Second-order effects of dislocations in anisotropic crystals

Abstract

An elementary method is presented for determining the stresses produced by a given continuous distribution of dislocations in a non-linearly elastic crystal. This contrasts with the method of Kröner and Seeger [1] which employs stress functions whose governing equations are derived using the methods of non-Riemannian geometry. Also, unlike the stress function approach, the formulation here presented is applicable to anisotropic media; as an illustration, the equations are solved to second order for a screw dislocation perpendicular to a plane of symmetry of an otherwise generally anisotropic crystal.