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International Journal for Multiscale Computational Engineering

Impact factor: 0.963

ISSN Print: 1543-1649
ISSN Online: 1940-4352

International Journal for Multiscale Computational Engineering

DOI: 10.1615/IntJMultCompEng.2011002688
pages 623-634

DETERMINATION OF NONLOCAL CONSTITUTIVE EQUATIONS FROM PHONON DISPERSION RELATIONS

Olaf Weckner
The Boeing Company, P.O. Box 3707, MC 42-26, Seattle, Washington, 98124-2207, USA
Stewart A. Silling
Multiscale Dynamic Material Modeling Department, Sandia National Laboratories, Albuquerque, New Mexico,87185, USA

ABSTRACT

All materials exhibit wave dispersion at "small" wavelengths leading to non-linearities in experimentally determined dispersion curves. Classical local elasticity fails to predict these non-linearities. Nonlocal continuum mechanics allows for the prediction of the elastic behavior over a considerably wider range of lengthscales. Starting from ab initio lattice dynamics calculations we determine the elastic constants and the phonon dispersion relation for silicon. We verify our results using inelastic neutron scattering data. Next we develop the theoretical and numerical framework to construct nonlocal constitutive equations for longitudinal and transverse acoustic modes.

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