A minimal continuum model for mesoscale plasticity was provided which explained the cellular dislocation structures observed in deformed crystals. The dislocation density tensor evolved from random, smooth initial conditions to form self-similar structures which were strikingly similar to those seen experimentally; reproducing both the fractal morphologies and some features of the scaling of cell sizes and misorientations analyzed experimentally. The model provided a framework for understanding emergent dislocation structures at the mesoscale, a bridge across a computationally demanding mesoscale gap in the multiscale modelling program, and a new example of self-similar structure formation in non-equilibrium systems

Bending Crystals: Emergence of Fractal Dislocation Structures. Y.S.Chen, W.Choi, S.Papanikolaou, J.P.Sethna: Physical Review Letters, 2010, 105[10], 105501