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# Dynamic Peierls-Nabarro equations for elastically isotropic crystals

Abstract : The dynamic generalization of the Peierls-Nabarro equation for dislocations cores in an isotropic elastic medium is derived for screw, and edge dislocations of the glide' and climb' type, by means of Mura's eigenstrains method. These equations are of the integro-differential type and feature a non-local kernel in space and time. The equation for the screw differs by an instantaneous term from a previous attempt by Eshelby. Those for both types of edges involve in addition an unusual convolution with the second spatial derivative of the displacement jump. As a check, it is shown that these equations correctly reduce, in the stationary limit and for all three types of dislocations, to Weertman's equations that extend the static Peierls-Nabarro model to finite constant velocities.
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https://hal-cea.archives-ouvertes.fr/cea-00412985
Contributor : Yves-Patrick Pellegrini <>
Submitted on : Wednesday, September 2, 2009 - 6:59:38 PM
Last modification on : Wednesday, February 17, 2021 - 3:26:04 PM

### Citation

Yves-Patrick Pellegrini. Dynamic Peierls-Nabarro equations for elastically isotropic crystals. Physical Review B: Condensed Matter and Materials Physics (1998-2015), American Physical Society, 2010, 81, pp.024101. ⟨10.1103/PhysRevB.81.024101⟩. ⟨cea-00412985⟩

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