A quasi-continuum model for human erythrocyte membrane based on the higher order Cauchy–Born rule

A nanoscale quasi-continuum (QC) model for exploring the mechanical properties of human erythrocyte/red blood cell (RBC) membranes is presented in this paper. The so-called higher order Cauchy–Born rule (HCB rule) is utilized as the linkage between the deformation of the spectrin network/cytoskeleton and that of the corresponding equivalent continuum. By incorporating the second order deformation gradients into kinematic description, the resulting QC model can capture the curvature effect of nanoscale membranes accurately in a geometrically consistent way. Based on the proposed QC model, a variationally consistent meshless computational scheme is developed for simulating the finite deformation of human erythrocyte/RBCs. The obtained deformation and wrinkling patterns are in good agreement with those from the existing experiments.