Some exactly solvable models for the statistical evolution of internal variables during plastic deformation

A class of exactly solvable statistical models for the evolution of internal (microstructural) variables in the course of plastic deformation is discussed. The common feature of these models is that the microstructural evolution is described in terms of stochastic differential equations (Langevin equations) which by a non-linear transformation can be mapped onto a Wiener or Ornstein–Uhlenbeck process. Examples include the textural evolution of planar polycrystals, the evolution of dislocation density distribution in unidirectional plastic deformation, and the combined dynamics of mobile dislocations and dislocation obstacles leading to slip-channel formation.