Exploiting symmetry and a new conservation law for designing multistable eight-fold origami structures

The nonlinearities inherent in the mechanics of origami make it a rich design space for multistable structures and metamaterials. In this talk, we investigate the multistability properties of a classic origami base: the symmetric eight-fold waterbomb. We present a design procedure for tuning the depth and the symmetry/asymmetry of its energy wells. While the waterbomb is thought to be strictly bistable, we have discovered tristable cases that can exist when the mountain and valley creases are pre-tensioned with respect to each other; that is, when the waterbomb does not have a stress-free configuration. Finally, we consider quasi-1D sheets of waterbombs. Here we discover an analog of Gauss's law in which the number of popped-up and popped-down vertices is determined simply through analysis of its boundaries. This is followed by a discussion of how the quasi-1D sheet may be designed to achieve stable states with various degeneracies, kinematics, and band-gaps. These discoveries and novel analysis techniques, as we work towards generalization, represent a powerful global design tool for useful origami structures.