Numerical computation of the elastic and mechanical properties of red blood cell membrane using the higher-order Cauchy–Born rule

Abstract

This paper employs the higher-order gradient theory to study the elastic and mechanical properties of red blood cell (RBC) membrane using the higher-order Cauchy–Born rule as an atomistic-continuum constitutive model that directly incorporates the microstructure of the spectrin network. The triangulated structure of the spectrin network is used to identify a representative cell or microstructure for the model as a symmetrical hexagon, which was then used together with the coarse-grained Helmholtz free energy density to construct a strain energy density function. Effects of the area and volume constraint coefficients on elastic and mechanical properties of RBC membrane were studied by conducting numerical experiments. The dependence of the membrane properties on various microstructure parameters and temperature was also studied. Finally, we investigated the mechanical response of the RBC membrane when subjected to tensile, shear and area dilation loading conditions using a representative microstructure. The results obtained shows that the elastic and mechanical properties of the membrane vary with increase in area and volume constraint coefficients; it also shows that these elastic and mechanical properties are affected by temperature and membrane microstructure parameters, which also influence the response of the membrane under various loading conditions.