Influence of carbon nanotubes on the buckling of microtubule bundles in viscoelastic cytoplasm using nonlocal strain gradient theory

Carbon nanotubes are a new class of microtubule-stabilizing agents since they interact with protein microtubules in living cells, interfering with cell division and inducing apoptosis. In the present work, a modified beam model is developed to investigate the effect of carbon nanotubes on the buckling of microtubule bundles in living cell. A realistic interaction model is employed using recent experimental data on the carbon nanotube-stabilized microtubules. Small scale and surface effects are taken into account applying the nonlocal strain gradient theory and surface elasticity theory. Pasternak model is used to describe the normal and shearing effects of enclosing filament matrix on the buckling behavior of the system. An exact solution is obtained for the buckling growth rates of the mixed bundle in viscoelastic surrounding cytoplasm. The present results are compared with those reported in the open literature for single microtubules and an excellent agreement is found. Finally, the effects of different parameters such as the size, chirality, position and surface energy of carbon nanotubes on the buckling growth rates of microtubule bundles are studied. It is found that the buckling growth rate may increase or decrease by adding carbon nanotubes, depending on the diameter and chirality of carbon nanotubes. Keywords: Microtubules, Carbon nanotubes, Buckling, Size effect

Nonlinear mechanics of nanoscale tubes via nonlocal strain gradient theory

A size-dependent nonlinear nonlocal strain gradient model for nanoscale tubes is proposed in this investigation and the forced mechanical behaviour is examined. This continuum model is better capable of incorporating size effects as it includes two independent length-scale parameters. The scale-dependent elastic energy and motion energy as well as the work carried out by the excitation load are formulated. The non-classical nonlinear differential equation of motion of the nanoscale tube is obtained using Hamilton's work/energy principle together with the nonlocal strain gradient elasticity. A precise numerical solution is presented for the nonlinear dynamic characteristics within the framework of Galerkin's scheme in conjunction with a continuation approach. The influences of nanosystem parameters such as the scale parameters, the length-to-gyration-radius ratio as well as the amplitude of the excitation force on the frequency/force responses are explored and discussed in details.Mergen H. Ghayesh, Ali Farajpou

A review on the mechanics of nanostructures

Understanding the mechanical behaviour of nanostructures is of great importance due to their applications in nanodevices such as in nanomechanical resonators, nanoscale mass sensors, electromechanical nanoactuators and nanogenerators. Due to the difficulties of performing accurate experimental measurements at nanoscales and the high computational costs associated with the molecular dynamics simulations, the continuum modelling of nanostructures has attracted a considerable amount of attention. Since size influences have a crucial role in the mechanics of structures at nanoscale levels, classical continuum-based theories have been modified to incorporate these effects. Among various modified continuum-based theories, the nonlocal elasticity and the nonlocal strain gradient elasticity have been employed to estimate the mechanical behaviour of nanostructures. In this review paper, first these two modified elasticity theories are briefly explained. Then, the nonlocal motion equations for different nanostructures including nanorods, nanorings, nanobeams, nanoplates and nanoshells are derived. Several papers which reported on the size-dependent mechanical behaviour of nanostructures using modified continuum models are reviewed. Furthermore, important results reported on the vibration, bending and buckling of nanostructures as well as the results of size-dependent wave propagation analyses are discussed.Ali Farajpour, Mergen H.Ghayesh, Hamed Farokh

Nonlinear coupled mechanics of nanotubes incorporating both nonlocal and strain gradient effects

The coupled nonlinear mechanical behavior of nonlocal strain gradient nanotubes subject to distributed excitation forcing is investigated for the first time. Both longitudinal displacements and transverse deflection are taken into consideration in both the continuum-based formulation and the numerical solution. The influences of being at the nanoscale level are modeled with the use of the nonlocal strain gradient theory. The coupled large amplitude motion characteristics are extracted via Galerkin's approach and a continuation method. The influences of scale coefficients, the slenderness ratio, and the force amplitude of the external forcing on the motion are examined.Mergen H. Ghayesh and Ali Farajpou

Global dynamics of fluid conveying nanotubes

In the present article, an effort is made to analyse the coupled global dynamics of nanoscale fluid-conveying tubes. The influences of geometric nonlinearity are captured through the nonlinear Euler–Bernoulli strain relation of beams. Moreover, the size influences related to the nanoscale tube are captured via developing a nonlocal strain gradient model of beams. The Beskok–Karniadakis theory is also used for capturing the size influences related to the nanofluid. In addition to size influences, Coriolis acceleration effects together with the influences of the centrifugal acceleration are taken into account. Hamilton's principle gives two coupled equations of motions, which are discretised utilising Galerkin's technique. A time integration scheme is used for extracting the global dynamic characteristics of the nanotube containing nanofluid flow. The non-dimensional critical speed associated with buckling is also determined. It is found that the nanofluid speed plays a crucial role in the global dynamics in both the subcritical and supercritical regimes.Mergen H. Ghayesh, Hamed Farokhi, Ali Farajpou

Large-amplitude parametric response of fluid-conveying nanotubes due to flow pulsations

In this article, the nonlinear parametric response of viscoelastic nanotubes conveying pulsatile flow is investigated. A two-parameter scale-dependent elasticity-based model is developed within the framework of a nonlocal theory with strain gradient influences. To model the effects of fluid molecules, which slip on the internal nanotube wall, on the parametric response, Karniadakis–Beskok approach is used. Viscoelastic effects are also described via Kelvin–Voigt scheme. Hamilton law, Galerkin and continuation techniques are, respectively, utilized in this analysis for obtaining, discretising and solving nonlinear coupled equations. Both subcritical and supercritical nonlinear parametric responses are examined considering various parameters such as the speed variation amplitude and frequency. The viscoelastic nanotube conveying pulsatile flow exhibits a hardening nonlinearity in the subcritical regime while it displays a softening nonlinearity in the supercritical regime.Ali Farajpour, Mergen H. Ghayesh, Hamed Farokh

Viscoelastic local dynamics of microtubes conveying fluid

In the present study, a nonlinear coupled scale-dependent continuum model is developed to examine the local dynamics of a pulsatile fluid-conveying microscale tube. The effect of the internal energy loss is described by the Kelvin-Voigt model of viscoelasticity. Parametric forces due to the pulsatile flow as well as Coriolis forces are taken into consideration in the nonlinear scale-dependent model. The Euler-Bernoulli beam theory is utilised for describing the deformation behaviour while scale effects are captured via the modified version of the theory of couple stress. Then, Hamilton’s principle is utilised so as to derive the differential equations of the pulsatile fluidconveying microscale tube. The local dynamic characteristics are determined near the parametric resonance of the viscoelastic microscale system in the supercritical regime.Mergen H. Ghayesh, Ali Farajpour and Hamed Farokh