From Pentamodes to Cable Webs to Masonry Structures

Overview

Thus the tension in one element determines the tension in the other elements, and by extension uniquely determines the stress in the entire metamaterial. Here we show how this key feature can be extended to discrete wire networks, supporting forces at the terminal nodes and which may have internal nodes where no forces are applied. In usual wire or cable networks, such as in a bridge or bicycle wheel, one distributes the forces by adjusting the tension in the wires. Here our discrete networks provide an alternative way of distributing the forces through the geometry of the network. In particular, the network can be chosen so it is uniloadable, i.e. supports only one set of forces at the terminal nodes. Such uniloadable networks provide the natural generalization of pentamode materials to discrete networks. We extend such a problem to compression-only 'strut nets' subjected to fixed and reactive nodal loads. These systems provide discrete element models of masonry bodies.  In particular, we solve the arch problem where one wants the strut net to avoid a given set of obstacles, and also allow some of the forces to be reactive ones. This is joint work with Ada Amendola, Guy Bouchitt{\'e},  Andrej Cherkaev, Antonio Fortunato, Fernando Fraternali, Ornella Mattei, and Pierre Seppecher.

Biography

Graeme Milton received his Ph.D degree in Physics from Cornell University in 1985, and a D.Sc from Sydney University in 2003 based on his book ”The Theory of Composites” now republished as a SIAM classic.  He is currently a distinguished professor of mathematics at the University of Utah, where he served as department chairman from 2002 to 2005. 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 SIAM fellow. 
His main interests are in the fields of composite materials, inverse problems, cloaking theory, discrete networks, electromagnetism and elasticity theory, with about 200 published papers. 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, etc.