title: Wrinkling instabilities in soft bilayered systems.
abstract: 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.'
authors.affiliation: Department of Applied Mechanics, University of Erlangen-Nuremberg, 91058 Erlangen, Germany.
authors.forename: Silvia
authors.initials: S
authors.lastname: Budday
authors.affiliation: Department of Applied Mechanics, University of Erlangen-Nuremberg, 91058 Erlangen, Germany.
authors.forename: Sebastian
authors.initials: S
authors.lastname: Andres
authors.affiliation: Department of Applied Mechanics, University of Erlangen-Nuremberg, 91058 Erlangen, Germany.
authors.forename: Bastian
authors.initials: B
authors.lastname: Walter
authors.affiliation: Department of Applied Mechanics, University of Erlangen-Nuremberg, 91058 Erlangen, Germany.
authors.forename: Paul
authors.identifier: http://orcid.org/0000-0003-1490-947X
authors.initials: P
authors.lastname: Steinmann
authors.affiliation: Department of Mechanical Engineering, Stanford University, Stanford, CA 94305, USA ekuhl@stanford.edu.
authors.forename: Ellen
authors.identifier: http://orcid.org/0000-0002-6283-935X
authors.initials: E
authors.lastname: Kuhl
keywords: bifurcation; instability; period-doubling; period-tripling; thin film