Kelvin-Voigt Research Articles

Numerical simulation of the hemodynamics and biomechanics of the arterial system

A mathematical model of blood flow in arterial vessels with account for the nonstationary character of the laminar flow and the time-varying pressure drop is considered. The viscosity of blood is assumed to obey a power law. The rheological properties of the walls of arterial vessels are described by i) the Voigt—Kelvin model, ii) the standard-body model, and iii) the three-component Voigt—Kelvin model. As a result of numerical simulation, flow-pressure characteristics of various arteries are obtained.

Nonlinear Oscillations of Viscoelastic Rectangular Plates

Nonlinear oscillations of viscoelastic simply supported rectangular plates are studied by assuming the Voigt–Kelvin constitutive model. Using Hamilton's principle in conjunction with the kinematics associated with Kirchhoff's plate model, the governing equations of motion including the effect of damping are represented in terms of the transversal deflection and a stress function. Utilizing the Bubnov–Galerkin method, the nonlinear partial differential equations are reduced to an ordinary differential equation which is studied geometrically by approximate construction of the Poincare maps. Explicit expressions are given for periodic solutions.

Extensional Recovery of an Intact Erythrocyte From a Tank-Treading Motion

Normal human erythrocytes suspended in shear flow are stretched into quasi ellipsoidal forms while their membranes rotate smoothly (tank-treading). Following abrupt cessation of shear the cells recover their discoidal shapes approximately exponentially, in the manner of a Kelvin-Voigt (K-V) solid. To test the hypothesis that the recovery process is membrane-controlled, the effects of initial deformation, cytoplasmic viscosity and membrane surface-to-volume ratio were studied. It was concluded that the membrane dynamics dominates the transient shape recovery, and that the characteristic recovery time is dependent on the initial deformation. Hence, the usual simplified analysis based on retraction of a plane sheet of K-V material with constant moduli appears to be an inadequate treatment of transient whole cell recovery.