It was noted that the theory of 2-dimensional anisotropic elasticity was studied extensively, although most applications were concerned with orthotropic systems in which the plane-strain and antiplane strain-fields were separable. Another special system for which the strain-fields no longer decoupled, but closed-form solutions were still obtainable, treated <111> line defects in cubic crystals; that is, defects whose lines were oriented in <111> directions. This system was important because <111> screw dislocations played a key role in the plastic deformation of body-centered cubic crystals. A set of relationships between the stress fields of a <111> dislocation and a <111> line force were derived, and these were used to check published stress expressions for <111> defects.

Linear Relationships between the Stress Fields of <111> Line Defects. Y.T.Chou, S.Lee: Journal of Applied Mechanics, 1998, 65[4], 1064-6