Semi-analytical modeling and simulation of human red blood cell deformation under non-linear strain

The study of red blood cell (RBC) deformability remains an active area of research due to its linkage to health and normal physiological functions of RBCs in the circulatory system. RBC deformability is commonly analyzed using force-based experimental and theoretical approaches. Complementary to these methods, geometric descriptions of RBC shape provide insight into curvature redistribution and bending energetics independent of explicit constitutive modeling. In this work, we present a semi-analytical, surface-based framework to study RBC deformation under axial stretching by imposing an affine geometric strain on a triangulated biconcave membrane, with volume conservation enforced throughout. Linear strain and a non-linear Hencky-type strain are compared. While linear strain reproduces experimental trends only for small deformations, nonlinear strain yields global shape variations-axial and transverse diameters and elongation index-that are consistent with reported optical tweezers data over a wide deformation range. The surface formulation enables detailed mapping of Gaussian and mean curvature redistribution during elongation. Evaluation of the Helfrich bending energy, including spontaneous curvature treated as an effective geometric parameter, yields energetically consistent values when non-linear strain is employed. Analysis of the curvature-bending energy of the RBC subjected to axial stretching suggests that nonlinear strain and spontaneous curvature should be the primary considerations to ensure that the membrane bending energy remains within the range of 10-100 eV during RBC biomechanical deformation. The framework does not resolve force balance or membrane constitutive behavior, but provides a computationally efficient geometric surrogate linking imposed deformation to curvature and bending energetics.