  A general linearisation procedure for the consistent tangent of a
small-strain visco-plastic material model is presented in this note. The
procedure is based on multi-variable linearisation around a so-called
'reference state'. In particular, the linerarisation of the time integration
scheme is found to yield an extra term compared to classical expressions, which
only appears because the material response is time-dependent. It has the effect
of yielding a very accurate initial guess for the Newton-Raphson protocol based
on the ongoing viscous flow. It is shown, using a modern variational FFT-based
solver, that the extra term reduces both the CPU time and the number of
Newton-Raphson iterations by around a factor two.
