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A method for homogenization of an elastic composite with periodic microstructure is presented, focusing on the Floquet-type elastic waves. The resulting homogenized frequency-dependent elasticity and mass density then automatically satisfy the overall conservation laws and by necessity produce the exact dispersion relations. It is also shown that the… (More)

- J R Willis, A B Movchan
- 2007

Dynamic weight functions are discussed, for arbitrary time-dependent loading of a plane semi-innnite crack extending at constant speed in an innnite isotropic elastic body. Then, the weight function appropriate to the case of general normal (or Mode I) loading is constructed explicitly, employing Fourier transforms to develop and solve a Wiener-Hopf… (More)

The paper addresses the problem of correlation within an array of parallel dislocations in a crystalline solid. The first two of a hierarchy of equations for the multi-point distribution functions are derived by treating the random dislocation distributions and the corresponding stress fields in an ensemble average framework. Asymptotic reasoning,… (More)

- A B Movchan, J R Willis
- 2007

Dynamic weight functions are constructed for general time{dependent shear loading of a plane semi{innnite crack propagating with constant speed in an innnite isotropic elastic body. The use of Fourier transforms reduces the problem to the analysis of a matrix Wiener{Hopf equation. The solution of the Wiener{Hopf problem is presented. An expression is… (More)

- Ankit Srivastava, John R Willis
- Proceedings. Mathematical, physical, and…
- 2017

All metamaterial applications are based upon the idea that extreme material properties can be achieved through appropriate dynamic homogenization of composites. This homogenization is almost always done for infinite domains and the results are then applied to finite samples. This process ignores the evanescent waves which appear at the boundaries of such… (More)

- Alexander B. Movchan, J. R. Willis, R. Bullough, Vladimir Karlin, Vladimir Maz'ya
- SIAM Journal of Applied Mathematics
- 2000

the Doctoral Committee members (all six of them present!). for 31 years (1974-2005), and who duly served this great public institution with affection. In remembering Dr. Brown, I take as my epitaph the meaning of " Outliers " from the book by Malcom Gladwell titled Outliers: The Story of Success (2008). Gladwell holds that: " Outliers " —a noun, has two… (More)

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