  Cellular patterns formed by self-organization of dislocations are a most
conspicuous feature of dislocation microstructure evolution during plastic
deformation. To elucidate the physical mechanisms underlying dislocation cell
structure formation, we use a minimal model for the evolution of dislocation
densities under load. By considering only two slip systems in a plane strain
setting, we arrive at a model which is easily amenable to analytical stability
analysis and numerical simulation. We use this model to establish analytical
stability criteria for cell structures to emerge, to investigate the dynamics
of the patterning process and establish the mechanism of pattern wavelength
selection. This analysis demonstrates an intimate relationship between
hardening and cell structure formation, which appears as an almost inevitable
corollary to strain hardening itself. Specific mechanisms such as cross slip,
by contrast, turn out to be incidental to the formation of cellular patterns.
