Landau-Type Theory of Planar Crystal Plasticity

We show that nonlinear continuum elasticity can be effective in modeling plastic flows in crystals if it is viewed as Landau theory with an infinite number of equivalent energy wells whose configuration is dictated by the symmetry group GL(3,Z). Quasi-static loading can be then handled by athermal dynamics, while lattice based discretization can play the role of regularization. As a proof of principle, we study in this Letter dislocation nucleation in a homogeneously sheared 2D crystal and show that the global tensorial invariance of the elastic energy foments the development of complexity in the configuration of collectively nucleating defects. A crucial role in this process is played by the unstable higher symmetry crystallographic phases, traditionally thought to be unrelated to plastic flow in lower symmetry lattices