1205.6213 (Graeme Walter Milton)

What nonlinear unimode metamaterials can one get with rigid bars and
pivots?    [PDF]

Graeme Walter Milton

A complete characterization is given of the possible trajectories of deformation of periodic nonlinear unimode metamaterials constructed from bars and pivots. In such materials the only continuous deformations of the structure are to other periodic structures having Bravais lattices which are continuous affine transformations of the underlying Bravais lattice in the original configuation (unlike a parallelogram array of bars, where there are many non-periodic deformations). Additionally the Bravais lattice can only deform along one trajectory in a six dimensional space with as axes the six invariants $|u|^2$, $|v|^2$, $|w|^2$, $u\cdot v$, $v\cdot w$, and $w\cdot u$, where $u$, $v$ and $w$ are the primitive lattice vectors. We show by explicit construction that any continuous trajectory is realizable to an arbitrarily high degree of approximation provided at all points along the trajectory the vectors $u$, $v$ and $w$ are never coplanar.

View original: http://arxiv.org/abs/1205.6213