An analytic model of two-level compressive buckling with applications in the assembly of free-standing 3D mesostructures

Recently developed methods for mechanically-guided assembly exploit stress release in prestretched elastomeric substrates to guide the controlled formation of complex three-dimensional (3D) mesostructures in advanced functional materials and integrated electronic devices. The techniques of interfacial photopolymerization allow for realization of such 3D mesostructures in free-standing forms, separated from their elastomeric substrate, via formation of an integrated base layer. Theoretical models for the complex modes of deformation associated with this scheme are essential in the optimal design of the process parameters. Here, we present an analytic finite-deformation model of an isolated double-ribbon structure to describe the buckling process and morphology change of the assembled mesostructures upon removal of the substrate. As validated by finite element analyses (FEA), this analytic model can accurately predict the profiles of the double-ribbon structure with a range of different design parameters. We further illustrate the extension of this model to the analyses of 3D mesostructures with different geometries. Inspired by analytic results for flexible base structures, combined experimental results and numerical simulations demonstrate that mechanical interactions between the two different layers can be leveraged to achieve hierarchical assembly of 3D mesostructures. These findings could be useful in further advances in designs of free-standing 3D mesostructures based on mechanically-guided assembly.