Twinning occurs when the slip systems are constrained or the critical resolved shear stress is such that the twinning is activated before slipping. So, your model should allow the system to deform through slipping as well. To answer your original question though, in FCC metal, the twin plain is the (111) and the twin direction is [112]. This is found in Mechanical Metallurgy by George Dieter 3rd ED.
At IMDEA Materials Institue, we develop an Open Source code called MMonCa. http://www.materials.imdea.org/MMonCa
In the Lattice-KMC module, for example, a twinning formation model is used to explain the the bi-modal growth of Si: http://dx.doi.org/10.1016/j.scriptamat.2011.10.036
It has also been used for Ge. http://dx.doi.org/10.1063/1.4776718
I don't know if that's what you are looking for, but anyway, do not hesitate to ask!