Continuous modeling of discontinuities in anisotropic rods

Slender structures with kinks and creases are ubiquitous in engineering applications such as frames, origami, and stretchable electronics. Due to the discontinuity of local tangent, modeling the mechanics of creased structures often requires cutting the folds and including specific boundary conditions. This work presents a continuous description of discontinuities in anisotropic rods using the distributed Heaviside-like function. We first apply this framework to study the folding and bistable behaviors of creased annular strips and polygonal frames (C^0 continuity), with their stability determined by the classical conjugate point test. Experiments confirmed these stable configurations predicted by our framework. Then we study the large deformation and postbuckling of a serpentine rod (C^1 continuity). The predictions unveil rich bifurcations and stable branches that are also observed in tabletop models. Both examples demonstrated the efficiency and convenience of this novel framework, which could facilitate the mechanical design of rods/strips-based deployable systems and morphable robots.