Postbuckling analyses of frame mesostructures consisting of straight ribbons for mechanically guided three-dimensional assembly

Abstract

Mechanically guided assembly through buckling-induced two-dimensional (2D)-to- three-dimensional (3D) transformation represents a versatile approach to the formation of 3D mesostructures, thanks to the demonstrated applicability to a wide range of length scales (from tens of nanometres to centimetres) and material types (from semiconductors, metals to polymers and ceramics). In many demonstrated examples of device applications, the 2D precursor structures are composed of ribbon-type components, and some of them exhibit frame geometries consisting of multiple straight ribbons. The coupling of bending/twisting deformations among various ribbon components of the frame mesostructures makes the analyses more complicated than the case with a single component, which requires the development of a relevant theory to serve as the basis of design optimization in practical applications. Here, an analytic model of compressive buckling in such frame mesostructures is presented in the framework of energetic approach, taking into account the contributions of spatial bending deformations and twisting deformations. Three different frame geometries are studied, including ‘+’, ‘T' and ‘H' shaped designs. As validated by the experiments and finite-element analyses (FEA), the developed model can predict accurately the assembled 3D configurations during the postbuckling of different precursor shapes. Furthermore, the theoretical analyses provide approximate analytic solutions to some key physical quantities (e.g. the maximum out-of-plane displacements and maximum strains), which can be used as design references in practical applications.

Mechanically-Guided 3D Assembly for Architected Flexible Electronics

“…Various 2D precursor designs, involving filamentary, ,,, kirigami, origami, , multilayer, and microlattice designs, were developed to enable formation of 3D architectures with high degrees of complexities and diversities (Figure b). Filamentary designs (Figure b, filamentary) typically consist of slender thin ribbons to ensure that large out-of-plane bending and twisting deformations can be induced to realize their transformation into desired 3D configurations such as helices and frameworks . Kirigami designs (Figure b, kirigami) feature the reduction of stress concentration during buckling-guided assembly by introducing strategic cuts, thereby enabling access to diverse 3D membrane mesostructures (e.g., bionic “tiger”) .…”

“…Various 2D precursor designs, involving filamentary, 103 , 209 , 223 , 236 kirigami, 120 origami, 210 , 213 multilayer, 121 and microlattice designs, 138 were developed to enable formation of 3D architectures with high degrees of complexities and diversities ( Figure 5 b). Filamentary designs ( Figure 5 b, filamentary) 236 typically consist of slender thin ribbons to ensure that large out-of-plane bending and twisting deformations can be induced to realize their transformation into desired 3D configurations such as helices 209 and frameworks.…”

“…Filamentary designs ( Figure 5 b, filamentary) 236 typically consist of slender thin ribbons to ensure that large out-of-plane bending and twisting deformations can be induced to realize their transformation into desired 3D configurations such as helices 209 and frameworks. 223 Kirigami designs ( Figure 5 b, kirigami) feature the reduction of stress concentration during buckling-guided assembly by introducing strategic cuts, thereby enabling access to diverse 3D membrane mesostructures (e.g., bionic “tiger”). 120 Origami designs ( Figure 5 b, origami) usually harness engineered folding creases in 2D precursors to form various 3D mesostructures by buckling-guided assembly.…”

An Inverse Design Method of Buckling-Guided Assembly for Ribbon-Type 3D Structures

“…For example, the structured elastomer substrates with kirigami designs can introduce local rotational motions of the bonding sites to enable the formation of structures with chiral features and morphable shapes [39]. To establish the relationship between the final 3D geometry of buckling assembly and the initial 2D configuration as well as the mechanical loadings, most previous studies [44][45][46][47][48][49][50][51] focused on the prediction of final 3D geometries based on prescribed 2D configurations and mechanical loadings, which can be regarded as a type of forward problem. However, it is almost impractical to obtain sophisticated mesostructures with desired 3D shapes through this type of forward analyses, because it requires massive calculations of the forward problem, which is a cumbersome iterative trial-and-error procedure with rather low efficiency.…”