Hidden symmetries generate rigid folding mechanisms in periodic origami.

We consider the zero-energy deformations of periodic origami sheets with generic crease patterns. Using a mapping from the linear folding motions of such sheets to force-bearing modes in conjunction with the Maxwell-Calladine index theorem we derive a relation between the number of linear folding motions and the number of rigid body modes that depends only on the average coordination number of the origami's vertices. This supports the recent result by Tachi [T.

Rigidity for sticky discs.

We study the combinatorial and rigidity properties of disc packings with generic radii. We show that a packing of discs in the plane with generic radii cannot have more than 2 - 3 pairs of discs in contact. The allowed motions of a packing preserve the disjointness of the disc interiors and tangency between pairs already in contact (modelling a collection of sticky discs).

Analytic analysis of auxetic metamaterials through analogy with rigid link systems.

In recent years, many structural motifs have been designed with the aim of creating auxetic metamaterials. One area of particular interest in this subject is the creation of auxetic material properties through elastic instability. Such metamaterials switch from conventional behaviour to an auxetic response for loads greater than some threshold value.

Anchored boundary conditions for locally isostatic networks.

Finite pieces of locally isostatic networks have a large number of floppy modes because of missing constraints at the surface. Here we show that by imposing suitable boundary conditions at the surface the network can be rendered effectively isostatic. We refer to these as anchored boundary conditions.