  Computational Fluid Dynamics (CFD) is currently used to design and improve
the hydraulic properties of biomedical devices, wherein the large scale blood
circulation needs to be simulated by accounting for the mechanical response of
red blood cells (RBCs) at mesoscales. In many practical instances, biomedical
devices work on time-scales comparable to the intrinsic relaxation time of
RBCs: thus, a systematic understanding of the time-dependent response of
erythrocyte membranes is crucial for the effective design of such devices. So
far, this information has been deduced from experimental data, which do not
necessarily adapt to the the broad variety of the fluid dynamic conditions that
can be encountered in practice. This work explores the novel possibility of
studying the time-dependent response of an erythrocyte membrane to external
mechanical loads via ab-initio, mesoscale numerical simulations, with a primary
focus on the detailed characterisation of the RBC relaxation time $t_c$
following the arrest of the external mechanical load. The adopted mesoscale
model exploits a hybrid Immersed Boundary-Lattice Boltzmann Method (IB-LBM),
coupled with the Standard Linear Solid model (SLS) to account for the RBC
membrane viscosity. We underscore the key importance of the 2D membrane
viscosity $\mu_{m}$ to correctly reproduce the relaxation time of the RBC
membrane. A detailed assessment of the dependencies on the typology and
strength of the applied mechanical loads is also provided. Overall, our
findings open interesting future perspectives for the study of the non-linear
response of RBCs immersed in time-dependent strain fields.
