A finite deformation model of planar serpentine interconnects for stretchable electronics

Abstract

Lithographically defined interconnects with filamentary, serpentine configurations have been widely used in various forms of stretchable electronic devices, owing to the ultra-high stretchability that can be achieved and the relative simple geometry that facilitates the design and fabrication. Theoretical models of serpentine interconnects developed previously for predicting the performance of stretchability were mainly based on the theory of infinitesimal deformation. This assumption, however, does not hold for the interconnects that undergo large levels of deformations before the structural failure. Here, an analytic model of serpentine interconnects is developed starting from the finite deformation theory of planar, curved beams. Finite element analyses (FEA) of the serpentine interconnects with a wide range of geometric parameters were performed to validate the developed model. Comparisons of the predicted stretchability to the estimations of linear models provide quantitative insights into the effect of finite deformation. Both the theoretical and numerical results indicate that a considerable overestimation (e.g., > 50% relatively) of the stretchability can be induced by the linear model for many representative shapes of serpentine interconnects. Furthermore, a simplified analytic solution of the stretchability is obtained by using an approximate model to characterize the nonlinear effect. The developed models can be used to facilitate the designs of serpentine interconnects in future applications.

Materials and Structures toward Soft Electronics

“…Serpentine interconnections have the meander‐shaped layout consisting of a number of periodically distributed unit cells that comprise two half‐circles connected by the straight lines ( Figure a) . When responding to the applied strain, the serpentine interconnections can rotate in plane and also buckle out of plane, resulting in greatly reduced strains in the serpentine material per se, as well as low effective stiffness on the system level .…”

Flexible and Stretchable Smart Display: Materials, Fabrication, Device Design, and System Integration

“…One approach focuses on engineering new structural constructs from conventionally established materials to engender flexibility and stretchability, whereas the other focuses on the use of nanomaterials and their percolation networks. Some representative structural layouts to accommodate flexibility and stretchability include ultrathin geometries, prestrained wavy structures, and strain‐tolerant designs such as serpentine interconnects . As several excellent reviews on flexible and stretchable electrodes based on structural methods are already available, we mainly focus on discussion of deformable electrodes based on nanomaterials and their percolating networks, such as Ag NWs, CNTs, graphene, and their hybrids.…”

Viscoelastic Characteristics of Mechanically Assembled Three-Dimensional Structures Formed by Compressive Buckling

“…Because of the base has larger modulus than the buckled ribbon, its deformation can be neglected during the vibration analysis. Due to the ribbon thickness (h) is much smaller than its width (b) and length (L), finite-deformation beam theory with no shear deformation [68][69][70] is adopted to establish an analytical model. In general, the deformations of a planar ribbon can be described by the displacement of the central axis u ¼ u i E i [71] and the twist angle w [68], where E i is the unit vector before deformation in the Cartesian coordinates (X, Y, Z), which all calculations are based on.…”