Mechanics of buckled serpentine structures formed via mechanics-guided, deterministic three-dimensional assembly

Many forms of stretchable electronic systems incorporate planar, filamentary serpentine structures to realize high levels of stretchability in ways that allow the use of high performance of inorganic functional materials. Recent advances in mechanics-guided, deterministic three-dimensional (3D) assembly provide routes to transform these traditional, two-dimensional (2D) serpentine layouts into 3D architectures, with significantly improved mechanics and potential for applications in energy harvesters, pressure sensors, soft robotics, biomedical devices and other classes of technologies. One challenge is that, by comparison to other geometries, the relatively low bending stiffnesses of the serpentine structures create difficulties in overcoming the interfacial adhesion energy to allow delamination from the underlying elastomeric substrate, as an essential aspect of the assembly process. An additional complication is that many of the functional materials widely used in stretchable electronics have a low strain threshold for failure such that damage can occur during buckling-induced assembly. Therefore, a clear understanding of the mechanics of buckled serpentine structures is essential to their design, fabrication and application. Through theoretical modeling and finite element analysis, we present models for the phase diagram of buckled states and the maximum strain in the globally-buckled serpentine structures. The analysis yield formulae in concise and explicit forms, clearly showing the effect of geometry/material parameters and the prestrain. The results can be used in designing buckled serpentine structures to ensure their compatibility with the mechanics-guided, deterministic 3D assembly and facilitate their applications in stretchable electronics.