International Journal of Solids and Structures
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.
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 Faculty Publications. 310.
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