  We develop a fractional return-mapping framework for power-law
visco-elasto-plasticity. In our approach, the fractional viscoelasticity is
accounted through canonical combinations of Scott-Blair elements to construct a
series of well-known fractional linear viscoelastic models, such as
Kelvin-Voigt, Maxwell, Kelvin-Zener and Poynting-Thomson. We also consider a
fractional quasi-linear version of Fung's model to account for stress/strain
nonlinearity. The fractional viscoelastic models are combined with a fractional
visco-plastic device, coupled with fractional viscoelastic models involving
serial combinations of Scott-Blair elements. We then develop a general
return-mapping procedure, which is fully implicit for linear viscoelastic
models, and semi-implicit for the quasi-linear case. We find that, in the
correction phase, the discrete stress projection and plastic slip have the same
form for all the considered models, although with different property and
time-step dependent projection terms. A series of numerical experiments is
carried out with analytical and reference solutions to demonstrate the
convergence and computational cost of the proposed framework, which is shown to
be at least first-order accurate for general loading conditions. Our numerical
results demonstrate that the developed framework is more flexible, preserves
the numerical accuracy of existing approaches while being more computationally
tractable in the visco-plastic range due to a reduction of $50\%$ in CPU time.
Our formulation is especially suited for emerging applications of fractional
calculus in bio-tissues that present the hallmark of multiple viscoelastic
power-laws coupled with visco-plasticity.
