Buckling and twisting of advanced materials into morphable 3D mesostructures

Abstract

Recently developed methods in mechanically guided assembly provide deterministic access to wide-ranging classes of complex, 3D structures in high-performance functional materials, with characteristic length scales that can range from nanometers to centimeters. These processes exploit stress relaxation in prestretched elastomeric platforms to affect transformation of 2D precursors into 3D shapes by in- and out-of-plane translational displacements. This paper introduces a scheme for introducing local twisting deformations into this process, thereby providing access to 3D mesostructures that have strong, local levels of chirality and other previously inaccessible geometrical features. Here, elastomeric assembly platforms segmented into interconnected, rotatable units generate in-plane torques imposed through bonding sites at engineered locations across the 2D precursors during the process of stress relaxation. Nearly 2 dozen examples illustrate the ideas through a diverse variety of 3D structures, including those with designs inspired by the ancient arts of origami/kirigami and with layouts that can morph into different shapes. A mechanically tunable, multilayered chiral 3D metamaterial configured for operation in the terahertz regime serves as an application example guided by finite-element analysis and electromagnetic modeling.

Keywords: kirigami; metamaterials; origami; three-dimensional fabrication.

Fig. 1.

Three-dimensional morphable mesostructures formed by mechanically guided buckling and twisting on elastomeric kirigami substrates. (A) Conceptual illustration of the fabrication process, through a sequence of FEA results: (i) prestretching a substrate with engineered kirigami cuts (key geometric parameters labeled in the magnified image) to 100% biaxial strain; (ii) bonding of a 2D precursor onto the prestretched kirigami substrate at selected regions (circular pads); (iii) releasing of the substrate prestrain to 40%, thereby causing the structure to buckle; (iv) further releasing of the substrate prestrain to 0%, thereby causing the structure to twist. (B) Experimental images (optical) of 3D structures that correspond to those predicted by FEA in A. (C) Plot of the rotation angles at the centers of an individual square unit in a typical kirigami elastomer substrate as a function of the applied biaxial strain. (D) Schematic illustration [top view and side view (dashed Inset)] of 2 different 3D ribbon shapes on a kirigami substrate at different stages of released prestrain. Shape I results from the release of stretching of the square units in the substrate (ε_prestrain = 40%), thereby causing a buckling deformation of the ribbon. Shape II results from the release of both stretching and rotating of these units (ε_prestrain = 0%), thereby causing twisting of the ribbon. (Scale bars, 500 µm.)

Fig. 2.

Dependence of the spatial maximum of the maximum principal strain and the unit rotation angles on the stretched kirigami substrate, as a function of geometric parameters of the cuts and applied biaxial prestrain from FEA. (A) Plots of the spatial maximum of the maximum principal strain as a function of the biaxial prestrain with different values of $2\delta /D$ (from 0.05 to 1). (B) Plots of the spatial maximum of the maximum principal strain as a function of $2\delta /D$ with different biaxial prestrain (24, 41, 66, and 100%). (C) Color representations of the distributions of the maximum principal strain in kirigami substrates with different $2\delta /D$ values and biaxial prestrain. (D) Plots of the rotation angle at the centers of the unit cells as a function of the biaxial prestrain with different $2\delta /D$ values (from 0.05 to 1). (E) Plots of the rotation angle at the centers of unit cells as a function of the $2\delta /D$ values with different biaxial prestrain (24, 41, 66, and 100%). (F) Color representations of the distributions of rotation angle in kirigami substrates with different $2\delta /D$ values and biaxial prestrain. The cutting width $w/D$ is 0.02 in these plots.

Fig. 3.

Three-dimensional morphable mesostructures based on buckling and twisting with diverse geometries and materials. (A) Two-dimensional geometries, FEA predictions, and experimental images (optical) of a morphable 3D chiral, propeller structure. (B) Two-dimensional geometries, FEA predictions, and experimental images (optical) of a morphable 3D box structure. Shape I and shape II correspond to the 3D shapes after releasing of the stretching mode (prestrain from 100 to 40%) and releasing of the rotating mode (prestrain from 40 to 0%). (C) Two-dimensional geometries, FEA predictions (showing normalized displacements in z direction), and experimental images (optical) of an array of creased structures based on twisting-induced folding. (D) Two-level square substrate cut pattern, 2D geometries, FEA predictions, and experimental images (optical) of a structure with multiple creases. (E) FEA predictions and experimental images (optical) of 3 mesostructures constructed with diverse materials. Scale bars, 1 mm for structures in A–D; 2 mm for Cu structures (E, Top); and 500 μm for Si/SU8 and SMP structures (E, Middle and Bottom).

Fig. 4.

Morphable 3D mesostructures constructed by incorporating twisting into a loading-path controlled scheme for mechanical assembly on kirigami substrates. (A) Temporal sequence of changes in applied strains for 2 different loading paths. (B) Undeformed and deformed configurations of an elastomeric substrate with rectangular units (aspect ratio = 2.5) at different positions (corresponding to the positions in A) along the loading paths. (C) Two-dimensional geometries, FEA predictions, and experimental images (optical) of 3 morphable 3D mesostructures that result from different loading paths on kirigami substrates. (Scale bars, 1 mm.)

Fig. 5.

Applications of 3D morphable multilayered microstructures as mechanically tunable optical chiral metamaterials. (A) Two-dimensional geometries, FEA predictions, and scanning electron microscope images of 2 exemplary 3D morphable multilayered microstructures on kirigami substrates with 2 different 3D shapes. (B) Measured and simulated optical CD of a morphable 3D trilayer microstructure with two 3D shapes (design I in A) in the 0.2–0.4-THz frequency range. (C) Simulated time-averaged surface current distributions in the 3D morphable microstructure with two 3D shapes (design I in A) under LCP and RCP. (Scale bars, 200 µm.)