One can use upd to define the displacement of the material frame with respect to the geometry frame, and take
u as an update solution of the equations solved by the Solid Mechanics interface on the material frame. (The corresponding deformation gradient
F connects the material and spatial frames.) Note that the virtual work on such a displacement update is done by the total stress, and to get the correct stress, one can use as
Fpd the deformation gradient connecting the geometry and material frames, and then set the elastic deformation gradient to
Alternatively, a time-dependent study can be used. In this situation, the above formula will be applied during each time step to recompute upd before the step, using the stored previous solution, while
u will represent a displacement increment computed during the time step. In addition, the density is updated as
ρ0/
Jpd where
Again, Fpd is the deformation gradient connecting the geometry and material frames, and it will be updated before each time step or parameter sweep value.
Note that both Fel and
Fpl represent the total deformations of their corresponding types, while
Fpd is the total (elastic and plastic) deformation gradient from the previous update.