arXiv subjects

Adam Reddy

Publications and source records attributed to Adam Reddy.

3 recordsLinked to original sources

arXiv2026

Complete closed-form solutions to the problem of inextensional bending for surfaces of translation and origami tessellations

Plates generally admit six deformation modes: three of which are high in strain energy, stretch the plate's midsurface and are called membrane modes; and three are low-energy, bend the midsurface without stretching it and are called bending modes. For origami tessellations, and other corrugated compliant thin shells, the modes are mixed and it is no longer clear what modes, if any, are low in energy in the sense that they are inextensional. Here, it is shown, by direct construction of closed-form solutions, that when the midsurface is a surface of translation, there exists three infinitesimally inextensional deformation modes that correspond to (1) stretching, with an effective Poisson's effect; (2) bending, with an effective synclastic or anti-clastic effect; and to (3) twisting. The provided expressions are valid irrespective of surface regularity and, in particular, properly handle any creases be them straight or curved. The results provide a powerful benchmark for the validation of numerical methods and further insight into the elastic stiffness of thin corrugated compliant shells.

math.DG↗

arXiv2023

Frustration Propagation in Tubular Foldable Mechanisms

Shell mechanisms are patterned surface-like structures with compliant deformation modes that allow them to change shape drastically. Examples include many origami and kirigami tessellations as well as other periodic truss mechanisms. The deployment paths of a shell mechanism are greatly constrained by the inextensibility of the constitutive material locally, and by the compatibility requirements of surface geometry globally. With notable exceptions (e.g., Miura-ori), the deployment of a shell mechanism often couples in-plane stretching and out-of-plane bending. Here, we investigate the repercussions of this kinematic coupling in the presence of geometric confinement, specifically in tubular states. We demonstrate that the confinement in the hoop direction leads to a frustration that propagates axially as if by buckling. We fully characterize this phenomenon in terms of amplitude, wavelength, and mode shape, in the asymptotic regime where the size of the unit cell of the mechanism~$r$ is small compared to the typical radius of curvature~$\rho$. In particular, we conclude that the amplitude and wavelength of the frustration are of order $\sqrt{r/\rho}$ and that the mode shape is an elastica solution. Derivations are carried out for a particular pyramidal truss mechanism. Findings are supported by numerical solutions of the exact kinematics.

math.DG↗

arXiv2023

Curved-crease origami for morphing metamaterials

We find a closed-form expression for the Poisson's coefficient of curved-crease variants of the ``Miura ori'' origami tessellation. This is done by explicitly constructing a continuous one-parameter family of isometric piecewise-smooth surfaces that describes the action of folding out of a reference state. The response of the tessellations in bending is investigated as well: \comment{using a numerical convergence scheme,} the effective normal curvatures under infinitesimal bending are found to occur in a ratio equal and opposite to the Poisson's coefficient. These results are the first of their kind and, by their simplicity, should provide a fruitful benchmark for the design and modeling of curved-crease origami and compliant shell mechanisms. Here, the developed methods are used to design a curved crease 3D morphing solid with a tunable self-locked state.

cond-mat.soft↗