Viscoelastic response of thin membranes with application to red blood cells

The rate-type constitutive analysis of viscoelastic response of thin membranes, which includes an instantaneous elastic response and viscous behavior in both shear and dilatation, is developed with the aim to study the mechanical response of red blood cells. A convenient set of generalized stress and strain variables is introduced, which facilitates the derivation and integration of the governing differential equations. Gradual or sudden loading and stepwise unloading histories are considered. The performed parametric study of the mechanical response illustrates the effects of the introduced material parameters on the coefficient of viscoelastic lateral contraction and the overall membrane deformation. A closed form solution to the problem of radial stretching of a viscoelastic hollow circular membrane is derived without referral to the correspondence principle, which is of interest for the micropipette aspiration experiment of the red blood cell. The effects of the material parameters on the instantaneous elastic response and the subsequent rate of creep are discussed.