[sfepy] Meaning/explanation of dw_tl_diffusion term

Hi! I need to solve a diffusion problem within a solid undergoing large deformations. There is the dw_tl_diffusion term, which may be equivalent to my model (with proper choice of parameters). I am looking at this example: http://sfepy.org/doc-devel/examples/large_deformation/perfusion_tl.html

What bothers me is that the displacement u in the deformation-dependent permeability K(u) "relates to the previous time step". The usage of the term looks like this:

equations = { ..., 'mass_balance' : """dw_tl_volume.i1.Omega( q, u ) + dw_tl_diffusion.i1.Omega( ps.k, ps.N_f, q, p, u[-1]) = dw_tl_volume.i1.Omega( q, u[-1] )""" }

My questions are:

• What is the meaning of u[-1]?
• What does it mean "relates to the previous time step"? Does it mean that quantities like deformation gradient and its determinant are computed from the relative displacement between the two time steps? If yes, can it still be called total lagrangian? (An article would probably help.)
• How can the term be used to work with total displacement?

Thanks, Jan.