Linear theory of dislocations in a smetic A

This is the authors' abstract. We don't add key points for this paper.

The distortions of a smectic phase with respect to a planar state of reference are described either by a displacement u of the layers (and the conjugated stresses σij), or by a rotation ω of the director (and the conjugated torques). In principle, the choice of ω as an independent variable is justified for the study of disclinations, and the choice of u for the study of dislocations of translation. In this latter case, and restricting the theory to small distortions, one extends various results in dislocation theory in solids to the case of smectics. With the help of the stress field due to an unit point force (Green's function), one is able to express the displacement field of a line as a surface integral, the line tension and the interaction energy with other lines as line integrals. In particular, one shows as a result that two mutually perpendicular line segments do not interact; one establishes the displacement field of an edge loop ; one obtains the Green's function of a homeotropic sample with one free boundary and one anchored boundary; the force image method is also introduced.