Three-dimensional (3D) helical mesostructures are attractive for applications in a broad range of microsystem technologies, due to their mechanical and electromagnetic properties as stretchable interconnects, radio frequency antennas and others. Controlled compressive buckling of 2D serpentine-shaped ribbons provides a strategy to formation of such structures in wide ranging classes of materials (from soft polymers to brittle inorganic semiconductors) and length scales (from nanometer to centimeter), with an ability for automated, parallel assembly over large areas. The underlying relations between the helical configurations and fabrication parameters require a relevant theory as the basis of design for practical applications. Here, we present an analytic model of compressive buckling in serpentine microstructures, based on the minimization of total strain energy that results from various forms of spatially dependent deformations. Experiments at micro- and millimeter-scales, together with finite element analyses (FEA), were exploited to examine the validity of developed model. The theoretical analyses shed light on general scaling laws in terms of three groups of fabrication parameters (related to loading, material and 2D geometry), including a negligible effect of material parameters and a square root dependence of primary displacements on the compressive strain. Furthermore, analytic solutions were obtained for the key physical quantities (e.g., displacement, curvature and maximum strain). A demonstrative example illustrates how to leverage the analytic solutions in choosing the various design parameters, such that brittle fracture or plastic yield can be avoided in the assembly process.

Formation of 3D mesostructures in advanced functional materials is of growing interest due to the widespread envisioned applications of devices that exploit 3D architectures. Mechanically guided assembly based on compressive buckling of 2D precursors represents a promising method, with applicability to a diverse set of geometries and materials, including inorganic semiconductors, metals, polymers, and their heterogeneous combinations. This paper introduces ideas that extend the levels of control and the range of 3D layouts that are achievable in this manner. Here, thin, patterned layers with well-defined residual stresses influence the process of 2D to 3D geometric transformation. Systematic studies through combined analytical modeling, numerical simulations, and experimental observations demonstrate the effectiveness of the proposed strategy through ≈20 example cases with a broad range of complex 3D topologies. The results elucidate the ability of these stressed layers to alter the energy landscape associated with the transformation process and, specifically, the energy barriers that separate different stable modes in the final 3D configurations. A demonstration in a mechanically tunable microbalance illustrates the utility of these ideas in a simple structure designed for mass measurement.

Efficient and highly functional three-dimensional systems that are ubiquitous in biology suggest that similar design architectures could be useful in electronic and optoelectronic technologies, extending their levels of functionality beyond those achievable with traditional, planar two-dimensional platforms. Complex three-dimensional structures inspired by origami, kirigami have promise as routes for two-dimensional to three-dimensional transformation, but current examples lack the necessary combination of functional materials, mechanics designs, system-level architectures, and integration capabilities for practical devices with unique operational features. Here, we show that two-dimensional semiconductor/semi-metal materials can play critical roles in this context, through demonstrations of complex, mechanically assembled three-dimensional systems for light-imaging capabilities that can encompass measurements of the direction, intensity and angular divergence properties of incident light. Specifically, the mechanics of graphene and MoS2, together with strategically configured supporting polymer films, can yield arrays of photodetectors in distinct, engineered three-dimensional geometries, including octagonal prisms, octagonal prismoids, and hemispherical domes.

Three-dimensional (3D) structures capable of reversible transformations in their geometrical layouts have important applications across a broad range of areas. Most morphable 3D systems rely on concepts inspired by origami/kirigami or techniques of 3D printing with responsive materials. The development of schemes that can simultaneously apply across a wide range of size scales and with classes of advanced materials found in state-of-the-art microsystem technologies remains challenging. Here, we introduce a set of concepts for morphable 3D mesostructures in diverse materials and fully formed planar devices spanning length scales from micrometres to millimetres. The approaches rely on elastomer platforms deformed in different time sequences to elastically alter the 3D geometries of supported mesostructures via nonlinear mechanical buckling. Over 20 examples have been experimentally and theoretically investigated, including mesostructures that can be reshaped between different geometries as well as those that can morph into three or more distinct states. An adaptive radiofrequency circuit and a concealable electromagnetic device provide examples of functionally reconfigurable microelectronic devices.

Complex 3D organizations of materials represent ubiquitous structural motifs found in the most sophisticated forms of matter, the most notable of which are in life-sustaining hierarchical structures found in biology, but where simpler examples also exist as dense multilayered constructs in high-performance electronics. Each class of system evinces specific enabling forms of assembly to establish their functional organization at length scales not dissimilar to tissue-level constructs. This study describes materials and means of assembly that extend and join these disparate systems-schemes for the functional integration of soft and biological materials with synthetic 3D microscale, open frameworks that can leverage the most advanced forms of multilayer electronic technologies, including device-grade semiconductors such as monocrystalline silicon. Cellular migration behaviors, temporal dependencies of their growth, and contact guidance cues provided by the nonplanarity of these frameworks illustrate design criteria useful for their functional integration with living matter (e.g., NIH 3T3 fibroblast and primary rat dorsal root ganglion cell cultures).