Coarse-grained kinematics of origami tessellations

Morphing shells hold a special position at the interface between structures and mechanisms: while they exhibit high rigidity under certain types of loadings, other loadings trigger global and highly nonlinear transformations of shape altering elongations and curvatures. Origami tessellations are one example of such shells where the interplay between soft creases and stiff panels produces diverse, however restricted, curved geometries out of an initially flat sheet and are therefore of interest in the design of robotic and actuated materials and structures. Here, we develop tools suitable for the analysis of the coarse grained kinematics of origami tessellations in the limit of fine crease patterns. In particular, we draw connections between the underlying geometry of the pattern and emergent mechanical properties such as the in-plane and out-of-plane Poisson's coefficients and comment on issues pertaining to stability, boundary control and the spatial distribution of soft modes.