cylindrical tubes under a finite torsion

Balbi, Valentina; Ciarletta, Pasquale

doi:10.1177/1081286514550570

Cited by 15 publications

(9 citation statements)

References 27 publications

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“…We perform the stability analysis over a physiological pressure range [5] of 0-170 mmHg. We plot the results in Fig.7(c) for the non-dimensional measure of pressureP = P/C (s) 1 . Then the physiological pressure range corresponds to 0 ≤P ≤ 75.5.…”

Section: Results For Soft Tissuesmentioning

confidence: 99%

Wrinkles in the opening angle method

Destrade

Lusetti

Mangan

et al. 2017

International Journal of Solids and Structures

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We investigate the stability of the deformation modeled by the opening angle method, often used to give a measure of residual stresses in arteries and other biological soft tubular structures. Specifically, we study the influence of stiffness contrast, dimensions and inner pressure on the onset of wrinkles when an open sector of a soft tube, coated with a stiffer film, is bent into a full cylinder. The tube and its coating are made of isotropic, incompressible, hyperelastic materials. We provide a full analytical exposition of the governing equations and the associated boundary value problem for the large deformation and for the superimposed small-amplitude wrinkles. For illustration, we solve them numerically with a robust algorithm in the case of Mooney-Rivlin materials. We confront the results to experimental data that we collected for soft silicone sectors. We study the influence of axial stretch and inner pressure on the stability of closed-up coated tubes with material parameters comparable with those of soft biological tubes such 1 arXiv:2009.03425v1 [cond-mat.soft] 7 Sep 2020 as arteries and veins, although we do not account for anisotropy. We find that the large deformation described in the opening angle method does not always exist, as it can become unstable for certain combinations of dimensions and material parameters.

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Section: Results For Soft Tissuesmentioning

confidence: 99%

Wrinkles in the opening angle method

Destrade

Lusetti

Mangan

et al. 2017

International Journal of Solids and Structures

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“…The incremental BVP is numerically solved using the impedance matrix method Biryukov [1985], Biryukov et al [1995]. Following a similar procedure used in Balbi and Ciarletta [2015], we introduce the matricant…”

Section: Impedence Matrix Methodsmentioning

confidence: 99%

“…Following Stroh [1962], we rewrite the system of partial differential equations Eq. ( 19) into a system of ordinary differential equations, by assuming the following variable separation ansatz for the incremental fields Ciarletta and Destrade [2014], Balbi and Ciarletta [2015] u…”

Section: Stroh Formulationmentioning

confidence: 99%

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Morphomechanical model of the torsional c-looping in the embryonic heart

Bevilacqua¹,

Ciarletta²,

Quarteroni³

2020

Preprint

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Before septation processes shape its four chambers, the embryonic heart is a straight tube that spontaneously bends and twists breaking the left-right symmetry. In particular, the heart tube is subjected to a cell remodelling inducing ventral bending and dextral torsion during the c-looping phase. In this work we propose a morphomechanical model for the torsion of the heart tube, that behaves as a nonlinear elastic body. We hypothesize that this spontaneous looping can be modeled as a mechanical instability due to accumulation of residual stresses induced by the geometrical frustration of tissue remodelling, which mimics the cellular rearrangement within the heart tube. Thus, we perform a linear stability analysis of the resulting nonlinear elastic boundary value problem to determine the onset of c-looping as a function of the aspect ratios of the tube and of the internal remodelling rate. We perform numerical simulations to study the fully nonlinear morphological transition, showing that the soft tube develops a realistic self-contacting looped shape in the physiological range of geometrical parameters.

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“…Buckling induced by confined axial growth, accompanied by twisting growth at the confined end has been revealed to cause helical shape of plant roots growing in mechanically heterogeneous environments [4]. Confined torsion will induce helical buckling [5]. Thirdly, growth can also cause material separated apart to come into contact and join each other [6], or it can tear originally joint tissue apart and create gaps [7], like cavitation in lotus root and bamboo shoots.…”

Section: Introductionmentioning

confidence: 99%

Growth induced buckling instability of anisotropic tube and its application in wound edge instability

Yang

Witten

Pidaparti

2017

Curved and Layered Structures

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Fiber reinforced anisotropic material abounds in biological world. It has been demonstrated in previous theoretical and experimental works that growth of biological soft tubular tissue plays a significant role in morphogenesis and pathology. Here we investigate growth-induced buckling of anisotropic cylindrical tissue, focusing on the effects of type of growth(constraint/unconstraint, isotropic/anisotropic), fiber property(orientation, density and strength), geometry and any interaction between these factors. We studied one-layer and two-layer models and obtained a rich spectrum of results. For one-layer model, we demonstrate that circumferential fiber orientation has a consistent stabilizing effect under various scenarios of growth. Higher fiber density has a destabilizing effect by disabling high-mode buckling. For two-layer model, we found that critical buckling strain at inner boundary is an invariant under same isotropic growth rate ratio between inner/outer layer(g i /g 0 ). Then we applied our model to wound healing and illustrate the effects of skin residual stress, fiber property, proliferation region width and wound size on the wound edge stability. We conclude that fiber-reinforcement is an important factor to consider when investigating growth induced instability of anisotropic soft tissue.

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Helical buckling of thick-walled, pre-stressed, cylindrical tubes under a finite torsion

Cited by 15 publications

References 27 publications

Wrinkles in the opening angle method

Wrinkles in the opening angle method

Morphomechanical model of the torsional c-looping in the embryonic heart

Growth induced buckling instability of anisotropic tube and its application in wound edge instability

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