Dynamic non-linear behavior and stability of a ventricular assist device

This paper investigates the non-linear dynamic behavior and stability of the internal membrane of a ventricular assist device (VAD). This membrane separates the blood chamber from the pneumatic chamber, transmitting the driving cyclic pneumatic loading to blood flowing from the left ventricle into the aorta. The membrane is a thin, nearly spherical axi-symmetric shallow cap made of polyurethane and reinforced with a cotton mesh. Experimental evidence shows that the reinforced membrane behaves as an isotropic elastic material and exhibits both membrane and flexural stiffness. So, the membrane is modeled as an isotropic pressure loaded shallow spherical shell and its dynamic behavior and snap-through buckling considering different types of dynamic excitation relevant to the understanding of the VAD behavior is investigated. Based on Marguerre kinematical assumptions, the governing partial differential equations of motion are presented in the form of a compatibility equation and a transverse motion equation. The results show that the shell, when subjected to compressive pressure loading, may loose its stability at a limit point, jumping to an inverted position. If the compressive load is removed, the shell jumps back to its original configuration. This non-linear behavior is the key feature in the VAD behavior.