Theory of disclinations: II. Continuous and discrete disclinations in anisotropic elasticity

A general theory of stationary disclinations for a linearly elastic, infinitely extended, homogeneous body is developed. Dislocation theory is extended in three different ways to include disclinations, i.e., from continuous distributions, discrete lines, and continuous distributions of infinitesimal loops. This leads to three independent definitions of the disclination, which can be uniquely related to each other. These interrelationships clarify Anthony and Mura's approaches to disclination theory, which at first appear to diverge from the present theory. Mura's "plastic distortion" and "plastic rotation" are identified as the dislocation and disclination loop densities. The clastic strain and bend-twist are derived as closed integrals in terms of the defect densities, and shown to be state quantities. The theory reduces to classical dislocation theory when the disclinations vanish. For every discrete disclination line, it is always possible to find a "dislocation model," which is a dislocation wall terminating on the line that gives exactly the same elastic strain and stress.