Lu Lu

“Multiple Equilibrium States of a Curved-Sided Hexagram: Elastic Stability and State Transitions”

Advised by Prof. Renee Zhao

Abstract: Elastic structures with multiple equilibrium states have widespread engineering applications ranging from shape-reconfigurable architectures, shape-morphing soft robots, mechanical metamaterials to flexible electronics. Here, we present a curved-sided hexagram having four basic equilibrium states, which are referred to as the star hexagram, the daisy hexagram, the 3-loop line, and the 3-loop “8”. Each of the four equilibrium states carries a uniform bending moment with different values in their initial states, and the moment depends on their natural curvatures and initial curvatures. Based on a combination of the Kirchhoff rod theory, finite element simulations, and experiments, we first studied the elastic stability of the curved-sided hexagram and identified the natural curvature range for stability of each state, and then investigated the transitions between the four equilibrium states with different natural curvatures within the elastic stability range under external bending loads. It is found that the four basic equilibrium states can be mutually stable when the curved-sided hexagram has a rectangular cross-section with height-to-thickness ratio larger than 3.4, and the stability range is determined by the lower stability limits of the 3-loop “8” and the upper stability limits of the 3-loop line. Our studies further demonstrate that the four states can transition between each other through inversion or folding when appropriate external stimuli are applied. We envision that the curved-sided hexagram with multiple equilibrium states could provide prospectives for the design of multi-functional deployable and foldable structures.