Duality of the Incompatibility Tensor

Abstract

Disclination resulting from kink deformation of the long-period stacking-ordered phase of Mg–Zn–Y alloy affects the strength of the alloy. In this study, we examined theoretical aspects of the kinematic equation of defects, including dislocations and disclinations, based on the dual structure of strain and stress space. Two types of disclination, related to dislocation and bend-twist, were identified. Disclination types were distinguished based on incompatibility. In “dual strain space”, we show that incompatibility is due to a generalized stress function, i.e., the Beltrami stress function, which is a three-dimensional version of the Airy stress function that includes non-diagonal components.