Dislocations and disclinations in gradient elasticity

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A special gradient theory of elasticity is employed to consider dislocations and disclinations with emphasis on the elimination of strain singularities appearing in the classical theory of elasticity. For dislocations, we give a brief summary of our earlier results pertaining to "non-singular" expressions for the elastic strains, as well as new results for "non-singular" expressions for the strain energies. For disclinations, we derive non-singular expressions for the elastic strains demonstrating that dipoles of straight disclinations of general type give zero or finite values for the strain components at the disclination line. The finite values depend strongly on the dipole arm d and exhibit a regular monotonous (wedge disclinations) or non-monotonous (twist disclinations) behavior for short-range (d < 10 √c) interactions. At annihilation distances (d → 0), the elastic strains tend smoothly to zero. Far from the disclination line (r ≫ 10 √c), gradient and classical solutions coincide. When the dipole arm d is much smaller than the scale unit √c, the elastic fields of a dipole of wedge disclinations transform into the elastic fields of an edge dislocation, as is the case in classical elasticity.

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Physica Status Solidi (B) Basic Research