From period-doubling to folding in stiff film/soft substrate system: The role of substrate nonlinearity

Zhuo, Lu; Zhang, Yin

doi:10.1016/j.ijnonlinmec.2015.05.002

Cited by 20 publications

(14 citation statements)

References 37 publications

(81 reference statements)

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“…Folding is associated with small ratios μ f /μ s and pre-stretches 1s , the mountain ridge mode with large ratios μ f /μ s and/or pre-stretches λ 0 1s and perioddoubling with intermediate combinations ( figure 15). These results agree well with previous studies investigating WDC with pre-stretch [20,22,33,36,37]. Although secondary instability patterns were predominantly determined by the stiffness ratio μ f /μ s and the substrate pre-stretch λ 0 1s , the film thickness t 0 and the origin of compression have a strong regulatory influence: they can suppress certain patterns and favour others.…”

Section: Discussionsupporting

confidence: 92%

The origin of compression influences geometric instabilities in bilayers

2018

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Geometric instabilities in bilayered structures control the surface morphology in a wide range of biological and technical systems. Depending on the application, different mechanisms induce compressive stresses in the bilayer. However, the impact of the chosen origin of compression on the critical conditions, post-buckling evolution and higher-order pattern selection remains insufficiently understood. Here, we conduct a numerical study on a finite-element set-up and systematically vary well-known factors contributing to pattern selection under the four main origins of compression: film growth, substrate shrinkage and whole-domain compression with and without pre-stretch. We find that the origin of compression determines the substrate stretch state at the primary instability point and thus significantly affects the critical buckling conditions. Similarly, it leads to different post-buckling evolutions and secondary instability patterns when the load further increases. Our results emphasize that future phase diagrams of geometric instabilities should incorporate not only the film thickness but also the origin of compression. Thoroughly understanding the influence of the origin of compression on geometric instabilities is crucial to solving real-life problems such as the engineering of smart surfaces or the diagnosis of neuronal disorders, which typically involve temporally or spatially combined origins of compression.

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Section: Discussionsupporting

confidence: 92%

The origin of compression influences geometric instabilities in bilayers

2018

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“…This observation demonstrates that the finite thickness of the film geometrically limits the emergence of higher-order wrinkling modes: the pattern remains constant as soon as self-contact occurs and folds appear [32], for instance in figure 4a. Notably, the folding mode can arise after period-doubling or period-tripling, which had been previously indicated computationally [22,31]. In general, folding occurs when the system favours inward displacement, while period-doubling occurs when the system favours outward displacements [16,18,33].…”

Section: Resultsmentioning

confidence: 74%

“…Another practical tool to explore multiple bifurcations is the finite-element method [20][21][22]. Primary wrinkling has been extensively studied [23][24][25][26] and recent experimental [10,18,27], theoretical [18,28,29] and computational [28,30,31] studies have significantly advanced our understanding of the perioddoubling mode. However, higher-order secondary wrinkling modes, such as period-tripling or period-quadrupling, remain unsatisfactorily understood [10].…”

Section: Motivationmentioning

confidence: 99%

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Wrinkling instabilities in soft bilayered systems

Budday

Andres

Walter

et al. 2017

Phil. Trans. R. Soc. A.

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Wrinkling phenomena control the surface morphology of many technical and biological systems. While primary wrinkling has been extensively studied, experimentally, analytically and computationally, higher-order instabilities remain insufficiently understood, especially in systems with stiffness contrasts well below 100. Here, we use the model system of an elastomeric bilayer to experimentally characterize primary and secondary wrinkling at moderate stiffness contrasts. We systematically vary the film thickness and substrate prestretch to explore which parameters modulate the emergence of secondary instabilities, including period-doubling, period-tripling and wrinkle-to-fold transitions. Our experiments suggest that period-doubling is the favourable secondary instability mode and that period-tripling can emerge under disturbed boundary conditions. High substrate prestretch can suppress period-doubling and primary wrinkles immediately transform into folds. We combine analytical models with computational simulations to predict the onset of primary wrinkling, the post-buckling behaviour, secondary bifurcations and the wrinkle-to-fold transition. Understanding the mechanisms of pattern selection and identifying the critical control parameters of wrinkling will allow us to fabricate smart surfaces with tunable properties and to control undesired surface patterns like in the asthmatic airway.This article is part of the themed issue 'Patterning through instabilities in complex media: theory and applications.'

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“…A major result arising from a weakly nonlinear analysis [6,21,28] is that there exists a critical stiffness ratio that marks the transition from sub-critical bifurcation to super-critical bifurcation. It can then be expected, and indeed confirmed by many recent numerical and experimental studies, that in the sub-critical regime localization is the norm [38] whereas in the super-critical regime stable periodic patterns and further secondary bifurcations are the norm [18,[39][40][41][42][43][44][45][46][47].…”

Section: Introductionmentioning

confidence: 78%

Post-buckling of an elastic half-space coated by double layers

Zhou¹,

Cai

2021

Mathematics and Mechanics of Solids

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We investigate the buckling and post-buckling properties of a hyperelastic half-space coated by two hyperelastic layers when the composite structure is subjected to a uniaxial compression. In the case of a half-space coated with a single layer, it is known that when the shear modulus [Formula: see text] of the layer is larger than the shear modulus [Formula: see text] of the half-space, a linear analysis predicts the existence of a critical stretch and wave number, whereas a weakly nonlinear analysis predicts the existence of a threshold value of the modulus ratio [Formula: see text] below which the buckling is super-critical and above which the buckling is sub-critical. It is shown that when another layer is added, a larger variety of behaviour can be observed. For instance, buckling can occur at a preferred wavenumber super-critically even if both layers are softer than the half-space although the top layer would need to be harder than the bottom layer. When the shear modulus of the bottom layer lies in a certain interval, the super-critical to sub-critical transition can happen a number of times as the shear modulus of the top layer is increased gradually. Thus, an extra layer imparts more flexibility in producing wrinkling patterns with desired properties, and our weakly nonlinear analysis provides a road map on the parameter regimes where this can be achieved.

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From period-doubling to folding in stiff film/soft substrate system: The role of substrate nonlinearity

Cited by 20 publications

References 37 publications

The origin of compression influences geometric instabilities in bilayers

The origin of compression influences geometric instabilities in bilayers

Wrinkling instabilities in soft bilayered systems

Post-buckling of an elastic half-space coated by double layers

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