Finite element characterization of the size-dependent mechanical behaviour in nanosystems

Abstract

Mechanical behaviour analysis plays an important role in the design of micro/nano-electromechanical system (MEMS/NEMS) devices for reliability. In this paper, the size-dependent mechanical properties of nanostructures are numerically studied with the finite element method (FEM) by developing a kind of surface element to take into account the surface elastic effect. This method is then applied to the investigation of the interaction between two pressurized nanovoids and the effective moduli of two-dimensional nanoporous material. The numerical results indicate that surface elasticity can significantly alter the nature of interaction forms and the effective moduli by inducing a strong size dependence in conventional results.

Nano-Contact Problem with Surface Effects on Triangle Distribution Loading

“…Substituting Equation (14) into Equation (5), the stresses component and displaces component are obtained as ( ) …”

“…Cammarata et al [13] considered the size-dependent deformation in thin film with surface effects. Gao et al [14] developed a finite-element method to account for the effect of surface elasticity. Wang et al [15] studied to a half-plane subjected to normal pressures with surface tension.…”

A unified computational framework for bulk and surface elasticity theory: a curvilinear-coordinate-based finite element methodology

“…Park et al (2006) ;Klein (2007, 2008) developed an alternative continuum framework, based on the surface Cauchy-Born model, to include surface stresses. Wei et al (2006) studied the size-dependent mechanical properties of nanostructures with the finite element method in two dimensions. Size effects observed in ZnO nanowires have been studied using surface elasticity theory (Agrawal et al, 2008;Yvonnet et al, 2011).…”

Multiscale modelling for composites with energetic interfaces at the micro- or nanoscale

“…This phenomenon has been investigated numerically using surface elasticity theory (see e.g. [24][25][26][27]). The strengthening effect due to the presence of energetic surfaces/interfaces has been studied recently using micromechanics approaches by [28][29][30].…”

“…Due to the geometry of the structure, the solution depends exclusively on x 3 . In such a case the interface equilibrium equations (29) lead to the classical traction continuity conditions and the equilibrium (27) reduces to a system of second-order ordinary differential equations. Solving the linear problem and using equation (25), the effective properties of the three-phase material (two bulk and one interface) are eventually obtained as…”