  We use mesoscale numerical simulations to investigate the unsteady dynamics
of a single red blood cell (RBC) subjected to an external mechanical load. We
carry out a detailed comparison between the {\it loading} (L) dynamics,
following the imposition of the mechanical load on the RBC at rest, and the
{\it relaxation} (R) dynamics, allowing the RBC to relax to its original shape
after the sudden arrest of the mechanical load. Such a comparison is carried
out by analyzing the characteristic times of the two corresponding dynamics,
i.e., $t_L$ and $t_R$. When the intensity of the mechanical load is small
enough, the two kinds of dynamics are {\it symmetrical} ($t_L \approx t_R$) and
independent of the typology of mechanical load (intrinsic dynamics); otherwise,
in marked contrast, an {\it asymmetry} is found, wherein the loading dynamics
is typically faster than the relaxation one. This asymmetry manifests itself
with non-universal characteristics, e.g., dependency on the applied load and/or
on the viscoelastic properties of the RBC membrane. To deepen such a
non-universal behaviour, we consider the viscosity of the erythrocyte membrane
as a variable parameter and focus on three different typologies of mechanical
load (mechanical stretching, shear flow, elongational flow): this allows to
clarify how non-universality builds up in terms of the deformation and
rotational contributions induced by the mechanical load on the membrane.
Finally, we also investigate the effect of the elastic shear modulus on the
characteristic times $t_L$ and $t_R$. Our results provide crucial and
quantitative information on the unsteady dynamics of RBC and its membrane
response to the imposition/cessation of external mechanical loads.
