A model of reversible cyclic deformation of a dislocation vein structure

A time-dependent continuum model of plastic flow consisting of two main ingredients is sketched in two space dimensions. First, an evolution equation for curved glide dislocations is set up. Second, equations of continuum mechanics are employed. The two parts are linked by the Orowan relation. The model takes the form of a set of coupled partial differential equations of evolution. Rather than looking for a numerical solution, simplifying assumptions are made. The model reduces to a boundary value problem for an inhomogeneous parabolic equation. Its periodic solution is found analytically. The relation of the proposed approach to established theories of continuum dislocation dynamics is briefly discussed.