A review on the mechanics of nanostructures

Abstract

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.

Mechanics of Fluid-Conveying Microtubes: Coupled Buckling and Post-Buckling

“…In order to compare the results of the classical elasticity theory with those of the MCS theory, the variation of the axial and lateral deflections of the microtube with the velocity of the flowing fluid is plotted in Figure 3 for both theories. It has been proven that size effects cannot be ignored at small-scale levels [43,[50][51][52][53][54][55][56]. While the length scale parameter is equal to zero for the classical theory, this parameter is assumed to be µ = 0.5746 for the MCS theory.…”

A coupled nonlinear continuum model for bifurcation behaviour of fluid-conveying nanotubes incorporating internal energy loss

“…in which 0 e , n ,  2 , E , g and  are the calibration constant, internal characteristics length, Laplace operator, elasticity modulus, strain gradient parameter and viscosity constant, respectively [55]. The above constitutive equation includes two different size parameters: 1) nonlocal parameter ( 0 n e ), and 2) strain gradient parameter ( g ).…”

Nonlocal strain gradient torsion of elastic beams: variational formulation and constitutive boundary conditions

“…Analysis and assessment of size-effects in nano-structures is currently a topic of major interest in the scientific community [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. Torsional deformations can frequently occur in structural elements of NEMS, and therefore, various size-dependent elasticity theories have been exploited in literature [21][22][23][24][25][26][27][28][29][30][31][32], as comprehensively discussed in review contributions [33,34].…”