Wedge dislocation in the geometric theory of defects

TLDR: In this article, the authors consider a wedge dislocation in the framework of elasticity theory and the geometric theory of defects, and they show that the geometry theory quantitatively reproduces all the results of linear approximation in the linear approximation.

Abstract: We consider a wedge dislocation in the framework of elasticity theory and the geometric theory of defects. We show that the geometric theory quantitatively reproduces all the results of elasticity theory in the linear approximation. The coincidence is achieved by introducing a postulate that the vielbein satisfying the Einstein equations must also satisfy the gauge condition, which in the linear approximation leads to the elasticity equations for the displacement vector field. The gauge condition depends on the Poisson ratio, which can be experimentally measured. This indicates the existence of a privileged reference frame, which denies the relativity principle.