On the three-dimensional Filon construct for dislocations

The relationship between dislocation theory and the difference of linear elastic solutions for two different sets of elastic moduli, derived by Filon in two-dimensions, is generalised to three-dimensions. Essential features are developed and illustrated by the examples of the edge and screw dislocation. The inhomogeneity problem is discussed within the same context, and related to Somigliana dislocations, and in the limit to the interstitial atom.