Buckling condensation in constrained growth

Dervaux, Julien; Amar, Martine Ben

doi:10.1016/j.jmps.2010.12.015

Cited by 82 publications

(79 citation statements)

References 58 publications

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“…A study to mimic the avascular development of thin solid tumors also showed that in a circular bilayer structure formed by the growth of the outer layer (ring) on a supporting core different kind of instabilities and patterns can be observed based on the stiffness ratio of the core to ring and thickness of the ring. With a high thickness of the growing ring and under special conditions interfacial wrinkles also were detected in the model [44]. Back to the bovine esophagi shown in Fig.…”

Section: Computational Resultsmentioning

confidence: 82%

Surface and interfacial creases in a bilayer tubular soft tissue

2016

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Surface and interfacial creases induced by biological growth are common types of instability in soft biological tissues. This study focuses on the criteria for the onset of surface and interfacial creases as well as its morphological evolution in a growing bilayer soft tube within a confined environment. Critical growth ratios for triggering surface and interfacial creases are investigated both analytically and numerically. Analytical interpretations provide preliminary insights into critical stretches and growth ratios for the onset of instability and formation of both surface and interfacial creases. However, the analytical approach cannot predict the evolution pattern of the model after instability, therefore non-linear finite element simulations are carried out to replicate the post-stability morphological patterns of the structure. Analytical and computational simulation results demonstrate that the initial geometry, growth ratio, and shear modulus ratio of the layers are the most influential factors to control surface and interfacial crease formation in this soft tubular bilayer. The competition between the stretch ratios in the free and interfacial surfaces is one of the key driving factors to determine the location of the first crease initiation. These findings may provide some fundamental understanding in the growth modeling of tubular biological tissues such as esophagi and airways as well as offering useful clues into normal and pathological functions of these tissues.

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Section: Computational Resultsmentioning

confidence: 82%

Surface and interfacial creases in a bilayer tubular soft tissue

2016

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“…Furthermore we assume that the wrinkles are increasingly confined to the surface as (n, ω) → ∞. This phenomenon has been observed in previous studies of buckling in nonlinear elasticity (Biot [1], Coman and Bassom [7], Dervaux and Amar [8], Hohlfeld and Mahadevan [14], Cao and Hutchinson [5], MacLaurin et al [19]). It is analogous to the surface buckling of compressed infinite half-spaces: since there is no characteristic lengthscale, all of the wavelengths go unstable simultaneously (Biot [1]).…”

Section: Introductionmentioning

confidence: 75%

“…Moulton and Goriely [21] observed similar results to ours in their various models of an externally compressed tube (without growth): the asymptotic limit of the critical pressure appears to occur well after the initial critical pressure. However when the bifurcation parameter was some form of growth 8 , the asymptotic limit of the critical growths of the modes was close to the critical growth of the initial mode to go unstable (Moulton and Goriely [21]). The authors observed a similar phenomenon in their modelling of the growthinduced buckling of tumour capillaries [19].…”

Section: Discussionmentioning

confidence: 99%

“…The wrinkling is often observed in biological materials, for example on the surfaces of cells, tumours (Dervaux and Amar [8]), tubular organs (such as airways Moulton and Goriely [22], the oesophagus Li et al [16], intestine and blood vessels MacLaurin et al [19]) or brain convolutions. It is also observed in nonbiological materials, such as the wrinkling of stretched elastic sheets with low bending modulus (Brau et al [2]), the wrinkling of thin films anchored to stiff substrates (Cao and Hutchinson [5]), the formation of sulci in compressed soft materials (Hohlfeld and Mahadevan [14]) or the wrinkling on the inner surface of a bent rubber block (Destrade et al [9]).…”

Section: Introductionmentioning

confidence: 99%

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The study of asymptotically fine wrinkling in nonlinear elasticity using a boundary layer analysis

MacLaurin

Chapman

Jones

et al. 2013

Journal of the Mechanics and Physics of Solids

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Fine sinusoidal wrinkling on the surfaces of mechanically compressed objects has been observed in many contexts over many years. In this paper we investigate such wrinkling through the application of a boundary layer analysis to an elastostatic problem in nonlinear elasticity. We determine the onset of buckling using a linear-stability analysis, and the leading-order postbuckling behaviour through consideration of higher-order terms of the energy. The object is assumed to (initially) 'preserve' its shape, so that these equations reduce to ordinary differential equations. We then apply a boundary-layer analysis to this problem, determining (in the asymptotic limit of large wavenumbers) the leading order behaviours of the eigenmode, the critical parameter, and the magnitude of the buckle. We find that the magnitude of a buckle with wavenumbers ςγ * 2 and ςγ * 3 (for fixed γ * 2 and γ * 3 ) has leading asymptotic order ς λ (2) , for an increment λ (2) of the critical parameter beyond the critical time of buckling. We provide electronic supplementary material which extends this analysis to that of incompressible elasticity. Finally we confirm the accuracy of our ansatz on a compressed NeoHookean ring.

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“…To name but a few examples, buckling under external stress has been related to morphogenesis for instance in growing spheroidal shells [40], or in the growth of other constrained systems [12,16]. More complex shapes, observed in plant organs such as long leaves [25], or in blooming flowers [11,26], have also been modelled by adapting the theory of elastic shells to a growing surface.…”

Section: Introductionmentioning

confidence: 99%

Encasement as a morphogenetic mechanism: The case of bending

Biscari

Susini

Zanzotto

2015

International Journal of Non-Linear Mechanics

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We study how the encasement of a growing elastic bulk within a possibly differently growing elastic coat may induce mechanical instabilities in the equilibrium shape of the combined body. The inhomogeneities induced in an incompressible bulk during growth are also discussed. These effects are illustrated through a simple example in which a growing elastic cylinder may undergo a shape transition towards a bent configuration.

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Buckling condensation in constrained growth

Cited by 82 publications

References 58 publications

Surface and interfacial creases in a bilayer tubular soft tissue

Surface and interfacial creases in a bilayer tubular soft tissue

The study of asymptotically fine wrinkling in nonlinear elasticity using a boundary layer analysis

Encasement as a morphogenetic mechanism: The case of bending

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