Abstract

Sometimes the properties of a composite are completely unlike those of the constituent materials, even when the structure is small compared to the wavelength: these composites are called metamaterials. Classic examples include bubbly fluids and stained glass windows made from suspensions of metal particles in glass. Other examples include metamaterials with negative thermal expansion made from materials all having positive thermal expansion; metamaterials with negative and/or possibly anisotropic mass density over a range of frequencies; metamaterials that get fatter as they are stretched (having a negative Poisson's ratio); materials with artificial and possibly negative magnetic permeability. The list goes on. Recent attention has been directed to space-time microstructures where the material moduli vary in both space and time. We will review some of the progress that has been made. One particular class of elastic metamaterials, known as pentamodes, has proved useful for guiding stress. Cable networks can also guide stress. It turns out that essentially any cable network under tension, and supporting a given loading, can be replaced by one in which at most four cables meet at any junction. Like pentamodes, these can support, up to a constant factor, only one stress field. Thus by tightening just one cable one gets the desired forces at all the terminal nodes. This last work is joint with Guy Bouchitte, Ornella Mattei and Pierre Seppecher.