Mechanics of nanowire buckling on elastomeric substrates with consideration of surface stress effects

• The surface stress effects are considered in the analysis of the out-of-surface buckling behavior of a nanowire integrated on an elastomeric substrate.
• The surface effects can greatly influence the critical buckling strain and potential energy of the buckled nanowire.
• For nanowires with small cross section sizes and low bulk modulus, the buckling mode may be changed by tuning the surface properties.
• The range of the parameters where the out-of-surface buckling and in-surface buckling take place is explicitly determined with the energy criterion.

In this paper, the surface stress effects are considered in the analysis of nanowire buckling on elastomeric substrates. Theoretical solutions of the buckling wavenumber, amplitude, and the critical strain for the out-of-surface buckling are derived firstly. After that, the influences of the surface properties, size, bulk modulus, and the shape of the cross section of the nanowire on the out-of-surface and in-surface buckling behavior are systematically discussed. Our study indicates that the buckling mode of the nanowire can be greatly influenced by the surface effects. For nanowires with small cross section sizes and low bulk modulus, the buckling mode may be varied by tuning the surface properties. Based on the energy criterion, we explicitly determine the range of the parameters where the two buckling modes take place.