ORCID ID
Ryan, Shawn/0000-0003-2468-1827
Document Type
Article
Publication Date
12-15-2012
Publication Title
International Journal of Solids and Structures
Abstract
We study a variation on the classical problem of the buckling of an elastica. The elastica models a nanoscale sheet that interacts with a rigid substrate by intermolecular forces. We formulate a buckling problem in which the sheet is perpendicular to the substrate and a load is applied to the edge of the sheet further from the substrate. Our study is motivated by problems in nanomechanics such as the bending of a graphene sheet interacting with a rigid substrate by van der Waals forces. After identifying a trivial branch, we combine computation and analysis to determine the stability and bifurcations of solutions along this branch. We also study the boundary-layer problem that arises if the length of the sheet is large compared to the characteristic length over which the van der Waals interaction is significant.
Repository Citation
Ryan, Shawn D.; Golovaty, Dmitry; and Wilber, Patrick, "An Elastica Model of the Buckling of a Nanoscale Sheet Perpendicular to a Rigid Substrate" (2012). Mathematics and Statistics Faculty Publications. 310.
https://engagedscholarship.csuohio.edu/scimath_facpub/310
DOI
10.1016/j.ijsolstr.2012.07.026
Version
Postprint
Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.
Volume
49
Issue
26
