Analytical Solutions for the Lateral-Torsional Buckling of Serpentine Interconnects in Stretchable Electronics

Abstract

Serpentine interconnects, as an integral part of island-bridge layouts, enable extremely large reversible deformation under the action of mechanical loads and are thus widely used in the emerging new field of stretchable electronics. In this paper, the lateral-torsional buckling is analytically studied for a simplified S-shaped serpentine structure that consists of five straight components rigidly connected at point joints. Simple analytic scaling laws between the dimensionless critical buckling load and the aspect ratio of the serpentine structure are newly derived and uniformly expressed in terms of generalized hypergeometric series for various types of boundary conditions, which can serve as the benchmark of numerical simulations. These scaling laws, fully verified by finite element analysis, may well capture the implied connection between stretching- and compression-induced buckling, the strong dependence of buckling modes on end conditions, and the monotonic/asymptotic properties of the critical load with respect to the aspect ratio of serpentine structures.