Strain compatibility and gradient elasticity in morphing origami metamaterials

The principles of origami design have proven useful in a number technological applications. Origami tessellations particular constitute class morphing metamaterials with unusual geometric and elastic properties. Although inextensible principle, fine creases allow to effectively deform non-isometrically. Determining the strains that are compatible coarse-grained kinematics as well corresponding elasticity functionals is paramount understanding controlling paths metamaterials. Here, within unified theory, we solve this problem for wide array well-known including Miura-ori its more formidable oblique, non-developable non-flat-foldable variants. We find these patterns exhibit two universal On one hand, they all admit equal but opposite in-plane out-of-plane Poisson’s ratios. other their bending energy detaches from strain depends instead on gradient. results illustrated over case study self-equilibrium geometry pillars.