Quantitative predictions of diverse wrinkling patterns in film/substrate systems

Xu, Fan; Potier‐Ferry, Michel

doi:10.1038/s41598-017-18267-0

Cited by 13 publications

(6 citation statements)

References 61 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Comparisons between planar and curved systems reveal that the surface curvature plays an important role in pattern formation and evolution. Most of these previous studies either focused on the various wrinkling modes on a curved surface [13,18,20], or emphasise the use of effective numerical methods for complex geometries [19,22].…”

Section: Introductionmentioning

confidence: 99%

Curvature delays growth-induced wrinkling

2018

View full text Add to dashboard Cite

Wrinkling patterns can be induced by the growth of a thin elastic film over a soft elastic substrate. While there is a good understanding of how this pattern is initiated on a flat geometry, wrinkling patterns over a curved surface are more complicated. Here, we consider this phenomenon within the framework of large deformation morphoelasticity by investigating surface wrinkling of a growing thin elastic film bonded to a large elastic cylinder. The system has two important dimensionless parameters: the ratio η of the film thickness by the cylinder radius and the relative stiffness of the two layers ξ. Depending on the values of ξ and η we identify four different regimes for which we find the critical growth and wrinkling mode number. By combining asymptotic methods with numerical computations we determine the effect of the curvature on the bifurcation and establish that it always induces a delay at the bifurcation: larger growth is needed on a curved surface to induce the same wrinkling instability. These results are crucial to understand pattern formation on surface with varying curvatures.

show abstract

Section: Introductionmentioning

confidence: 99%

Curvature delays growth-induced wrinkling

2018

View full text Add to dashboard Cite

show abstract

“…The curved substrate could trigger more diverse wrinkling patterns than a planar substrate under simple a strain condition. [ 19–31 ] For example, Shao et al. successfully fabricated hierarchical wrinkled surfaces on plasma‐treated PDMS elastomers which initially have sinusoidal curvature on top.…”

Section: Introductionmentioning

confidence: 99%

Hierarchical Surface Patterns via Global Wrinkling on Curved Substrate for Fluid Drag Control

Lin

Zhao

et al. 2020

Adv Materials Inter

View full text Add to dashboard Cite

In this paper, the results of an investigation on the global wrinkling of stiff coatings resting on curved compliant substrates are presented. It is found that the overall stiffness of the corrugated coatings can dominate the deformation mode and induce the global wrinkling when the coating thickness exceeds certain critical value. It is demonstrated that hierarchical wrinkling patterns with small wrinkles superposing on large wrinkles, either parallel or perpendicularly, can be generated via the global wrinkling processes. Through a combination of theoretical model, experimental studies, and numerical simulations, the formation mechanism and controlling parameters of the hierarchical wrinkling patterns are systematically investigated. The quantitative expression of the critical loading strain, critical wavelength, and critical coating thickness of the global wrinkling as a function of the initial substrate curvatures and loading conditions are revealed. Inspired by the resemblance between the hierarchical surface patterns and the surface riblets on sharks and dolphins, the potential application of utilizing the hierarchical wrinkling patterns to reduce fluid drag through computational fluid dynamics (CFD) studies is further investigated. Reduced drag resistance is observed on the hierarchical wrinkled surface with small wrinkles and large wrinkles perpendicular to each other.

show abstract

“…We refer to Bowden et al [10,11], Li et al [12], the book by Goriely [13], and the more recent papers by Wang and Zhao [14] and Holland et al [15] for a comprehensive review of the literature and applications. As a prototypical structure, the buckling and post-buckling of a thin-film/substrate bilayer structure has probably received the most attention, partly because of the variety of behaviors that it exhibited and their obvious relevance to more complicated structures [16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34]. If both the layer and substrate are composed of neo-Hookean materials with shear moduli µ f and µ s , respectively, then there exists a critical moduli ratio which is approximately equal to 1.74 such that the initial wrinkling bifurcation is supercritical when µ f /µ s > 1.74 and subcritical otherwise [35,36].…”

Section: Introductionmentioning

confidence: 99%

Effects of pre-stretch, compressibility and material constitution on the period-doubling secondary bifurcation of a film/substrate bilayer

Cai

2019

International Journal of Non-Linear Mechanics

View full text Add to dashboard Cite

We refine a previously proposed semi-analytical method, and use it to study the effects of pre-stretch, compressibility and material constitution on the period-doubling secondary bifurcation of a uni-axially compressed film/substrate bilayer structure. It is found that compared with the case of incompressible neo-Hookean materials for which the critical strain is approximately 0.17 when the thin layer is much stiffer than the substrate, the critical strain when the Gent materials are used is a monotonically increasing function of the constant J m that characterizes material extensibility, becoming as small as 0.12 when J m is equal to 1, whereas for compressible neo-Hookean materials the critical strain is a monotonically decreasing function of Poisson's ratio; the period-doubling secondary bifurcation seems to become impossible when Poisson's ratio is approximately equal to 0.307. The latter result may indicate that when Poisson's ratio is small enough there are other preferred secondary bifurcations -an example is given where a secondary bifurcation mode with 7/4 times the original period occurs at a lower strain value. The effect of a pre-stretch (compression or extension) in the substrate is not monotonic, giving rise to a critical strain that varies between 0.15 and 0.22.

show abstract

Quantitative predictions of diverse wrinkling patterns in film/substrate systems

Cited by 13 publications

References 61 publications

Curvature delays growth-induced wrinkling

Curvature delays growth-induced wrinkling

Hierarchical Surface Patterns via Global Wrinkling on Curved Substrate for Fluid Drag Control

Effects of pre-stretch, compressibility and material constitution on the period-doubling secondary bifurcation of a film/substrate bilayer

Contact Info

Product

Resources

About