Shape optimization of non-rigid origami leading to emerging bistability

Origami structures are a type of thin-walled flexible structures that undergo large deformation. Their inherent non-rigid characteristic empowers them with great potential for applications in space structures, metamaterials, and robotics. To understand the large deformation of origami structures, consideration of nonlinear mechanics is necessary. However, most origami structures are still designed by pure geometric approaches without considering their non-rigid behavior. In this work, we propose a computational design framework that incorporates nonlinear mechanics into the design procedure of origami. Guided by minimization of stored energy, under prescribed displacement boundary conditions, we optimize the configuration of origami structures. Difficulties arise due to the complex energy landscape of origami structures that inevitably induces bifurcation. We develop strategies to keep track of a stable deformation branch during the optimization process. A surprising outcome is that our approach naturally leads to self-emerging bistable structures, which is demonstrated by a series of numerical examples. We believe that our new approach would make substantial contribution to computational design of non-rigid origami structures, benefiting applications in origami-inspired solutions for science and engineering.