Including Surface Stress Research Articles

Investigation of the Bending Behavior in Silicon Nanowires: A Nanomechanical Modeling Perspective

Nanowires (NWs) play a crucial role across a wide range of disciplines such as nanoelectromechanical systems, nanoelectronics and energy applications. As NWs continue to reduce in dimensions, their mechanical properties are increasingly affected by surface attributes. This study conducts a comprehensive examination of nanomechanical models utilized for interpreting large deformations in the bending response of silicon NWs. Specifically, the Heidelberg, Hudson, Zhan, SimpZP and ExtZP nanomechanical models are explored regarding their capability to predict the elastic properties of silicon NWs with varying critical dimensions and crystal orientations. Molecular dynamics simulations are employed to model silicon NWs with unreconstructed surface states. The calculation of intrinsic stresses and the methodology for quantifying surface properties, including surface stresses and surface elasticity constants, are carried out using atomistic modeling. The findings reveal significant disparities of up to 100 GPa among nanomechanical models in interpreting a singular force-deflection response obtained for a silicon NW. Inadequate consideration of surface and intrinsic effects in nanomechanical modeling of NWs leads to substantial variability in their mechanical properties. This investigation yields valuable insights into the surface characteristics of silicon NWs, thereby enhancing our understanding of the essential role played by nanomechanical models in the intricate interpretation of mechanical properties at the nanoscale.

Theoretical prediction of proteins network-induced nonlocal response in molecules-resonator biosensor with hydrogen bonds including van der waals interactions

The present study investigates the adsorption-induced resonance frequency shift of a biomolecule-resonator system, considering the shear distortion effect, distributed adatoms, and small-scale effects using nonlocal elasticity theory. The adsorption-induced energy is modeled using a distributional approach for both the bio-receptor and spike protein. The dynamic behavior model for a microbeam resonator is derived, incorporating surface stress. The functional microbeam approach and the localized biomolecule approach are employed, along with van der Waals (vdW) interactions using the Lennard-Jones (6–12) potential to calculate the influence of all applied conditions. Explicit inertia moment and shear force are determined based on the nonlocal Timoshenko beam equations, with residual stress applied as an additive axial load. Numerical results demonstrate that the computed frequency shift depends on the active surface parameters, adsorbed adatoms, as well as the localized receptor and spike. The evaluation of results indicates that interatomic phenomena make the microsystem softer, emphasizing the importance of considering it in computations. Thus, the derived model is suitable for investigating the dynamic behavior of the biomolecule-resonator, applicable for determining both mass and density of spike and virus in the presence of adatom bonds.

Phase field theory for fracture at large strains including surface stresses

Phase field theory for fracture is developed at large strains with an emphasis on a correct introduction of surface stresses at nanoscale. This is achieved by multiplying the cohesion and gradient energies by the local ratio of the crack surface areas in the deformed and undeformed configurations and with the gradient energy in terms of the gradient of the order parameter in the reference configuration. This results in an expression for the surface stresses which is consistent with the sharp surface approach. Namely, the structural part of the Cauchy surface stress represents an isotropic biaxial tension, with the magnitude of a force per unit length equal to the surface energy. The surface stresses are a result of the geometric nonlinearities, even when strains are infinitesimal. They make multiple contributions to the Ginzburg-Landau equation for damage evolution, both in the deformed and undeformed configurations. Important connections between material parameters are obtained using an analytical solution for two separating surfaces, as well as an analysis of the stress-strain curves for homogeneous tension for different degradation and interpolation functions. A complete system of equations is presented in the deformed and undeformed configurations. All the nanoscale phase field parameters are obtained utilizing the existing first principle simulations for the uniaxial tension of Si crystal in the [100] and [111] directions.

Nanotube formation from self-curling nanofilms driven by intrinsic surface-stress imbalance

The theoretical analysis for fabricating nanotubes from self-curling of nanofilms due to intrinsic surface stress imbalance was given in this paper. A nanofilm was curled into a nanotube along tangential direction, while the other in-plane direction (cylindrical direction) was only elongated but wasn’t curled or bent. Film bending behavior is usually described by using Stoney formula, but the Poisson’s effect of cylindrical direction should be considered for describing mechanical behavior of curling up phenomenon. Stoney formula assumes that the surface stress is isotropic and the bending is also isotropic, but the shape of nanotube is anisotropic. On the other hand, surface effects and symmetry lowering effect strongly affect the mechanical properties of nonafilms. Here, we gave a more accurate curling theory by including surface stress, surface elasticity, symmetry lowering and Poisson’s effect of cylindrical direction.

Effects of Machined Surface Integrity on High-Temperature Low-Cycle Fatigue Life and Process Parameters Optimization of Turning Superalloy Inconel 718

Machined surface integrity characteristics, including surface stresses, physical-mechanical properties and metallographic structures, play important roles in the fatigue performance of machined components. This work aimed at investigating the effects of machined surface integrity on high-temperature low-cycle fatigue life. The process parameters were optimized to obtain required surface integrity and fatigue life of the turning superalloy Inconel 718. The relationships between low-cycle fatigue life and machined surface integrity characterization parameters were established based on the low-cycle fatigue tests at a high temperature (650 °C). The sensitivities of turning process parameters to high-temperature low-cycle fatigue life were analyzed, and the optimization parameters were proposed with the goal of antifatigue manufacturing. Experimental results indicated that the impact order of the characterization parameters of machined surface integrity on the high-temperature low-cycle fatigue life were the degree of work hardening RHV, the residual stress in the cutting speed direction S22, the fatigue stress concentration factor Kf, the degree of grain refinement RD and the residual stress in the feed direction S33. In the range of turning parameters of the experiments in this research, the cutting speeds could be 80~110 m/min, and the feed rate could be 0.10~0.12 mm/rev to achieve a longer high-temperature low-cycle fatigue life. The results can be used for guiding the fatigue-resistant manufacturing research of aeroengine superalloy turbine disks.

Large-amplitude oscillations of composite conical nanoshells with in-plane heterogeneity including surface stress effect

In the current investigation, a new formulation for nonlinear vibration behaviors of functionally graded (FG) composite conical nanoshells are constructed using Gurtin-Murdoch elasticity theory based on higher-order shear deformation shell theory (HSDFST) framework. Both Voigt and Reuss homogenization procedures are considered for the estimation of the mechanical characteristics of FG materials. Using generalized differential quadrature method (GDQM) together with Galerkin technique, the surface elastic-based nonlinear frequency-responses of FG composite conical nanoshell are obtained. It has been illustrated that the decrease of material property gradient index or transformation of boundary condition from full simply supported to full clamped, surface stress effect on the nonlinear frequency of a FG composite conical nanoshell reduces. Also, decreasing semi-vertex angle increases the frequency ratio of ωNL/ωL which reveals higher geometrical nonlinearity. However, it is seen that surface elasticity effect on the nonlinear vibration behavior of FG composite conical nanoshells is not significant.

Surface elastic shell model for nonlinear primary resonant dynamics of FG porous nanoshells incorporating modal interactions

The surface to volume ratio becomes significant at nanoscale, so the surface stress plays an essential role in the mechanical responses of nanostructures. The focus of the present study is on an accurate analytical nonlinear primary resonance solution of functionally graded (FG) porous nanoshells under an external soft harmonic excitation including surface stress effects. To this end, the constitutive differential equations are adopted within the framework of the Gurtin-Murdoch theory of elasticity. In order to capture more accurate results, the nonlinear modal interactions between the main oscillation mode and higher symmetric vibration modes are taken into account. In addition, the mechanical properties of the FG porous nanoshell are estimated on the basis of the closed-cell Gaussian-Random field scheme. Thereafter, with the aid of the multiple time-scales technique, analytical expressions are expressed for the nonlinear surface elastic-based frequency-responses and amplitude-responses associated with the nonlinear primary resonance of FG porous nanoshells corresponding to various nonlinear modal interactions. It is demonstrated that by taking the modal interaction between higher symmetric vibration modes with the main oscillation mode into account, the frequency-response of FG porous nanoshells changes from the hardening behavior to the softening one. As a consequence, the modal interaction causes to shift the peak of the nonlinear resonance from the excitation frequency range of Ω/ω > 1 to Ω/ω < 1.

Phase field modeling of crack growth with double-well potential including surface effects

A thermodynamically consistent phase field approach for fracture including surface stresses is presented. The surface stresses which are distributed inside a finite width layer at the crack surface are introduced as a result of employing some geometrical nonlinearities, i.e., by defining energy terms per unit volume at the current time and evaluating gradient of the order parameter in the current configuration. A double-well barrier term is included in the structure of the Helmholtz free energy which allows one to use the energy terms per unit volume at the current time when introducing the surface stresses in the current approach. Thus, the surface stresses are introduced in a similar way to the interfacial stresses in phase transformations. The differences in the modeling of crack growth with considering the surface stresses and without it are discussed. It is shown how the surface stresses affect the stress fields and consequently the crack nucleation and propagation. The finite element method is utilized to solve the coupled equations of mechanics and crack phase field. It is emphasized that the surface stresses affect the driving force for both the crack nucleation and propagation by disturbing the momentum balance. Thus, a different external loading is required in the presence of the surface stresses.

Propagation and Reflection of Plane Waves in a Rotating Magneto-Elastic Fibre-Reinforced Semi Space with Surface Stress

Abstract The present paper investigates the propagation of quasi longitudinal (qLD) and quasi transverse (qTD) waves in a magneto elastic fibre-reinforced rotating semi-infinite medium. Reflections of waves from the flat boundary with surface stress have been studied in details. The governing equations have been used to obtain the polynomial characteristic equation from which qLD and qTD wave velocities are found. It is observed that both the wave velocities depend upon the incident angle. After imposing the appropriate boundary conditions including surface stress the resultant amplitude ratios for the total displacements have been obtained. Numerically simulated results have been depicted graphically by displaying two and three dimensional graphs to highlight the influence of magnetic field, rotation, surface stress and fibre-reinforcing nature of the material medium on the propagation and reflection of plane waves.

Wind modulation by variable roughness of ocean surface

Recent results concerning transient effects of variation of short sea-surface wave roughness on near-surface turbulent wind are briefly outlined. This variation can be caused by oil, surfactants, inhomogeneous currents, internal waves, ship wakes, etc. To describe the wind parameters including surface stress and turbulent energy density, we use a direct solution of the Reynolds-type equations in the boundary-layer approximation. The solutions include a sharp and smooth roughness variation, 2-D surface variation, and a moving slick. The applicability of the theory was verified by comparison with laboratory data. Further on, the theory was applied to a problem related to the devastating tsunami near Fukushima Daichi in 2011.

Nonlocal Dynamic Stability of DWCNTs Containing Pulsating Viscous Fluid Including Surface Stress and Thermal Effects Based on Sinusoidal Higher Order Shear Deformation Shell Theory

AbstractIn this study, the dynamic stability of double-walled carbon nanotubes (DWCNTs) conveying pulsating viscous fluid located on visco-Pasternak medium is investigated. The effects of small scale are considered using Eringen's non-local theory. The surrounding medium of DWCNT is anticipated as a visco-Pasternak foundation including the normal, shear, and damping forces. The van der Waals (vdWs) force is considered among the inner and outer layers of DWCNT. Three types of temperature changes, i.e. uniform, linear and sinusoidal temperature rise, through the thickness are studied. The equations of motion are obtained using higher order sinusoidal shear deformation shell theory (SSDT), in which the surface effects are included. Dynamical equations of DWCNT are extracted using the energy method and Hamilton's principle. Due to orthogonal conditions, the governing equations are solved based on Bolotin method. The effects of different parameters such as surface stress, non-local parameter, fluid velocity, Knudsen's number, fluid density, dimensions ratio and various temperature loadings on the dynamic stability regions of DWCNTs are discussed.

Nonlinear resonance responses of geometrically imperfect shear deformable nanobeams including surface stress effects

In this work, a thorough investigation is presented into the nonlinear resonant dynamics of geometrically imperfect shear deformable nanobeams subjected to harmonic external excitation force in the transverse direction. To this end, the Gurtin–Murdoch surface elasticity theory together with Reddy’s third-order shear deformation beam theory is utilized to take into account the size-dependent behavior of nanobeams and the effects of transverse shear deformation and rotary inertia, respectively. The kinematic nonlinearity is considered using the von Kármán kinematic hypothesis. The geometric imperfection as a slight curvature is assumed as the mode shape associated with the first vibration mode. The weak form of geometrically nonlinear governing equations of motion is derived using the variational differential quadrature (VDQ) technique and Lagrange equations. Then, a multistep numerical scheme is employed to solve the obtained governing equations in order to study the nonlinear frequency–response and force–response curves of nanobeams. Comprehensive studies into the effects of initial imperfection and boundary condition as well as geometric parameters on the nonlinear dynamic characteristics of imperfect shear deformable nanobeams are carried out through numerical results. Finally, the importance of incorporating the surface stress effects via the Gurtin–Murdoch elasticity theory, is emphasized by comparing the nonlinear dynamic responses of the nanobeams with different thicknesses.

Effect of surface energy on nano-resonator dynamic behavior

Presented herein is a comprehensive analysis on the size-dependent dynamic behaviors of electrostatically actuated nano-resonator including surface stresses effect. To this end, partial differential equation of nano-resonator based on Gurtin–Murdoch and Euler–Bernoulli theories is converted to ordinary differential equation utilizing assumed mode method.Effect of applied DC voltage on stability and bi-stability of nano-resonator is investigated and it revealed that surface elasticity and stress affect the bi-stability region of nano-resonator. By plotting frequency response of the resonator, hardening and softening behavior of nano-resonator are analyzed and it is shown that surface effect may change the hardening and softening behavior of nano-resonators.

Geometrically nonlinear free vibration and instability of fluid-conveying nanoscale pipes including surface stress effects

This paper is aimed to examine the geometrically nonlinear vibration and stability of nanoscale pipe conveying fluid incorporating surface stress effect. To approach this, the von-Karman hypothesis and Timoshenko beam theory are used to model the nanoscale pipe as a nonlinear Timoshenko nanobeam. Then, Hamilton’s principle and the Gurtin–Murdoch continuum elasticity are used to derive the governing equations of motion and associated boundary conditions incorporating the surface stress effect. Afterward, by the generalized differential quadrature method and harmonic balance method, the obtained nonlinear differential equations are discretized and simplified, before solving numerically through the Newton–Raphson method. The effects of the surface stress parameters on the stability and imaginary and real parts of frequency of nanopipes are discussed. Results are performed for nanopipes with different end supports made of silicon (Si) and aluminum (Al).

On the bending and stability of nanowire using various HSDTs

In this article, various higher-order shear deformation theories (HSDTs) are developed for bending and buckling behaviors of nanowires including surface stress effects. The most important assumption used in different proposed beam theories is that the deflection consists of bending and shear components and thus the theories have the potential to be utilized for modeling of the surface stress influences on nanowires problems. Numerical results are illustrated to prove the difference between the response of the nanowires predicted by the classical and non-classical solutions which depends on the magnitudes of the surface elastic constants.

Surface stress effects on the nonlinear postbuckling characteristics of geometrically imperfect cylindrical nanoshells subjected to axial compression

For structures at nanoscale, the surface effects can be important due to the high ratio of surface area to volume. In the current investigation, the nonlinear axial postbuckling behavior of geometrically imperfect cylindrical nanoshells is studied including surface stress effects. For this purpose, Gurtin–Murdoch continuum elasticity theory in conjunction with von Karman–Donnell-type geometric nonlinearity is implemented into the classical shell theory. By the developed size-dependent shell model, the surface effects which include surface elasticity and residual surface stress are taken into account. In order to satisfy balance conditions on the surfaces of nanoshell, a linear variation through the thickness is considered for the normal stress component of the bulk. Based on the variational approach using virtual work's principle, the non-classical governing differential equations are derived. In order to solve the nonlinear problem, a boundary layer theory is employed which contains simultaneously the nonlinear prebuckling deformations, initial geometric imperfections and large deflections corresponding to the postbuckling domain. Subsequently, a two-stepped singular perturbation methodology is utilized to predict the nonlinear critical buckling loads as well as the postbuckling equilibrium paths. It is observed that by taking surface stress effects into account, the both critical buckling load and critical end-shortening of a cylindrical nanoshell made of Silicon increase.

Surface stress effects on the nonlinear postbuckling characteristics of geometrically imperfect cylindrical nanoshells subjected to torsional load

The prime aim of the current investigation is to predict the nonlinear torsional buckling and postbuckling behavior of geometrically imperfect cylindrical nanoshells including surface stress effects. To this end, the size-dependent governing differential equations of cylindrical nanoshell based on von Karman–Donnell-type of kinematic nonlinearity are derived using a combination of Gurtin–Murdoch elasticity theory and the classical shell theory, and employing the principle of virtual work. Subsequently, by considering the transverse displacement and Airy stress function as independent variables, a boundary layer theory is put to use which takes surface stress effects into account in conjunction with the nonlinear prebuckling deformations, large postbuckling deflections and initial geometric imperfection. Finally, an efficient solution methodology based on a two-stepped singular perturbation technique is conducted to obtain the size-dependent postbuckling equilibrium paths of nanoshells. It is revealed that after the minimum point of postbuckling load, by increasing the value of applied torsional load, the difference between postbuckling load-deflection curves corresponding to the perfect and imperfect nanoshells tends to decrease.

Surface stress effects on the postbuckling behavior of geometrically imperfect cylindrical nanoshells subjected to combined axial and radial compressions

Because of surface free energy effects at nanoscale, study of the mechanical behavior of nanostructures including surface stress effects is a topic of substantial interest. Herein, the nonlinear buckling and postbuckling characteristics of geometrically imperfect cylindrical nanoshells under combined axial and radial compressive loads are investigated in the presence of surface stress effects. An efficient size-dependent shell model is proposed based on Gurtin–Murdoch elasticity theory and von Karman–Donnell-type of kinematic nonlinearity. On the basis of variational approach using the principle of virtual work, the non-classical governing differential equations are derived. Afterwards, a boundary layer theory is employed incorporating surface stress effects in conjunction with nonlinear prebuckling deformations, initial geometric imperfections and large postbuckling deflections. Then a two-stepped singular perturbation methodology is put to use in order to solve the size-dependent nonlinear problem corresponding to axial dominated and radial dominated loading cases. It is shown that in the case of radial dominated loading, the combination of hydrostatic pressure with axial compression causes to decrease approximately the effect of surface stress compared to the absence of axial load. However, for the axial dominated loading case, in comparison with no applied radial load, the surface stress effects is more significant in the presence of hydrostatic pressure.

On the postbuckling behavior of geometrically imperfect cylindrical nanoshells subjected to radial compression including surface stress effects

The main objective of the present study is to investigate the effect of surface stress on the nonlinear buckling and postbuckling behavior of cylindrical nanoshells with initial geometric imperfection subjected to radial compressive load. Gurtin–Murdoch elasticity theory is implemented into the classical shell theory to develop a size-dependent shell model which is capable to capture surface stress effects efficiently. In order to satisfy balance conditions on the surfaces of nanoshell, a linear variation through the thickness is considered for the normal stress component of the bulk. The principle of virtual work is put to use in order to formulate the non-classical governing differential equations. Afterwards, a boundary layer theory is employed including the nonlinear prebuckling deformations, initial geometric imperfection and large postbuckling deflections. Finally, a two-stepped singular perturbation methodology is utilized to obtain the size-dependent critical buckling loads and the postbuckling equilibrium paths of imperfect nanoshells corresponding to both lateral and hydrostatic pressure loading cases. It is found that for the positive and negative values of surface elastic constants, the both critical buckling load and critical end-shortening of nanoshell increase and decrease, respectively.

Nonlocal plate model for dynamic pull-in instability analysis of circular higher-order shear deformable nanoplates including surface stress effect

In the present paper, dynamic pull-in instability and free vibration characteristics of circular higher-order shear deformable nanoplates subjected to hydrostatic and electrostatic forces are studied including surface stress effect. For this purpose, Eringen’s nonlocal elasticity continuum in conjunction with the Gurtin-Murdoch elasticity theory is incorporated into the classical higher-order shear deformation plate theory to develop size-dependent plate model able to consider both of small scale and surface stress effects. The non-classical governing differential equations are then discretized along with simply supported and clamped edge supports by employing generalized differential quadrature (GDQ) method. To evaluate the size-dependent pull-in voltage of nanoplates, the hydrostatic-electrostatic actuation is assumed to be calculated by neglecting the fringing field effects and utilizing the parallel plate approximation. It is demonstrated that the pull-in instability occurs at lower voltages for nanoplates with higher values of nonlocal parameters. Moreover, it is found that surface stress effect can increase or decrease the pull-in voltage of nanoplates which depends on the sign of surface elastic constants.