ArticlePhilosophical magazine (Abingdon, England)
Period-doubling and period-tripling in growing bilayered systems.
Article in Philosophical magazine (Abingdon, England). The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 21 papers.
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Who cites it
21 citing papers in PubMed.
- Model-driven exploration of poro-viscoelasticity in human brain tissue: be careful with the parameters!Interface focus · 2024Article
- Exploring the role of different cell types on cortical folding in the developing human brain through computational modeling.Scientific reports · 2024Article
- Morphoelastic modelling of pattern development in the petal epidermal cell cuticle.Journal of the Royal Society, Interface · 2023Article
- Exploring the role of the outer subventricular zone during cortical folding through a physics-based model.eLife · 2023Article
- Post-buckling behaviors of thin-film soft-substrate bilayers with finite-thickness substrate.Scientific reports · 2022Article
- Mechanism Exploration of 3-Hinge Gyral Formation and Pattern Recognition.Cerebral cortex communications · 2021Article
- Folding drives cortical thickness variations.The European physical journal. Special topics · 2020Article
- Bioinspired Multiscale Wrinkling Patterns on Curved Substrates: An Overview.Nano-micro letters · 2020Review
- Growth and remodelling of living tissues: perspectives, challenges and opportunities.Journal of the Royal Society, Interface · 2019Review
- Post-buckling behaviour of a growing elastic rod.Journal of mathematical biology · 2019Article
- Exploring 3-hinge gyral folding patterns among HCP Q3 868 human subjects.Human brain mapping · 2018Article
- Mathematical and computational modelling of skin biophysics: a review.Proceedings. Mathematical, physical, and engineering sciences · 2017Review
- Rayleigh-Taylor instability in soft elastic layers.Philosophical transactions. Series A, Mathematical, physical, and engineering sciences · 2017Article
- Wrinkling instabilities in soft bilayered systems.Philosophical transactions. Series A, Mathematical, physical, and engineering sciences · 2017Article
- Instabilities of soft films on compliant substrates.Journal of the mechanics and physics of solids · 2017Article
- Ultradonut topology of the nuclear envelope.Proceedings of the National Academy of Sciences of the United States of America · 2016Article
- Elastosis during airway wall remodeling explains multiple co-existing instability patterns.Journal of theoretical biology · 2016Article
- Mechanics of the brain: perspectives, challenges, and opportunities.Biomechanics and modeling in mechanobiology · 2015Review
- Emerging Brain Morphologies from Axonal Elongation.Annals of biomedical engineering · 2015Article
- Physical biology of human brain development.Frontiers in cellular neuroscience · 2015Review
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3 authors.
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Abstract
Growing layers on elastic substrates are capable of creating a wide variety of surface morphologies. Moderate growth generates a regular pattern of sinusoidal wrinkles with a homogeneous energy distribution. While the critical conditions for periodic wrinkling have been extensively studied, the rich pattern formation beyond this first instability point remains poorly understood. Here we show that upon continuing growth, the energy progressively localizes and new complex morphologies emerge. Previous studies have often overlooked these secondary bifurcations; they have focused on large stiffness ratios between layer and substrate, where primary instabilities occur early, long before secondary instabilities emerge. We demonstrate that secondary bifurcations are particularly critical in the low stiffness ratio regime, where the critical conditions for primary and secondary instabilities move closer together. Amongst all possible secondary bifurcations, the mode of period-doubling plays a central role - it is energetically favorable over all other modes. Yet, we can numerically suppress period-doubling, by choosing boundary conditions, which favor alternative higher order modes. Our results suggest that in the low stiffness regime, pattern formation is highly sensitive to small imperfections: surface morphologies emerge rapidly, change spontaneously, and quickly become immensely complex. This is a common paradigm in developmental biology. Our results have significantly applications in the morphogenesis of living systems where growth is progressive and stiffness ratios are low.
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