We have analyzed various phase field and sharp interface models for the description of moving boundary problems concerning the physical meaning of the driving forces. We contrasted the difference between the partial work, that is typically used in variational phase field models, where a virtual energy change is calculated while all other physical fields are kept constant, to a total work expression, where also for the trial move of the interface all physical fields are adjusted instantaneously. Although the latter is typically not used in phase field modeling, we argued that it should be the proper driving force in cases where the interface motion is slow in comparison to the kinetics of the other fields.
We demonstrated, that in cases of coupling to fast diffusion and static elasticity the two driving force expressions, which can be considered as limiting cases, coincide, and therefore the usual approach of the partial variational derivative should be appropriate.
This, however, is different for models with plasticity, because they contain additional internal variables which follow separate dynamics. These are usually not derived from the same free energy functional as the evolution equations for the other fields. Consequently, the partial and total work approach lead to different expressions for the driving forces. One central difference is that the latter contains also nonlocal terms which result from plastic bulk dissipation. The usual assumption is, however, that only the interface dissipation should play a role for the front propagation, and therefore it seems unlikely that bulk terms can be relevant. We therefore generalized the expression by proposing the true interface dissipation (where all other fields are slaved by the phase field) as driving force. It turns out, that this physically motivated expression coincides again with the partial work expression, provided that the material does not grow in different defect states than the underlying substrate phase. Otherwise, interface pinning and destabilization effects may occur, as well as the splitting of the direct and inverse transition curves, that is relevant for many solid-state transformations.