Buckling of Graphene Layers Supported by Rigid Substrates

TL;DR

This paper develops a nonlinear continuum model to analyze the buckling behavior of supported graphene sheets, examining how boundary conditions, substrate composition, and length influence buckling, with numerical illustrations of snap-buckling phenomena.

Contribution

It introduces a novel nonlinear continuum model for supported graphene sheets and applies bifurcation theory to study buckling behavior under various conditions.

Findings

Buckling depends on boundary conditions and substrate composition.

Numerical results show snap-buckling behavior.

Model provides insights into stability of supported graphene sheets.

Abstract

We formulate a nonlinear continuum model of a graphene sheet supported by a flat rigid substrate. The sheet is parallel to the substrate and loaded on a pair of opposite edges. A typical cross-section of the sheet is modeled as an elastica. We use elementary techniques from bifurcation theory to investigate how the buckling of the sheet depends on the boundary conditions, the composition of the substrate, and the length of the sheet. We also present numerical results that illustrate snap-buckling of the sheet.