The C interface allows to define some physical models (like mobility etc.) within a rigid set of equations - drift-diffusion equations (current continuity equations for electrons and holes and Poisson equation) or quasi-hydrodynamic equations (plus maybe heat transport equation for lattice temperature). If your model does not fit within drift-diffusion - there is no chance to make use of Atlas or similar tools.
The biggest problem with "memristors" is the lack of first-principle models or theory. There are only empirical models, and the "chemical" or "process" related effects are very difficult if possible at all to capture in models that would be predictive.