Electronic and optoelectronic materials deployed in complex, three-dimensional (3D) structures can offer qualitatively expanded levels of functionality compared to those in their corresponding two-dimensional (2D) planar counterparts. Many examples demonstrate clearly the value of 3D structures in achieving unique properties with simple constituent materials1–5. Progress in this area is often limited by the relatively small range of choices in controlled, reliable, reproducible strategies for producing 3D geometrical forms in advanced functional materials6–11. Among the most recently introduced methods is a scheme in which compressive buckling associated with a stretched elastomeric substrate guides the mechanical assembly of elaborate 3D mesostructures, some with designs reminiscent of those achieved in macroscale structures by origami/kirigami, with specified shapes and with sizes that can span several orders of magnitude in characteristic dimensions, down to the submicron regime in lateral features and to a few tens of nanometers in thickness12–15. These ideas leverage an intimate interplay between materials and microstructural mechanics, with diverse examples of use with silicon membranes, metallic electrodes, and polymer films in hundreds of different 3D geometries13–16. Full, quantitative modeling of the mechanics forms an essential aspect of design in all such cases; without such theoretical guidance, the buckling process itself can lead to cracking and/or defect formation in the constituent materials in ways that can deteriorate their properties. Physical toughness and materials structure geometries are, therefore, critically important in maximizing the diversity of realizable 3D structures.