The Theory of Composites

Graeme W. Milton is a distinguished professor of mathematics at the University of Utah. He has been awarded Sloan and Packard Fellowships, the 2003 SIAM Ralph Kleinman Prize for research bridging the gap between mathematics and applications, the 2007 Society for Engineering Science Prager Medal for contributions to theoretical mechanics, the 2012 Landauer Medal of the ETOPIM Association for seminal contributions to the field of composite material science, and the 2015 International Prize Tullio Levi-Civita for the Mathematical and Mechanical Sciences. He is a fellow of the Society for Industrial and Applied Mathematics.

His main interests are in the fields of composite materials, inverse problems, cloaking theory, discrete networks, electromagnetism, and elasticity theory. He has published over 190 papers and written 2 books and edited a third. He, with his collaborators, are best known for: the ““Bergman–Milton”” bounds on the complex moduli of composites; the Milton zeta and eta parameters that partly govern the electrical and elastic response of microstructures; the CLM (Cherkaev, Lurie, and Milton) theorem giving exact results for the effective elastic moduli of 2d-composites; the general theory of exact relations for composites; pentamode materials that are a sort of anisotropic gel that can guide stress; metamaterials that can reverse the Hall coefficient; the discoveries of anomalous resonance, ghost sources, cloaking due to anomalous resonance, and active exterior cloaking; and the discovery of a new type of wave, called a field pattern, in microstructures where the moduli vary in both time and space.