  The spontaneous emergence of heterogeneous dislocation patterns is a
conspicuous feature of plastic deformation and strain hardening of crystalline
solids. Despite long-standing efforts in the materials science and physics of
defect communities, there is no general consensus regarding the physical
mechanism which leads to the formation of dislocation patterns. In order to
establish the fundamental mechanism, we formulate an extremely simplified,
minimal model to investigate the formation of patterns based on the continuum
theory of fluxes of curved dislocations. We demonstrate that strain hardening
as embodied in a Taylor-type dislocation density dependence of the flow stress,
in conjunction with the structure of the kinematic equations that govern
dislocation motion under the action of external stresses, is already sufficient
for the formation of dislocation patterns that are consistent with the
principle of similitude.
