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- 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)

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)

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)

- 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

- N. A. Fleck, J. W. Hutchinson, J. R. Willis
- 2014

A critical examination is made of two classes of strain gradient plasticity theories currently available for studying micrometre-scale plasticity. One class is characterized by certain stress quantities expressed in terms of increments of strains and their gradients, whereas the other class employs incremental relationships between all stress quantities and… (More)

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