Elastically Buckled Film-Substrate System as a Two-dimensional Crystal
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866929720332910592 |
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| author | Zhu, Wenqing |
| author_facet | Zhu, Wenqing |
| contents | 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 desired in applications where the surface topologies are modulated to achieve multifunctionalities. Here we reformulate the finite-deformation 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 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 former 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_13864 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Elastically Buckled Film-Substrate System as a Two-dimensional Crystal Zhu, Wenqing Materials Science 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 desired in applications where the surface topologies are modulated to achieve multifunctionalities. Here we reformulate the finite-deformation 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 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 former 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. |
| title | Elastically Buckled Film-Substrate System as a Two-dimensional Crystal |
| topic | Materials Science |
| url | https://arxiv.org/abs/2502.13864 |