English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

Curved-sided hexagrams with multiple equilibrium states have great potentialin engineering applications such as foldable architectures, deployableaerospace structures, and shape-morphing soft robots. In Part I, the classicalstability criterion based on energy variation was used to study the elasticstability of the curved-sided hexagram and identify the natural curvature rangefor stability of each state for circular and rectangular rod cross-sections.Here, we combine a multi-segment Kirchhoff rod model, finite elementsimulations, and experiments to investigate the transitions between four basicequilibrium states of the curved-sided hexagram. The four equilibrium states,namely the star hexagram, the daisy hexagram, the 3-loop line, and the 3-loop"8", carry uniform bending moments in their initial states, and the magnitudesof these moments depend on the natural curvatures and their initial curvatures.Transitions between these equilibrium states are triggered by applying bendingloads at their corners or edges. It is found that transitions between thestable equilibrium states of the curved-sided hexagram are influenced by boththe natural curvature and the loading position. Within a specific naturalcurvature range, the star hexagram, the daisy hexagram, and the 3-loop "8" cantransform among one another by bending at different positions. Based on thesefindings, we identify the natural curvature range and loading conditions toachieve transition among these three equilibrium states plus a folded 3-loopline state for one specific ring having a rectangular cross-section. Theresults obtained in this part also validate the elastic stability range of thefour equilibrium states of the curved-sided hexagram in Part I. We envisionthat the present work could provide a new perspective for the design ofmulti-functional deployable and foldable structures.

Multiple equilibrium states of a curved-sided hexagram: Part II-Transitions between states