Self-folding of a slender microbeam and thin film: an elastica model

Thin wires or films can be spontaneously folded into different shapes, and such phenomena hold promising applications in engineering, especially at micro and nanoscales.Based upon the established potential energy functional, we derived the governing equation and adhesive boundary condition for a self-folding system.Considering the inextensible condition of the structure, a closed-form solution for the deflection of a racket-like structure was obtained in terms of elliptical integrals, which applies for both macro and nanodimensions.We then determined the critical adhesive length under specified geometric and energetic constraints.The results show that self-folding is energetically favorable and thermodynamically stable with the cohesive work being strong enough and the structure being sufficiently flexible.As soon as the self-folding configuration is formed, the slender structure must possess an initial adhesive length.These conclusions are beneficial for the design of nanostructures, and the enhancement of their mechanical, chemical, optical, and electronic properties.