Mechanics Design for Buckling of Thin Ribbons on an Elastomeric Substrate Without Material Failure

Abstract

The ribbons selectively bonded to a prestrained elastomeric substrate may buckle into three-dimensional (3D) microstructures after the prestrain release, leading to three possible deformation modes, global, local, and no buckling, depending on the adhesion between the ribbons and substrate. This note establishes analytically the critical length-to-thickness ratio of ribbons, above which the global buckling mode (preferred for mechanically guided 3D deterministic assembly) occurs without material failure.