corresponds to a mixed array consisting of four regular table structures, four tilted tables, four tents, and one double-floor tent at the center. Some other 3D mesostructures (e.g., raised ring, scaffold, toroid inside a flower, nested box, etc.) appear in fig. S14. These networks exhibit geometries that agree quantitatively with FEA predictions. An important point is that all 3D mesostructures—even those with the highest complexity and largest extent in the out-of-plane direction—are deterministic and form consistently into unique geometries because the strain energies of the first-order buckling modes (i.e., energetically the most probable configuration) are lower than those of all other modes by approximately a factor of 2 or more (fig. S15).
Summarized in Fig. 4A and fig. S16 are results that illustrate the applicability of this assembly approach to additional classes of materials, including metals (e.g., Ni), dielectrics (e.g., polyimide and epoxy), and patterned combinations of these, in polycrystalline and amorphous forms. Submicrometer features are also possible, as demonstrated in a “starfish” framework that incorporates silicon ribbons with widths of 800 nm and thicknesses of 100 nm (Fig. 4B). Two more examples of submicrometer features are provided in fig. S17. Here, the large differences in contact areas between the filaments and the bonding sites provide the necessary contrast in adhesion. The same strategy also enables the assembly of micrometer-sized 3D silicon features with ribbon widths of 3 μm and thicknesses of 300 nm (fig. S18). In these and all other cases, mechanical strain applied to the assembly platforms can affect reversible, controlled changes in the geometries of the supported structures, thereby providing tunable 3D configurations. The results in Fig. 4C show top and angled views of the influence of uniaxial tensile deformation (50%) on a structure with a variant of the starfish layout, in which all six tip corners serve as sites for bonding. Overlaid FEA results exhibit quantitative agreement with the observed geometries. Results in fig. S19 demonstrate that the 3D mesostructures are bendable and can be placed on curved surfaces.