Plasticity, internal structure and phase field model

The model presented here is based on the assumption that the plastic phase is due to a variation of the strain generating a dislocation migration, which in turn implies a different material response. That is, the transition from elastic to plastic behavior is related with two different internal or mesoscopic structures. So, within the Landau theory on phase transitions, and via the notion of order parameter, we suggest a model for a hardening plasticity by a second order phase transition, able to describe the elastic–plastic transformation. The differential problem related with this new variable will be represented by the Ginzburg–Landau equation. The model is supplemented by a differential constitutive equation among the strain, the stress, and the order parameter. By this system, we are able to obtain the classical behavior of hardening plastic phase diagrams.