Nonlinear instability of hydrostatic pressurized microtubules surrounded by cytoplasm of a living cell including nonlocality and strain gradient microsize dependency

Abstract

As one of the most important components of a cytoskeleton, microtubules made from tubular polymers of tubulin can be found throughout the cytoplasm of eukaryotic cells. The role of microtubules in maintaining the structures of a living cell under external mechanical load is essential, so it is necessary to anticipate their size-dependent mechanical characteristics. In the present study, the size-dependent nonlinear instability of microtubules embedded in the biomedium of a living cell and under hydrostatic pressure is analyzed at different temperatures. For this objective, a more comprehensive size-dependent elasticity theory such as nonlocal strain gradient theory of elasticity is implemented to a refined hyperbolic shear deformation shell theory. Through deduction of the nonclassical governing equations to boundary layer-type ones and then employing a two-stepped perturbation solving process, explicit analytical expressions are established for nonlocal strain gradient stability paths of hydrostatic pressurized microtubules surrounded by the cytoplasm of a living cell. It is observed that for a microtubule under hydrostatic pressure, an initial extension occurs in the prebuckling regime until the critical buckling pressure. The nonlocality size effect decreases this initial extension, but the strain gradient size dependency increases it.