Elastically Buckled Film-Substrate System as a Two-dimensional Crystal

TL;DR

This paper develops a nonlinear elastic model for film-substrate buckling, revealing its equivalence to a two-dimensional crystal and demonstrating dynamic modulation through cyclic stress simulations.

Contribution

It reformulates elastic buckling theory using phase-field crystal concepts, providing a quantitative phase diagram and linking buckling patterns to 2D crystal structures.

Findings

Quantitative agreement with experimental buckling transitions

Emergence of hexagonal buckling as a 2D crystal

Simulation of cyclic stress inducing reversible buckling

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 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.