Fields of stress and electric displacement produced by dislocations and disclinations in three-dimensional, anisotropic, elastic and piezoelectric media: elliptical Frank disclination

摘要

A statement is made on the theory of continuous distributions of dislocations and disclinations in anisotropic elastopiezoelectric media. The basic field equations governing the fields of stress functions, electric vector potential and incompatibility are presented and solved to give the fields of stress and electric displacement caused by a distribution of dislocations and disclinations. They are expressed in terms of the dislocation- and disclination-density tensors by means of the convolution integrals, extended throughout the medium, and the Fourier integrals. To treat the fields around discrete defects, that is dislocation and/or Frank disclination, the convolution integrals are replaced by the line integrals belonging to the loop of the defect. The fields of stress and electric displacement are given in terms of three quadruple integrals, which are converted into single integrals of explicitly given functions, in the case where the loop of the defect is elliptical. Numerical computations are carried out to estimate the fields in gallium arsenide. The values of those fields at a certain point of the body are presented. The contours and zero lines of the fields of dilatational stress and electric displacement in the plane placed parallel to and at a certain distance from the loop are illustrated.