Short note on the bending models for a membrane in capsule mechanics: Comparison between continuum and discrete models

With regard to the out-of-plane bending energy of an elastic surface membrane, capsule deformation was compared between Helfrich's isotropic continuum model and discrete models using a triangulated surface. The in-plane deformation of the membrane was modeled by the neo-Hookean or Skalak law. Two mechanical problems were numerically simulated. One was the deformation of a spherical capsule under simple shear flow and the other was the equilibrium shape of a capsule with a nonzero excess surface area, assuming the shape mechanics of a normal red blood cell. The numerical simulations demonstrated that a discrete model based on locally averaged mean curvature satisfactorily reproduces the mechanical behavior determined by Helfrich's isotropic continuum model, whereas a discrete model without the averaging exhibited different deformation behavior. Differences in the mechanical behavior between bending models may cause differences in estimated bending rigidity values of up to one order of magnitude.