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Buckling and post-buckling analysis of thin films is significant for the design, optimization and fabrication of stretchable electronic devices based on compression buckling. Aiming to achieve a more accurate and reliable way for the dynamic stability analysis of stiff films considering geometric nonlinearity, an implicit dynamic element-free Galerkin method based on the Strain-Rotation decomposition theorem is developed in this paper to investigate the dynamic buckling behavior of stiff films. Convergence and comparison studies are conducted to validate the numerical stability and accuracy of the proposed numerical method. The influences of compression loading rate and thickness to length ratio on the buckling/post-buckling of stiff thin films subjected to dynamic load are numerically analyzed and discussed in parametric studies. This work provides an effective way for the engineering computation of flexible electronic technology.

Morphable three-dimensional (3D) structures capable of reversible shape changes between distinct geometric configurations have widespread applications in many important engineering areas. Recent advances in mechanically-guided 3D assembly provided a powerful approach to achieve morphable 3D mesostructures in a broad set of high-performance materials, over length scales from several micrometers to tens of centimeters. This approach relies on prestrained elastomer substrates released with different sequences to trigger the stabilization of distinct 3D buckling modes in specially engineered 2D precursor structures. Many of the reported 2D precursor structures are constructed with ribbon components that incorporate creases with reduced stiffness at strategic locations. The design of crease geometries and crease locations is essential to the structural bistability through this loading-path approach, which requires the development of a theory to serve as the design basis. This paper presents a finite-deformation model to analyze the stability of different buckling modes induced during the simultaneous and sequential compressions of structures with cross-shaped ribbon geometries, a very representative class of precursor patterns. By introducing a perturbation method to obtain an analytic solution to the deformed configuration of a uniform beam, a theoretical model is developed to predict the postbuckling deformations in cross-shaped ribbon structures with a prescribed number of creases. Based on the analyses of the strain-energy landscape, a stability coefficient is proposed to evaluate the bistability of cross-shaped ribbon structures. The developed model is validated by finite element analyses (FEA) and experimental measurements of structures with a broad range of cross-shaped geometries. This model allows the construction of design diagrams to identify the bistability for a variety of geometric parameters, including the normalized width and location of each crease in the cross-shaped patterns. These results elucidate how to select the various design parameters to achieve bistable 3D structures through the loading-path approach. Furthermore, the developed model is extended to the bistability analyses of precursor structures with generalized cross patterns and cross-shaped patterns consisting of locally stiffened elements. This study offers a theoretical reference for the design of ribbon-shaped mesostructures to achieve diverse morphable microelectronic devices.

Stretchable electronic systems based on controllable compressive buckling can be further endowed with superior compliance and stretchability. However, such systems are usually restrained by the interference from different loads in practical applications, so it is desirable to study their dynamic behaviors. In this article, an analytical model is developed on the linear free vibrations of a buckled thin film attached to a flexible substrate, whose results can be verified by the finite element analysis (FEA). In the model, the film is considered as an Euler–Bernoulli beam, and the substrate is assumed as a Pasternak foundation with Kelvin viscoelasticity. The natural frequencies and their corresponding vibration modes of the buckled film with the substrate are obtained. The results indicate that the increases of stiffness and damping of the substrate have negative effects on the natural frequencies. The damping influences the low-order modes a lot but not the high-order modes. This study may provide some suggestions for the dynamic design of buckled thin films on flexible substrates. For example, the controllable vibration attenuation can be achieved by choosing the substrate with appropriate viscoelasticity.

Buckling stability of thin films on compliant substrates is universal and essential in stretchable electronics. The dynamic behaviors of this special system are unavoidable when the stretchable electronics are in real applications. In this paper, an analytical model is established to investigate the vibration of post-buckled thin films on a compliant substrate by accounting for the substrate as an elastic foundation. The analytical predictions of natural frequencies and vibration modes of the system are systematically investigated. The results may serve as guidance for the dynamic design of the thin film on compliant substrates to avoid resonance in the noise environment.

Popping materials and devices from 2D into 3D Curved, thin, flexible complex three-dimensional (3D) structures can be very hard to manufacture at small length scales. Xu et al. develop an ingenious design strategy for the microfabrication of complex geometric 3D mesostructures that derive from the out-of-plane buckling of an originally planar structural layout (see the Perspective by Ye and Tsukruk). Finite element analysis of the mechanics makes it possible to design the two 2D patterns, which is then attached to a previously strained substrate at a number of points. Relaxing of the substrate causes the patterned material to bend and buckle, leading to its 3D shape. Science , this issue p. 154 ; see also p. 130

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 micrometers to millimeters. The approaches rely on elastomer platforms deformed in different time sequences to elastically alter the 3D geometries of supported mesostructures via non-linear 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 radio frequency circuit and a concealable electromagnetic device provide examples of functionally reconfigurable microelectronic devices.

Buckling-driven assembly of 3D mesostructures from releasable multilayers offers versatile design options for unique applications., Capabilities for assembly of three-dimensional (3D) micro/nanostructures in advanced materials have important implications across a broad range of application areas, reaching nearly every class of microsystem technology. Approaches that rely on the controlled, compressive buckling of 2D precursors are promising because of their demonstrated compatibility with the most sophisticated planar technologies, where materials include inorganic semiconductors, polymers, metals, and various heterogeneous combinations, spanning length scales from submicrometer to centimeter dimensions. We introduce a set of fabrication techniques and design concepts that bypass certain constraints set by the underlying physics and geometrical properties of the assembly processes associated with the original versions of these methods. In particular, the use of releasable, multilayer 2D precursors provides access to complex 3D topologies, including dense architectures with nested layouts, controlled points of entanglement, and other previously unobtainable layouts. Furthermore, the simultaneous, coordinated assembly of additional structures can enhance the structural stability and drive the motion of extended features in these systems. The resulting 3D mesostructures, demonstrated in a diverse set of more than 40 different examples with feature sizes from micrometers to centimeters, offer unique possibilities in device design. A 3D spiral inductor for near-field communication represents an example where these ideas enable enhanced quality (Q) factors and broader working angles compared to those of conventional 2D counterparts.

Formation of three-dimensional (3D) mesostructures in advanced functional materials is of growing interest due to the widepread 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 heteogenous intergration. This paper introduces ideas that extend the levels of control and and the range of 3D layouts that are achievable in these systems. 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 micro-balance illustrates the utility of these ideas in a simple structure designed for mass measurement.

Lithographically defined electrical interconnects with thin, filamentary serpentine layouts have been widely explored for use in stretchable electronics supported by elastomeric substrates. We present a systematic and thorough study of buckling physics in such stretchable serpentine microstructures, and a strategic design of the serpentine layout for an ultra-stretchable electrode, via analytical models, finite element method (FEM) computations, and quantitative experiments. Both the onset of buckling and the postbuckling behaviors are examined, to determine scaling laws for the critical buckling strain and the limits of elastic behavior. Two buckling modes, namely the symmetric and anti-symmetric modes, are identified and analyzed, with experimental images and numerical results that show remarkable levels of agreement for the associated postbuckling processes. Based on these studies and an optimization of the design layout, we demonstrate routes for application of serpentine interconnects in an ultra-stretchable electrode that offer, simultaneously, an areal coverage as high as 81% and a biaxial stretchability as large as ∼170%.

Fractal-inspired designs for interconnects that join rigid, functional devices can ensure mechanical integrity in stretchable electronic systems under extreme deformations. The bonding configuration of such interconnects with the elastomer substrate is crucial to the resulting deformation modes, and therefore the stretchability of the entire system. In this study, both theoretical and experimental analyses are performed for postbuckling of fractal serpentine interconnects partially bonded to the substrate. The deformation behaviors and the elastic stretchability of such systems are systematically explored, and compared to counterparts that are not bonded at all to the substrate.