The results of application of gradient theory of elasticity to a description
of elastic properties of dislocations and disclinations are reviewed. The main
achievement made in this approach is the elimination of the classical
singularities at defect lines and the possibility of describing short-range
interactions between them on a nanoscale level. Non-singular solutions for
elastic fields and energies of dislocations in an infinite isotropic medium
are represented in a closed analitycal form and discussed in detail. Similar
solutions for straight disclinations are also considered with application to
the specific case of disclination dipoles. A special attention is paid to the
nanoscopic behavior and stress fields of dislocations near interfaces.
Recent non-singular solutions for both the dislocation stresses and "image"
forces on dislocations are demostrated in a general integral form and
corresponding peculiarities in dislocation behavior near interfaces are
discussed.
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