Symmetry breaking in spoke double-ring structures formed by buckling-guided 3D assembly

• Preservation or breaking of rotational symmetry in spoke double-ring structures formed through buckling-guided 3D assembly. • An energy analysis for understanding the mechanism of symmetry breaking. • Diagrams of the deformation mode under various parameter combinations. The buckling-guided three-dimensional (3D) assembly method has arisen increasing attention for its advantages in forming complex 3D architectures with a rich diversity of geometric shapes in a broad spectrum of inorganic functional materials. Such an assembly method relies on the controlled lateral bucking of a 2D precursor structure integrated with a pre-stretched substrate at selective regions. In the assembly process, the preservation or breaking of rotational symmetry is crucial for understanding the mechanism of 2D-to-3D geometric transformation. Here, we present a fundamental study on the rotational symmetry of 3D spoke double-ring structures formed through buckling-guided assembly. An energetic method is introduced to analyze the rotational symmetry and to understand the symmetry-breaking mechanism. Such symmetry-breaking phenomenon is validated by experiments and finite element analyses (FEA). Phase diagrams of the deformation mode are established to shed light on the influences of various geometric parameters (e.g., initial rotational symmetry order, radius ratio, and location of bonding sites). This work offers new insights into the underlying mechanism of 2D-to-3D geometric transformation in ribbon-type structures formed by compressive buckling.