High contrast composites with unusual properties

English

Séminaire Modèles et Algorithmes Déterministes: EDP-MOISE

14/09/2012 - 14:00 Mr MILTON Graeme (University of Utah) Salle 1 - Tour IRMA

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.