I read some articles that talk about how a FE software solves an elastoplastic problem in large deformations with a multiplicative decompositon of the total deformation gradient F into an elastic (F_e) and plastic (F_p) part. It is said that the unknown variable to be computed is F_p(the plastic deformation gradient). The equation that is discretized is written in terms of this unknown variable and the total deformation gradient F]. I infer that F is given, but I can't see how. The boundary conditions may not be written in terms of displacement, so how does the software evaluate F ?