Developing models for predicting various production quality characteristics (i.e., strength, ductility, surface roughness, closeness to the desired geometric form) for pressure treatment processing of metals. The models are based on multiscale models of structurally-inhomogeneous materials.

Developing a model of contact friction in pressure treatement processes. The model is based on the notion of a "third body", the layer separating the specimen and the instrument. The "third body" is viewed as a structurally inhomogeneous porous medium introduced in (Beygelzimer 1986); see the review below for details. Unlike previous models, this model explains friction strain that is due to the initial shift of the workpiece with respect to the instrument. This is very important for such processes as rolling, settling, and drop forging---processes with zones where metal sticks to the instrument. The model also takes into account the presence of lubrication that is locked in the micropores of the "third body".

Investigating parameter sensitivity of pressure treatement problems. The analysis led to a new method for investigating pressure treatement processes. Based on a few experimental values obtained for certain settings of parameters, the method allows one to theoretically predict the solution for other settings.