Stress Field Near a Nanosized Spheroidal Cavity under Bi-Axial Tension Perpendicular to the Revolution Axis

2008 ◽  
Vol 33-37 ◽  
pp. 1005-1010
Author(s):  
Zhi Ying Ou ◽  
Gang Feng Wang ◽  
Tie Jun Wang
Keyword(s):  
Surface Energy ◽  
Stress Field ◽  
Elasticity Theory ◽  
Surface Elasticity ◽  
Elastic Field ◽  
Classical Elasticity ◽  
Axial Tension ◽  
Spheroidal Cavity ◽  
Shape And Size ◽  
The Revolution

The elastic field around a nanosized spheroidal cavity is derived on the basis of surface elasticity theory. The effects of surface energy, shape and size of the cavity are discussed. It is seen that the stress field near the nanosized cavity depends on the shape and the size of the cavity as well as the properties of the surface. These new characteristics are different from those predicted by the classical elasticity and may illuminate some new mechanisms at nanoscale.

A new isogeometric Timoshenko beam model incorporating microstructures and surface energy effects

2020 ◽  
Vol 25 (10) ◽  
pp. 2005-2022 ◽  
Author(s):  
Shuohui Yin ◽  
Yang Deng ◽  
Gongye Zhang ◽  
Tiantang Yu ◽  
Shuitao Gu
Keyword(s):  
Surface Energy ◽  
Elasticity Theory ◽  
Timoshenko Beam ◽  
Couple Stress Theory ◽  
Surface Elasticity ◽  
Numerical Results ◽  
Beam Model ◽  
Timoshenko Beam Model ◽  
Order Continuity ◽  
Microstructure Effect

A new isogeometric Timoshenko beam model is developed using a modified couple stress theory (MCST) and a surface elasticity theory. The MCST is wildly used to capture microstructure effects that includes only one material length scale parameter, while the Gurtin–Murdoch surface elasticity theory containing three surface elasticity constants is employed to approximate the nature of surface energy effects. A new effective computational approach is presented for the current nonclassical Timoshenko beam model based on isogeometric analysis with high-order continuity basis functions of non-uniform rational B-splines, which effectively fulfills the higher continuity requirements in MCST. To validate the new approach and quantitatively illustrate both the microstructure and surface energy effects, the numerical results obtained from the developed approach for static deflection and natural frequencies of beams are compared with the analytical results available in the literature. Numerical results reveal that both the microstructure effect and surface energy effect should be considered in very thin beams, which also explains the size-dependent behavior.

Nonlinear Analysis for Bending, Buckling and Post-buckling of Nano-Beams with Nonlocal and Surface Energy Effects

2019 ◽  
Vol 19 (11) ◽  
pp. 1950130 ◽  
Author(s):  
Thai Binh Nguyen ◽  
J. N. Reddy ◽  
Jaroon Rungamornrat ◽  
Jintara Lawongkerd ◽  
Teerapong Senjuntichai ◽  
...  
Keyword(s):  
Surface Energy ◽  
Elasticity Theory ◽  
Mechanical Response ◽  
Bulk Material ◽  
Surface Elasticity ◽  
Closed Form Solution ◽  
Buckling Load ◽  
Material Surface ◽  
Material Layer ◽  
Post Buckling

The modeling and analysis for mechanical response of nano-scale beams undergoing large displacements and rotations are presented. The beam element is modeled as a composite consisting of the bulk material and the surface material layer. Both Eringen nonlocal elasticity theory and Gurtin–Murdoch surface elasticity theory are adopted to formulate the moment–curvature relationship of the beam. In the formulation, the pre-existing residual stress within the bulk material, induced by the residual surface tension in the material layer, is also taken into account. The resulting moment-curvature relationship is then utilized together with Euler–Bernoulli beam theory and the elliptic integral technique to establish a set of exact algebraic equations governing the displacements and rotations at the ends of the beam. The linearized version of those equations is also established and used in the derivation of a closed-form solution of the buckling load of nano-beams under various end conditions. A discretization-free solution procedure based mainly upon Newton iterative scheme and a selected numerical quadrature is developed to solve a system of fully coupled nonlinear equations. It is demonstrated that the proposed technique yields highly accurate results comparable to the benchmark analytical solutions. In addition, the nonlocal and surface energy effects play a significant role on the predicted buckling load, post-buckling and bending responses of the nano-beam. In particular, the presence of those effects remarkably alters the overall stiffness of the beam and predicted solutions exhibit strong size-dependence when the characteristic length of the beam is comparable to the intrinsic length scale of the material surface.

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 effect on deformation around an elliptical hole by surface energy density theory

2019 ◽  
Vol 25 (2) ◽  
pp. 337-347
Author(s):  
Liyuan Wang
Keyword(s):  
Energy Density ◽  
Surface Energy ◽  
Hoop Stress ◽  
Surface Effect ◽  
Plane Deformation ◽  
Surface Elasticity ◽  
Closed Form Solution ◽  
Elliptical Hole ◽  
External Loading ◽  
Surface Energy Density

The finite plane deformation of nanomaterial surrounding an elliptical hole subjected to remote loading is systematically investigated using a recently developed continuum theory. A complex variable formulation is utilized to obtain a closed-form solution for the hoop stress along the edge of the hole. The results show that when the size of the hole reduces to the same order as the ratio of the surface energy density to the applied remote stress, the influence of the surface energy density plays an even more significant role, and the shape of the hole coupled with surface energy density has a significant effect on the elastic state around the hole. Surprisingly, in the absence of any external loading, the hoop stress induced solely by surface effects is identical to that for a hole with surface energy in a linearly elastic solid derived by the Gurtin–Murdoch surface elasticity model. The results in this paper should be useful for the precise design of nanodevices and helpful for the reasonable assessment of test results of nano-instruments.

Corona Treatment of Filled Dual-polymer Dispersion Coatings: Surface Properties and Grease Resistance

2017 ◽  
Vol 25 (4) ◽  
pp. 257-266 ◽  
Author(s):  
Sami-Seppo Ovaska ◽  
Pavel Geydt ◽  
Ringaudas Rinkunas ◽  
Tadeusz Lozovski ◽  
Robertas Maldzius ◽  
...  
Keyword(s):  
Surface Energy ◽  
Direct Current ◽  
Photoelectron Spectroscopy ◽  
Rapeseed Oil ◽  
Surface Composition ◽  
Surface Elasticity ◽  
Contact Angles ◽  
Treatment Unit ◽  
Barrier Coating ◽  
Corona Treatment

Dispersion coating layers consisting of hydroxypropylated starch, 0–30 pph of barrier-grade talc and 0–10 pph of styrene-butadiene latex were subjected to both positive and negative direct-current corona treatments utilizing a specially developed dynamic treatment unit. The effects of the surface composition (barrier coating) on the response to the direct current corona treatment were evaluated by measuring contact angles and determining the surface energy. The effects of corona treatment on the properties of the barrier coating were further determined by measuring the contact angle of rapeseed oil and the grease resistance. It was found that the grease resistance of the corona-treated barrier coatings was substantially lower than that of untreated samples, which was ascribed to holes caused by corona discharge strike-through and to chemical changes on the treated surfaces. The corona treatment lowered the surface energy of the coatings, as indicated by an increase in the contact angles of water and rapeseed oil. Changes in the dispersion part of the surface energy were recorded, particularly after positive treatment voltage, whereas a negative discharge led to greater changes in the polar part of the surface energy. X-ray photoelectron spectroscopy (XPS) tests revealed an increase in the proportion of talc at the surface after corona treatment, which indicates a migration caused by the applied electric field. The peak force tapping mode of an atomic force microscope revealed moderate topographical changes in the coatings and a decrease in surface elasticity, supporting the migration of talc particles. In addition, significant changes in the physicochemical properties of the untreated reverse side were observed.

Effects of Surface Elasticity on Scattering of P Waves by an Elastic Half-Plane with a Nanosized Semi-Cylindrical Inclusion

2013 ◽  
Vol 303-306 ◽  
pp. 2661-2666
Author(s):  
Zhi Ying Ou ◽  
Cheng Liu ◽  
Xiao Wei Liu
Keyword(s):  
Surface Energy ◽  
Half Plane ◽  
Surface Effect ◽  
Surface Elasticity ◽  
Expansion Method ◽  
Cylindrical Inclusion ◽  
P Waves ◽  
Wave Function Expansion Method ◽  
Plane P Waves ◽  
Incident Waves

The scattering of plane P waves by a nanosized semi-cylindrical inclusion embedded in an elastic half-plan has been studied in this paper. To account for the surface effect at nanoscale, the surface elasticity is also adopted. When the boundary condition at the straight edge of the half-plane is traction free, the analytical solutions of stress fields of the half plan with semi-cylindrical inclusion are expressed by employing a wave function expansion method. The results show that surface energy has a significant effect on the scattering of plane P waves as the radius of the semi-cylindrical inclusion shrinks to nanoscale. For incident waves with different frequencies, radius of semi-cylindrical inclusion, the effects of surface energy on the dynamic stress concentration near the semi-cylindrical inclusion are discussed in detail.

Effects of Surface Energy on Scattering of SH Waves by an Elastic Half-Plane with a Semi-Cylindrical Cavity

2012 ◽  
Vol 627 ◽  
pp. 698-704
Author(s):  
Zhi Ying Ou ◽  
Xiao Wei Liu ◽  
Qiong Deng
Keyword(s):  
Surface Energy ◽  
Cylindrical Cavity ◽  
Dynamic Stress ◽  
Shear Waves ◽  
Surface Elasticity ◽  
Expansion Method ◽  
Stress Fields ◽  
Sh Waves ◽  
Wave Function Expansion Method ◽  
Incident Waves

When the radius of materials and structral devices reduces to nanometers, the influence of surface energy becomes prominent in its mechanical behavior. In the frame of surface elasticity, the scattering of anti-plan shear waves by an elastic half-plan with a semi-cylindrical cavity considered the surface energy are investigated in this paper. When the boundary condition at the straight edge of the half-plan is traction free, the analytical solutions of stress fields of the half plan with semi-culindrical cavity are expressed by employing a wave function expansion method. The results show that surface energy has a significant effect on the scattering of anti-plan shear waves as the radius of the semi-cylindrical cavity shrinks to nanoscale. The effects of incident waves with different frequencies and incident angel, radius of semi-cylindrical cavity and surface energy on the dynamic stress concentration around the semi-cylindrical cavity are discussed in detail.

Static and dynamic instability of nanowire-fabricated nanoelectromechanical systems: effects of flow damping, van de Waals force, surface energy and microstructure

2016 ◽  
Vol 94 (6) ◽  
pp. 594-603 ◽  
Author(s):  
Maryam Keivani ◽  
Ali Koochi ◽  
Naeime Abadian ◽  
Morteza Rezaei ◽  
Mohamadreza Abadyan
Keyword(s):  
Surface Energy ◽  
Governing Equation ◽  
Dynamic Instability ◽  
Surface Elasticity ◽  
Circular Cross Section ◽  
Continuum Theory ◽  
Nanoelectromechanical Systems ◽  
Gas Damping ◽  
Static And Dynamic Instability ◽  
Lagrange Strain

Surface energy and microstructure-dependent size phenomena can play significant roles in physical performance of nanoelectromechanical systems (NEMS). Herein, the static and dynamic pull-in instability of cantilever and double-clamped NEMS fabricated from conductive cylindrical nanowires with circular cross section is studied. The Gurtin–Murdoch surface elasticity in combination with the couple stress continuum theory is employed to incorporate the coupled effects of surface energy and microstructure-dependent size phenomenon. Using Green–Lagrange strain, the higher order surface stress components are incorporated into the governing equation. The effect of gas damping is considered in the model as well as structural damping. The nonlinear governing equation is solved using analytical reduced order method. The effects of various parameters on the static and dynamic pull-in parameters, phase plans, and stability threshold of the nanowire-based structures are demonstrated.

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