While planar displays remain the dominant form of displays, emerging applications, from wearable devices, smart skin to curved optics, soft robotics, and home embellishment, require three-dimensional curved structures. Consequently, curved displays have gained popularity as one of next-generation display technologies that combines functionality and attractivity. With consumers’ ever-increasing demand for both aesthetics and practicality, curved displays have seen a recent surge in development.

Bending has been a widely used method to realize curved displays. Flexible display production technology has matured and is currently utilized in various electronic devices, lighting, billboards, etc. Typically, organic light-emitting diode (OLED) displays in foldable smartphones are a prime example of the rapid development of flexible displays. However, planar-substrate-based flexible displays are intrinsically incompatible with non-developable surfaces. It has been shown from fundamental theorems of differential geometry that the Gaussian curvature remains invariant in isometric transformations. As a result, flexible but non-stretchable planar displays can only be bent into developable surfaces, such as tubes or cones.

In line with the methodologies for stretchable or its enabled curved electronics in general, several methods exist to make a display stretchable. Formerly, the dominant scheme was to mount rigid components onto an elastic substrate, or to connect rigid islands with stretchable interconnects to achieve global stretchability. However, due to the low stiffness and short fatigue life of stretchable materials (e.g. polydimethylsiloxane (PDMS), Eco-flex, dragon skin, PEDOT), the luminescent or conductive materials embedded in them are prone to damage. For example, Larson et al. reported a stretchable capacitive display driven by AC. The ZnS phosphors were embedded in Eco-Flex and sandwiched in electrodes made of elastic matrix (polyacrylamide, PAM). The phosphors emit light when an AC voltage is applied to the electrode. Unfortunately, because the silicone and hydrogel undergo large deformation under tension, the density of the phosphors decreases and even cracks occur, leading to device failure. Another feasible strategy is to connect rigid islands of illuminant elements with geometrically stretchable interconnections. Rogers et al. developed a technique to connect the μ-ILED array using serpentine interconnects and then transfer to 400 μm thick pre-stretched PDMS slices and achieve 48% stretchability. In addition, Tripathi et al. reported a 32 × 32 AMLED stretchable display connected with 2 mm long horseshoe metal interconnects. However, such displays based on stretchable interconnects often rely on elastic material as the substrate, which creates limitations similar to those described above. In addition, stretchable interconnects expose the shortcomings of complex structure, difficult manufacturing and high cost, which are not conducive to mass production.

Lately, some original schemes have emerged to implement stretchable or curved displays. Xiang et al. reported that the display textiles woven from conductive weft and luminescent warp fibers present flexibility, water resistance, and interaction function, etc. However, the degradation of organic materials (such as electroluminescence materials) used in displays still exists. Besides, Orderly arranged sub-pixels (RGB) are indispensable for colorful display (such as mainstream PenTile and Delta arrangement for OLED), while the weft-warp arranged electroluminescent units almost obliterates the potential for achieving colorful display textiles. Deng et al. proposed a scheme combining programmed origami tessellations with LED chips to realize a curved display. They optimized the original Miura-origami pattern by entitling the vertexes extra degrees of freedom to design tessellation patterns and folded it into the desired shapes with minimum total potential energy. Unfortunately, the display fabricated by MEMS-based process is inadequate for the larger curved surface.

Auxetics, known as the structure or materials with negative Poisson's ratio, has been studied geometrically and mechanically for decades since the 1980s. Various cut units that make up 2D auxetic structures have been developed, including rectangles, triangles, hexagons, stars, and their hybrids, etc. Typically, the auxetic structure composed of square tessellations has the potential to fabricate stretchable display due to its regular structure and homogeneous global deformation when stretched. However, traditional auxetic structures consisting of rotating units are often damaged due to the enormous strains at rigid nodes, which obliterates the possibility of laying circuits. Further, to achieve higher stretchability of the kirigami-based auxetic metastructures, Tang et al. designed the geometry and structure of the cut units by combining the line cut, cut-out, and hierarchy of the structure, which dramatically improved its stretchability. However, line cut can only produce stretchable metastructures. The incompressibility beyond their inherent cut structure will restrict their potential applications in electronics, where stretchability and compressibility are often required for functionality.

In this study, inspired by kirigami-based auxetic metastructures, we propose a concept to fabricate a stretchable and adaptive curved display by integrating thin vertical interconnects connected rotating squares and LED chips. Thin vertical interconnects overcome the inability to pattern circuits at rigid nodes, and the space they free up allows the rotating squares to be compressible. We constructed the matrix circuit on an ultra-thin FPCB and patterned the vertical interconnects layout by laser cutting. Surface mount technology (SMT) was used to place illuminant elements onto the FPCB and the molds guidance process was used to fold planar interconnects into the vertical configuration. After encapsulation, the display can be locally stretched or compressed to match the surface with different Gaussian curvature adaptively owe to vertical interconnects distortion. Digital image correlation (DIC) and 3D finite element method (FEM) model of rotating square structure were used to analyze its local and global mechanical behavior and geometrical morphology under tension. It presents that the introduction of vertical interconnects into rotating square tessellations dramatically reduces the stress concentration effect and improves the adaptability of the structure.