Dislocations and disclinations in gradient elasticity

A special gradient theory of elasticity is employed to consider dislocation s and disclinations with emphasis on the elimination of strain singularitie s appearing in the classical theory of elasticity. For dislocations, we giv e a brief summary of our earlier results pertaining to "non-singular" expre ssions for the elastic strains, as well as new results for "non-singular" e xpressions for the strain energies. For disclinations, we derive non-singul ar expressions for the elastic strains demonstrating that dipoles of straig ht disclinations of general type give zero or finite values for the strain components at the disclination line. The finite values depend strongly on t he dipole arm d and exhibit a regular monotonous (wedge disclinations) or n on-monotonous (twist disclinations) behavior for short-range (d < 10 root c ) interactions. At annihilation distances (d --> 0), the elastic strains te nd smoothly to zero. Far from the disclination line (r >> 10 root c), gradi ent and classical solutions coincide. When the dipole arm d is much smaller than the scale unit root c, the elastic fields of a dipole of wedge discli nations transform into the elastic fields of an edge dislocation, as is the case in classical elasticity.