  We develop a thermodynamically consistent, fractional visco-elasto-plastic
model coupled with damage for anomalous materials. The model utilizes
Scott-Blair rheological elements for both visco-elastic/plastic parts. The
constitutive equations are obtained through Helmholtz free-energy potentials
for Scott-Blair elements, together with a memory-dependent fractional yield
function and dissipation inequalities. A memory-dependent Lemaitre-type damage
is introduced through fractional damage energy release rates. For
time-fractional integration of the resulting nonlinear system of equations, we
develop a first-order semi-implicit fractional return-mapping algorithm. We
also develop a finite-difference discretization for the fractional damage
energy release rate, which results into Hankel-type matrix-vector operations
for each time-step, allowing us to reduce the computational complexity from
$\mathcal{O}(N^3)$ to $\mathcal{O}(N^2)$ through the use of Fast Fourier
Transforms. Our numerical results demonstrate that the fractional orders for
visco-elasto-plasticity play a crucial role in damage evolution, due to the
competition between the anomalous plastic slip and bulk damage energy release
rates.
