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Elastically buckled film-substrate system as a two-dimensional crystal

Wenqing Zhu (朱文清)*

  • *Contact author: wz379@cam.ac.uk
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Phys. Rev. B 112, L100101 – Published 4 September, 2025

DOI: https://doi.org/10.1103/96bg-xbc1

Abstract

Compressive mechanical stress exceeding a critical value leads to the formation of periodic surface buckling patterns in film-substrate systems. A comprehensive understanding of this buckling phenomenon is essential in applications where the surface topologies are modulated to achieve multifunctionalities. Here, we reformulate the elastic theory of a film-substrate system by treating the compliant substrate as a nonlinear elastic solid. The resulting elastic free energy functional of the deflection field is shown to be equivalent to a minimal density functional of the phase-field crystal theory plus a Gaussian curvature-related term. The proposed elastic model constructs a phase diagram based on free energy minimization, quantitatively agreeing with the buckling transitions observed in previous experiments. The emerging hexagonal buckling system is shown to be equivalent to a two-dimensional crystal with proper scalings. We further conducted simulations of repeated buckling under cyclic stress to demonstrate a dynamically modulated structural adhesive, which resembles the physical process of repeated crystallization and melting near a critical temperature.

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Phys. Rev. B 112, L100101– Published 4 September, 2025
  • Received 20 February 2025
  • Accepted 22 August 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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