Revisiting the wrinkling of elastic bilayers II: Post-bifurcation analysis

Hamza Alawiye*, Patrick E. Farrell, Alain Goriely

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

Abstract

We examine the problem of an elastic film bonded to an elastic substrate and subjected to compressive stress (induced by growth of the film or lateral compression of the whole system). Following the linear analysis previously carried out to determine the critical growth/compression ratio required to induce wrinkling in the film, we carry out a weakly-nonlinear analysis to derive an amplitude equation that describes the evolution of the wrinkling amplitude beyond the bifurcation point. We carry out a comprehensive numerical bifurcation analysis of the problem using the finite element method and show excellent agreements between the weakly-nonlinear analysis and the numerical experiments. We are also able to solve directly for the bifurcation point in our discretized system and characterize the effect of implementation details such as the aspect ratio of the computational domain on the observed bifurcation point. Finally, we explore solutions of the amplitude equation in the case that the wrinkling amplitude is allowed to vary over long spatial and/or temporal scales.

Original languageEnglish
Article number104053
JournalJournal of the Mechanics and Physics of Solids
Volume143
DOIs
Publication statusPublished - Oct 2020

Keywords

  • Asymptotic analysis
  • Buckling
  • Finite elements
  • Nonlinear elasticity
  • Stability and bifurcation

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