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- James G. Berryman, Lawrence Livermore, Graeme W. Milton
- 1988

For practical applications of variational bounds to the eeective properties of composite materials, the information available is often not that required by the formulas for the optimal bounds. It is therefore important to determine what can be said rigorously about various unknown material properties when some other properties are known. The key quantities… (More)

In this paper, we investigate how the form of the conventional elastodynamic equations changes under curvilinear transformations. The equations get mapped to a more general form in which the density is anisotropic and additional terms appear which couple the stress not only with the strain but also with the velocity, and the momentum gets coupled not only… (More)

Eshelby showed that if an inclusion is of elliptic or ellipsoidal shape then for any uniform elastic loading the field inside the inclusion is uniform. He then conjectured that the converse is true, i.e. that if the field inside an inclusion is uniform for all uniform loadings, then the inclusion is of elliptic or ellipsoidal shape. We call this the weak… (More)

Typically, the electrical and elastic properties of composite materials are strongly microstructure dependent. So it comes as a nice surprise to come across exact formulae for (or linking) eeective tensor elements that are universally valid no matter what the microstructure. Here we present a systematic theory of exact relations embracing the known exact… (More)

- Hyeonbae Kang, Eunjoo Kim, Graeme W. Milton
- SIAM Journal of Applied Mathematics
- 2008

Eshelby conjectured that if for a given uniform loading the field inside an inclusion is uniform, then the inclusion must be an ellipse or an ellipsoid. This conjecture has been proved to be true in two and three dimensions provided that the inclusion is simply connected. In this paper we provide an alternative proof of Cherepanov’s result that an inclusion… (More)

- Graeme W. Milton, Alan W. Smith
- The Journal of physiology
- 1956

In an electromagnetic cloak based on a transformation approach, reduced sets of material properties are generally favored due to their easier implementation in reality, although a seemingly inevitable drawback of undesired scattering exists in such cloaks. Here, the authors suggest the use of high-order transformations to create smooth moduli at the outer… (More)

- Fernando Guevara Vasquez, Graeme W. Milton, Daniel Onofrei
- Physical review letters
- 2009

A new cloaking method is presented for 2D quasistatics and the 2D Helmholtz equation that we speculate extends to other linear wave equations. For 2D quasistatics it is proven how a single active exterior cloaking device can be used to shield an object from surrounding fields, yet produce very small scattered fields. The problem is reduced to finding a… (More)

- Fernando Guevara Vasquez, Graeme W. Milton, Daniel Onofrei
- Optics express
- 2009

It is shown how a recently proposed method of cloaking is effective over a broad range of frequencies. The method is based on three or more active devices. The devices, while not radiating significantly, create a "quiet zone" between the devices where the wave amplitude is small. Objects placed within this region are virtually invisible. The cloaking is… (More)

- Graeme W. Milton, Nicolae-Alexandru P. Nicorovici, +5 authors Ross C. McPhedran
- 2014

Solutions for the fields in a coated cylinder where the core radius is bigger than the shell radius are seemingly unphysical, but can be given a physical meaning if one transforms to an equivalent problem by unfolding the geometry. In particular, the unfolded material can act as an impedance matched hyperlens, and as the loss in the lens goes to zero finite… (More)