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Creating Two-Dimensional Patterned Substrates for Protein and Cell Confinement
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Pattern selection when a layer buckles on a soft substrate.

Nontawit Cheewaruangroj1, John S Biggins

  • 1Cavendish Laboratory, University of Cambridge, 19 JJ Thomson Avenue, Cambridge CB3 0HE, UK. jsb56@cam.ac.uk.

Soft Matter
|May 2, 2019
PubMed
Summary
This summary is machine-generated.

Equibiaxial growth in neo-Hookean elastic layers causes buckling into patterns. Hexagonal patterns form subcritically and are energetically favored due to broken symmetry, unlike square or stripe patterns.

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Area of Science:

  • Solid Mechanics
  • Materials Science
  • Physics of Soft Matter

Background:

  • Equibiaxial growth of elastic layers on substrates can lead to pattern formation.
  • Understanding the selection of these patterns requires advanced theoretical and numerical approaches.

Purpose of the Study:

  • To predict the topographic patterns formed in a growing neo-Hookean elastic layer adhered to a neo-Hookean substrate.
  • To analyze the energetic favorability of hexagonal, square, and stripe patterns beyond the buckling threshold.

Main Methods:

  • Higher-order perturbation theory to expand elastic energy series.
  • Finite element numerics to verify theoretical predictions.
  • Landau-like energy expansion in topography amplitude.

Main Results:

  • Square and stripe patterns exhibit supercritical instabilities due to topography inversion symmetry.
  • Hexagonal patterns display subcritical instabilities, making them energetically favored, with dents favored in incompressible systems and bumps in compressible ones.
  • A stiff layer between identical substrates/superstrates leads to supercritical hexagons and favored square patterns.

Conclusions:

  • Large strain geometry breaks topography inversion symmetry, explaining experimentally observed hexagonal dent patterns.
  • Previous simplified models incorrectly predicted square patterns by assuming symmetry.
  • The study provides a robust framework for predicting pattern selection in growing elastic systems.