Related papers: On rigid origami III: local rigidity analysis
For origami structures, perforating or cutting slits along creases is an effective method to define fold lines and alleviate stress concentrations at vertices. In this letter we show numerically and experimentally that for…
We map the problem of determining flat-foldability of the origami diagram onto the ground-state search problem of spin glass model on random graphs. If the origami diagram is locally flat-foldable around each vertex, a pre-folded diagram,…
Ring origami, consisting of closed-loop rods, is a class of shape-morphing structures that undergo shape transformation through folding enabled by snap-buckling instabilities, referred to as snap-folding instabilities. Previous studies have…
We are interested in the question of stability in the field of shape optimization, with focus on the strategy using second order shape derivative. More precisely, we identify structural hypotheses on the hessian of the considered shape…
Three types of rigidity theorem for orbifold elliptic genus of level N are proved. The first type deals with the case where N is relatively prime to the orders of all isotropy groups. If the top exterior power of the tangent bundle is…
We develop a geometric approach to understand the mechanics of perforated thin elastic sheets, using the method of strain-dependent image elastic charges. This technique recognizes the buckling response of a hole under external load as a…
The dramatic effect kirigami, such as hole cutting, has on the elastic properties of thin sheets invites a study of the mechanics of thin elastic frames under an external load. Such frames can be thought of as modular elements needed to…
We show how rigidity emerges in experiments of sheared frictional granular materials by using generalizations of two methods for identifying rigid structures. Both approaches, the force-based dynamical matrix and the topology-based rigidity…
A new continuous model of shearable rod, subject to large elastic deformation, is derived from nonlinear homogenization of a one-dimensional periodic microstructured chain. As particular cases, the governing equations reduce to the Euler…
The packing of elastic bodies has emerged as a paradigm for the study of macroscopic disordered systems. However, progress is hampered by the lack of controlled experiments. Here we consider a model experiment for the isotropic…
In this paper, we proved a rigidity theorem of the Hodge metric for concave horizontal slices and a local rigidity theorem for the monodromy representation.
Kirigami, the creative art of paper cutting, is a promising paradigm for mechanical metamaterials. However, to make kirigami-inspired structures a reality requires controlling the topology of kirigami to achieve connectivity and rigidity.…
Combinatorial rigidity theory seeks to describe the rigidity or flexibility of bar-joint frameworks in R^d in terms of the structure of the underlying graph G. The goal of this article is to broaden the foundations of combinatorial rigidity…
This study presents a fractional-order continuum mechanics approach that allows combining selected characteristics of nonlocal elasticity, typical of classical integral and gradient formulations, under a single frame-invariant framework.…
Origami is the art of paper folding, and it borrows its name from two Japanese words \emph{ori} and \emph{kami}. In Japanese, {ori} means folding, and the paper is called {kami}. While origami is just a hobby to most, there is a lot more to…
A rigidity theory is developed for bar-joint frameworks in $\mathbb{R}^{d+1}$ whose vertices are constrained to lie on concentric $d$-spheres with independently variable radii. In particular, combinatorial characterisations are established…
A ring is rigid if there is no nonzero locally nilpotent derivation on it. In terms of algebraic geometry, a rigid coordinate ring corresponds to an algebraic affine variety which does not allow any nontrivial algebraic additive group…
Rigidity is an emergent property of materials - it is not a feature of individual components that comprise the structure, but instead arises from interactions between many constituent parts. Recently, it has been recognized that…
This work focuses on the bearing rigidity theory, namely the branch of knowledge investigating the structural properties necessary for multi-element systems to preserve the inter-units bearings when exposed to deformations. The original…
We develop recursion equations to describe the three-dimensional shape of a sheet upon which a series of concentric curved folds have been inscribed. In the case of no stretching outside the fold, the three-dimensional shape of a single…