A two-dimensional time-dependent continuum model for plastic flow was presented in which an evolution equation for curved glide dislocations was combined with continuum mechanics equations. These 2 features were linked by the Orowan relationship. The model took the form of a set of coupled partial differential evolution equations. Simplifying assumptions were sought, rather than attempting numerical solution. The model could be reduced to a boundary-value problem for an inhomogeneous parabolic equation, and a periodic solution was found analytically.

A Model of Reversible Cyclic Deformation of a Dislocation Vein Structure. R.Sedláček: Materials Science and Engineering A, 1997, 234-236, 643-5