Static equilibria and bifurcations of interlaced bigon rings*

We propose a numerical framework to study mechanics of elastic strip networks. Each strip is modeled as a Kirchhoff rod, and the entire strip network is formulated as a two-point boundary value problem (BVP). We first study the buckling behavior of a bigon, which consists of two strips fixed with prescribed angles at the two ends. We find that both the end angles and the aspect ratios of the strip's cross section contribute to make a bigon buckle out of plane. Then we study a bigon ring that connects a series of bigons and forms a closed loop. A bigon ring is generally multistable. We find both experimentally and numerically that a bigon ring can fold into multiply-covered loops, similar to the folding of a bandsaw blade. Finally we explore the static equilibria and bifurcations of a 6-bigon ring, and identify several families of equilibria. Our numerical implementation can be applied to general elastic rod/strip networks that may contain flexible joints, naturally curved strips of different lengths, etc. The folding and multistable behaviors of a bigon ring may inspire the design of novel deployable and morphable structures.