Pull-In Instability of Functionally Graded Cantilever Nanoactuators Incorporating Effects of Microstructure, Surface Energy and Intermolecular Forces

2018 ◽  
Vol 10 (08) ◽  
pp. 1850091 ◽  
Author(s):  
Mohamed A. Attia ◽  
Salwa A. Mohamed
Keyword(s):  
Residual Stress ◽  
Surface Energy ◽  
Boundary Conditions ◽  
Van Der Waals ◽  
Surface Elasticity ◽  
Van Der Waals Forces ◽  
Functionally Graded ◽  
Surface Residual Stress ◽  
Electrically Actuated ◽  
Classical Boundary

In this paper, an integrated non-classical continuum model is developed to investigate the pull-in instability of electrostatically actuated functionally graded nanocantilevers. The model accounts for the simultaneous effects of local-microstructure, surface elasticity and surface residual in the presence of fringing field as well as Casimir and van der Waals forces. The modified couple stress and Gurtin–Murdoch surface elasticity theories are employed to conduct the scaling effects of microstructure and surface energy, respectively, in the context of Euler–Bernoulli beam hypothesis. Bulk and surface material properties are varied according to the power-law distribution through the beam thickness. The physical neutral axis position for mentioned FG nanobeams is considered. Hamilton principle is employed to derive the nonlinear size-dependent governing equations and the non-classical boundary conditions. The resulting nonlinear differential equations are solved utilizing the generalized differential quadrature method (GDQM). In addition, the non-classical boundary conditions of nanocantilever beams due to surface residual stress are exactly implemented. After validation of the obtained results by previously available data in the literature, the influences of different geometrical and material parameters on the pull-in instability of the FG nanocantilevers are examined in detail. It is concluded that the pull-in behavior of electrically actuated FG micro/nanocantilevers is significantly influenced by the material distribution, material length scale parameter, surface elasticity constant, surface residual stress, initial gap, slenderness ratio, Casimir, and van der Waals forces. The obtained results can be considered for modeling and analysis of electrically actuated FG nanocantilevers.

Surface Energy Effects on the Nonlinear Free Vibration of Functionally Graded Timoshenko Nanobeams Based on Modified Couple Stress Theory

2019 ◽  
Vol 19 (11) ◽  
pp. 1950127 ◽  
Author(s):  
Mohamed A. Attia ◽  
Rabab A. Shanab ◽  
Salwa A. Mohamed ◽  
Norhan A. Mohamed
Keyword(s):  
Surface Energy ◽  
Boundary Conditions ◽  
Nonlinear Vibration ◽  
Surface Stress ◽  
Couple Stress ◽  
Surface Elasticity ◽  
Functionally Graded ◽  
Residual Surface Stress ◽  
Stress Surface ◽  
Modified Couple Stress

An integrated nonlinear couple stress-surface energy continuum model is developed to study the nonlinear vibration characteristics of size-dependent functionally graded nanobeams for the first time. The nanobeam theory is formulated based on the Timoshenko kinematics, augmented by von Kármán’s geometric nonlinearity. The modified couple stress and Gurtin–Murdoch surface elasticity theories are incorporated to capture the long-range interaction and surface energy, respectively. Unlike existing Timoshenko nanobeam models, the effects of surface elasticity, residual surface stress, surface mass density and Poisson’s ratio, in addition to bending and axial deformations, are incorporated in the newly developed model. A power law function is used to model the material distribution through the thickness of the beam, considering the gradation of bulk and surface material parameters. A variational formulation of the nonlinear nonclassical governing equations and associated nonclassical boundary conditions is established by employing Hamilton’s principle. The generalized differential quadrature method is exploited in conjunction with either the Pseudo-arclength continuation or Runge–Kutta method to solve the problem with an exact implementation of the nonclassical boundary conditions. The formulation and solution procedure presented are verified by comparing the obtained results with available ones. Based on the parametric study, it is concluded that the nonclassical boundary conditions, material length scale parameter, residual surface stress, surface elasticity, bulk elasticity modulus, gradient index, nonlinear amplitude and thickness have important influences on the linear and nonlinear vibration responses of functionally graded Timoshenko nanobeams.

scholarly journals Effect of Curvature-Dependent Surface Elasticity on the Flexural Properties of Nanowire

2021 ◽  
Vol 2021 ◽  
pp. 1-5
Author(s):  
Mengjun Wu ◽  
Quan Yuan ◽  
Honglin Li ◽  
Bin Wu ◽  
Lin Fang ◽  
...  
Keyword(s):  
Residual Stress ◽  
Flexural Rigidity ◽  
Rectangular Cross Section ◽  
Surface Elasticity ◽  
Surface Curvature ◽  
Flexural Properties ◽  
Bending Rigidity ◽  
Surface Residual Stress ◽  
The Difference ◽  
Stress Influence

Surface elasticity and residual stress strongly influence the flexural properties of nanowire due to the excessively large ratio of surface area to volume. In this work, we adopt linearized surface elasticity theory, which was proposed by Chhapadia et al., to capture the influence of surface curvature on the flexural rigidity of nanowire with rectangular cross section. Additionally, we have tried to study the bending deformation of circular nanowire. All stresses and strains are measured relative to the relaxed state in which the difference in surface residual stress between the upper and lower faces of rectangular nanowire with no external load induces additional bending. The bending curvature of nanowire in the reference and relaxed states is obtained. We find that flexural rigidity is composed of three parts. The first term is defined by the precept of continuum mechanics, and the last two terms are defined by surface elasticity. The normalized curvature increases with the decrease in height, thereby stiffening the nanowire. We also find that not only sizes but also surface curvature induced by surface residual stress influence the bending rigidity of nanowire.

Effect of Surface Relaxation on Characteristics of Nanomachined Surface

2011 ◽  
Vol 211-212 ◽  
pp. 742-746
Author(s):  
Yu Lan Tang ◽  
Ya Ting He ◽  
Guo Zhi Liu ◽  
Jing Xiang Fu ◽  
Hong Sun ◽  
...  
Keyword(s):  
Residual Stress ◽  
Surface Energy ◽  
Mechanical Systems ◽  
Surface Hardness ◽  
Surface Relaxation ◽  
Surface Residual Stress ◽  
Machined Surface ◽  
Micro Electro Mechanical Systems ◽  
Machined Parts ◽  
Effect Of Surface

With the development of Micro-electro-mechanical systems (MEMS) and Nano-electro-mechanical systems (NEMS), dimension of their parts is required to nanometer scale, and the characteristics of machined-surface of nano-scale parts affect strongly its application. Surface relaxation plays an important role to the characteristics of the machined-surface. In this paper, machined-surface of monocrystal copper used as the specimen of surface relaxation, and its surface relaxation process is simulated. The influences of surface relaxation on surface energy, atom array, surface roughness, surfaces hardness and surface residual stress of the monocrystal copper are analyzed. Results show that surface energy and surface hardness decrease due to relaxation; work-hardening can’t be completely eliminated by the relaxation; compression residual stress of the machined surface is changed gradually to tensile stress during the relaxation. These research results are very helpful to the application of nano-machined parts.

scholarly journals van der Waals forces influencing adhesion of cells

2015 ◽  
Vol 370 (1661) ◽  
pp. 20140078 ◽  
Author(s):  
K. Kendall ◽  
A. D. Roberts
Keyword(s):  
Cell Adhesion ◽  
Surface Energy ◽  
Adhesion Molecules ◽  
Adhesion Force ◽  
Van Der Waals ◽  
Van Der Waals Forces ◽  
Surface Molecules ◽  
Molecular Adhesion ◽  
Surface Active ◽  
Water Cut

Adhesion molecules, often thought to be acting by a ‘lock and key’ mechanism, have been thought to control the adhesion of cells. While there is no doubt that a coating of adhesion molecules such as fibronectin on a surface affects cell adhesion, this paper aims to show that such surface contamination is only one factor in the equation. Starting from the baseline idea that van der Waals force is a ubiquitous attraction between all molecules, and thereby must contribute to cell adhesion, it is clear that effects from geometry, elasticity and surface molecules must all add on to the basic cell attractive force. These effects of geometry, elasticity and surface molecules are analysed. The adhesion force measured between macroscopic polymer spheres was found to be strongest when the surfaces were absolutely smooth and clean, with no projecting protruberances. Values of the measured surface energy were then about 35 mJ m −2 , as expected for van der Waals attractions between the non-polar molecules. Surface projections such as abrasion roughness or dust reduced the molecular adhesion substantially. Water cut the measured surface energy to 3.4 mJ m −2 . Surface active molecules lowered the adhesion still further to less than 0.3 mJ m −2 . These observations do not support the lock and key concept.

Effect of surface elasticity on extensional and torsional stiffnesses of isotropic circular nanorods

2018 ◽  
Vol 24 (6) ◽  
pp. 1613-1629 ◽  
Author(s):  
Prakhar Gupta ◽  
Ajeet Kumar
Keyword(s):  
Residual Stress ◽  
Axial Force ◽  
Surface Elasticity ◽  
Surface Residual Stress ◽  
Molecular Statics ◽  
Stress Components ◽  
Stress Free State ◽  
Tungsten Material ◽  
Analytical Expressions ◽  
Effect Of Surface

We present a continuum formulation to obtain the effects of surface residual stress and surface elastic constants on extensional and torsional stiffnesses of isotropic circular nanorods. Analytical expressions of axial force, twisting moment, and extensional and torsional stiffnesses are obtained. Unlike the case of rectangular nanorods, we show that the stiffnesses of circular nanorods also depend on surface residual stress components. This is attributed to non-zero surface curvature inherent in circular nanorods. We further normalize these expressions and analyze their asymptotic limits in the limit of the nanorod’s radius approaching both zero and infinity, corresponding to surface-dominated and bulk-dominated regimes, respectively. Finally, we use the recently proposed helical Cauchy–Born rule and perform molecular statics calculations to obtain axial force, twisting moment, and stiffnesses of the tungsten nanorod. The tungsten material is selected since its bulk crystal exhibits isotropy in the stress-free state. The results from molecular statics calculations are shown to match the derived continuum formulas accurately.

scholarly journals Surface energy and wettability of van der Waals structures

Nanoscale ◽  
2016 ◽  
Vol 8 (10) ◽  
pp. 5764-5770 ◽  
Author(s):  
Meenakshi Annamalai ◽  
Kalon Gopinadhan ◽  
Sang A. Han ◽  
Surajit Saha ◽  
Hye Jeong Park ◽  
...  
Keyword(s):  
Surface Energy ◽  
Van Der Waals ◽  
Van Der Waals Forces ◽  
Layered Materials ◽  
2D Layered Materials ◽  
Dipole Interactions

Our study shows that the surface energy of all 2D layered materials is undoubtedly dominated by London–van der Waals forces with little contribution from dipole–dipole interactions.

Abrasive Waterjet Peening With Elastic Prestress: Effect of Boundary Conditions

2008 ◽  
Author(s):  
Balaji Sadasivam ◽  
Alpay Hizal ◽  
Dwayne Arola
Keyword(s):  
Residual Stress ◽  
Yield Strength ◽  
Boundary Conditions ◽  
Stress Fields ◽  
Abrasive Waterjet ◽  
Surface Residual Stress ◽  
Prosthetic Devices ◽  
Metal Implants ◽  
Removal Technique ◽  
Stored Elastic Energy

Abrasive Waterjet Peening (AWJP) has emerged as a potential surface treatment process for metal implants and prosthetic devices. An elastic tensile prestress has been shown to increase the magnitude and depth of residual stress that can be obtained. In the present investigation, the subsurface residual stress fields resulting from AWJ peening of Ti6Al4V with load control and displacement control elastic prestress were compared. Prestress ranged from 0 to 75% of the material’s yield strength and the subsurface residual stress distribution was quantified using the layer removal technique. Results showed that the surface residual stress was dependent on the boundary conditions for prestress levels less than 60% of the materials yield strength. The magnitude of surface residual stress and the stored elastic energy were up to 50% and 100% larger respectively when load controlled boundary conditions were used. However, the boundary condition did not affect the depth of compressive residual stress.

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