  The red blood cell (RBC) membrane is composed of a lipid bilayer and a
cytoskeleton interconnected by protein junction complexes, allowing for
potential sliding between the lipid bilayer and the cytoskeleton. Despite this
biological reality, it is most often modelled as a single-layer model, a
hyperelastic capsule or a fluid vesicle. Another approach involves
incorporating the membrane's composite structure using double layers, where one
layer represents the lipid bilayer and the other represents the cytoskeleton.
In this paper, we computationally assess the various modelling strategies by
analysing RBC behaviour in extensional flow and four distinct regimes that
simulate RBC dynamics in shear flow. The proposed double-layer strategies, such
as the vesicle-capsule and capsule-capsule models, account for the fluidity and
surface incompressibility of the lipid bilayer in different ways. Our findings
demonstrate that introducing sliding between the layers offers the cytoskeleton
a considerable degree of freedom to alleviate its elastic stresses, resulting
in a significant increase in RBC elongation. Surprisingly, our study reveals
that the membrane modelling strategy for RBCs holds greater importance than the
choice of the cytoskeleton's reference shape. These results highlight the
inadequacy of considering mechanical properties alone and emphasise the need
for careful integration of these properties. Furthermore, our findings
fortuitously uncover a novel indicator for determining the appropriate
stress-free shape of the cytoskeleton.
