Lecture of Graeme Milton, University of Utah on "Metamaterials: high contrast composites with unusual properties"

Composite materials can have properties unlike any found in nature, and in this case they are known as metamaterials. Recent attention has been focussed on obtaining metamaterials which have an interesting dynamic behavior. Their effective mass density can be anisotropic, negative, or even complex. Even the eigenvectors of the effective mass density tensor can vary with frequency. Within the framework of linear elasticity, internal
masses can cause the effective elasticity tensor to be frequency dependent, yet not contribute at all to the effective mass density at any frequency. One may use coordinate transformations of the elastodynamic equations to get novel unexpected behavior. A classical propagating wave can have a strange behavior in the new abstract 
coordinate system. However the problem becomes to find metamaterials  which realize the behavior in the new coordinate system. This can be solved at a discrete level, by replacing the original elastic material with a network of masses and springs and then applying transformations to this network. The realization of the transformed network requires a new
type of spring, which we call a torque spring. The forces at the end of the torque spring are equal and opposite but not aligned with the line joining the spring ends. We show how torque springs can theoretically be realized.