Rectangular disclination loops I. A universal technique

Abstract

The elastic properties of rectangular disclination loops in an infinite isotropic medium are examined in terms of linear elasticity. For the calculation of the disclination stress tensor, an effective method is proposed which is based on the representation of the initial loop in the form of a continuous distribution of infinitesimal disclination loops, their rotation axes being displaced with respect to the centres. The stresses and self-energies of rectangular twist and wedge disclination loops are obtained in an analytical form. To calculate the elastic fields of the disclination and dislocation defects constructed by some mutually perpendicular segments, a mathematical technique for transforming the rectangular-loop solutions is developed. The stress fields of angular disclinations are studied by considering the defect to be a superposition of U-shaped disclinations with infinitesimal arms.