Surface Stress Effects Research Articles

Grating Bio-Microelectromechanical Platform Architecture for Multiple Biomarker Detection.

A label-free biosensor based on a tunable MEMS metamaterial structure is proposed in this paper. The adopted structure is a one-dimensional array of metamaterial gratings with movable and fixed fingers. The moving unit of the optical detection system is a component of the MEMS structure, driven by the surface stress effect. Thus, these suspended optical nanoribbons can be moved and change the grating pattern by the biological bonds that happened on the modified cantilever surface. Such structural variations lead to significant changes in the optical response of the metamaterial system under illuminating angled light and subsequently shift its resonance wavelength spectrum. As a result, the proposed biosensor shows appropriate analytical characteristics, including the mechanical sensitivity of Sm = 11.55 μm/Nm-1, the optical sensitivity of So = Δλ/Δd = 0.7 translated to So = Δλ/Δσ = 8.08 μm/Nm-1, and the quality factor of Q = 102.7. Also, considering the importance of multi-biomarker detection, a specific design of the proposed topology has been introduced as an array for identifying different biomolecules. Based on the conducted modeling and analyses, the presented device poses the capability of detecting multiple biomarkers of disease at very low concentrations with proper precision in fluidic environments, offering a suitable bio-platform for lab-on-chip structures.

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.

Linear stability analysis of a droplet under an axisymmetric thermal gradient

We study the linear stability of a droplet placed at the center of a horizontal disk under the effect of surface stress promoted by an axisymmetric thermal gradient. Since the fluid volume is constant, we solve the non-steady base flow and the perturbation simultaneously as they evolve over time. The numerical results show that the base state migrates from a droplet to a ring shape, with the front position and maximum thickness following power laws with time. The perturbations travel with the same velocity as the advancing front and develop their maxima close to the contact line. All of them initially decrease their amplitudes, later showing an increment with the growth rates depending on the wavenumber and time. The dominant wavenumber increases with time, in agreement with recent experimental work.

Simulation of surface stress and solid solution modification phase field of nanowire electrocaloric effect

Composite films with ferroelectric nanowires serving as fillers, exhibit high adiabatic temperature change to meet the requirement for solid-state refrigeration, and their parallel-distributed filled nanowires are considered to be the key factor because their orientation is different from the orientation of the conventional perpendicularly distributed filled nanowires. However, the underlying mechanism of the electrocaloric effect of parallel-distributed nanowires has not been well understood. In this paper, a parallel-distributed PbTiO<sub>3</sub> nanowire model is established to investigate the effects of surface stress and solid solution modification on their electrocaloric effects through phase field simulations. The results show that an adiabatic temperature change of 5 K can be obtained near 200 ℃ with 1.5% compressive stress under an electric field of 260 kV/cm. In order to further reduce its operating temperature, the electrocaloric effects of PST nanowires with different Sr contents are calculated, and it is found that the lower the doping amount of Sr, the higher the phase transition temperature of PST nanowires is. When the doping amount of Sr is 0.45, the phase transition temperature of the nanowires can be reduced to near 100 ℃, and an adiabatic temperature change of more than 8 K can be obtained under an electric field of 600 kV/cm. Even in the low-temperature interval from 50 to 100 ℃ the nanowires exhibit an adiabatic temperature change close to 8 K. The nanowires are also characterized by an adiabatic temperature change in a low-temperature interval from 50 to 100 ℃. At the same time, by combining the evolution of the simulated three-dimensional domain structure, it is revealed that the underlying mechanism of the change of the electrocaloric effect under surface stress and solid solution modification is due to different types of domain transformations. Finally, the combinations of components and surface stresses corresponding to the maximum value of the electrocaloric effect at different operating temperatures are discussed and analyzed. The present study provides useful theoretical guidance for developing solid-state refrigeration based on parallel-distributed ferroelectric nanowires.

Aero-Hygro-Thermoelastic size-dependent analysis of NCMF-reinforced GNPs sector microplates located between piezoelectric patches in supersonic flow considering surface stress effects

Lately, metal foams have been widely used in various engineering structures due to their exceptional mechanical properties, including their lightweight. However, scientists have proposed adding nano-fillers like graphene nanoplatelets (GNPs) to overcome the issue of low stiffness caused by increased porosity. Hence, aerodynamic stability and vibrational behaviors of nanocomposite metal foams (NCMF)-reinforced GNPs sector microplate with piezoelectric/metallic face sheets are provided in this work. The microstructure is sited on Kerr elastic substrate and also is in a hygro-thermo-electrical media, subjected to supersonic flow based on first-order piston’s theory (FPT). Gaussian random field (GRF), Halpin-Tsai, and extended rule of mixture (ERM) in conjunction with Gurtin-Morduch, modified strain gradient theories, and Hamilton’s principle are used to derive the governing equations and linked boundary conditions. Generalized differential quadrature (GDQ) scheme is chosen to attain the results. By validating the results’ precision, the effects of different parameters on the natural frequencies (NFs) and critical aerodynamic pressures (CAPs) are observed. It is perceived that adding GNPs enhances both NFs and CAPs significantly, and increasing porosity up to seventy percent, leads the results to drop. Various industries use simpler models to evaluate the microstructure, therefore the present model can pave the way for future uses and push the boundaries of knowledge in these industries based on the results it produces.

Large Deflection and Post-Buckling Analysis of Cantilever Nanorods Including Effects of Couple and Surface Stresses by Intrinsic Coordinate Finite Elements

This paper presents a novel approach to the analysis of large deflection and post-buckling behavior of cantilever nanorods under different load conditions. The proposed approach utilizes a variational method, incorporating the Gurtin–Murdoch surface elasticity theory and the consistent couple stress theory to account for size-dependency effects. By accounting for the strain energy contributions of the bulk material, surface layer, and load conditions, this approach expresses the behavior of the nanorods in terms of their intrinsic coordinates. A finite element method was used to solve this numerical problem, generating a system of non-linear equations that were iteratively solved using the Newton–Raphson method. The results obtained from the finite element method were confirmed by those from the shooting method. Also, it highlights the effectiveness of the variational model in predicting the large deflection and post-buckling behavior of cantilever nanorods while considering both surface stress and couple stress effects. Furthermore, the study investigated the influence of surface stress and couple stress on the response of the nanorods to point and uniform loads. The results showed that incorporating both effects enhanced the stiffness of the nanorods compared to scenarios in which these effects were neglected. In addition, the couple stress effect was found to have a greater influence on the stiffening of nanorods for the same value of unitless parameters compared to surface stress effects. These findings offer valuable insights into the large deflection and post-buckling behavior of cantilever nanorods and highlight the importance of surface stress and couple stress effects. The model proposed in this study has potential applications in advanced technological device designs by providing a comprehensive understanding of the mechanical response of nanorods, allowing for more accurate predictions and enhanced device performance.

Nonlinear dynamic stability analysis of CNTs reinforced piezoelectric viscoelastic composite nano/micro plate under multiple physical fields resting on smart foundation

This study analyzes the nonlinear dynamic stability of carbon nanotube reinforced composite (CNTRC) piezoelectric viscoelastic nano/micro plate under time dependent harmonic compressive biaxial mechanical loading. The nano/micro plate is single-layer with a uniform and rectangular cross section. Polyvinylidene fluoride (PVDF) is the material used for the nano/micro plate. Also, it is located on a nonlinear viscoelastic piezoelectric foundation made of Zinc Oxide (ZnO). Single-walled carbon nanotubes (SWCNTs) have been used to strengthen nano/micro plate. Using Kelvin-Voigt model, the material properties of the system are assumed to be viscoelastic. Nano/micro plate is subjected to 2D magnetic field and electric potential. Magnetic field effects are incorporated using Maxwell’s relations. An alternating and direct voltage is applied to the nano/micro plate and also smart foundation in thickness direction. Eshelby-Mori-Tanaka approach is used to estimate the effective elastic properties. Additionally, follower force and uniform thermal gradient is applied to nano/micro plate in this study. The nonlinear strain–displacement relations are based on the Von-Kármán theory. According to classical, first order, third order, sinusoidal, parabolic, hyperbolic and exponential shear deformation plate theories, a new formulation is proposed incorporating surface stress effects through the Gurtin-Murdoch elasticity theory. In order to consider small scale parameters, this research is based on modified strain gradient theory (MSGT). Using the energy method and Hamilton’s principle, the non classical governing equations are derived. For nano/micro plate, simply supported boundary conditions are considered. For the purpose of solving differential equations, an analysis based on Galerkin procedure and finally the Bolotin method will be used to obtain the dynamic instability region (DIR). It is the objective of this study to investigate the impact of such parameters as small-scale parameters, alternating and direct applied voltage, intensity of magnetic field, surface effects, thermal environment and static load factor on the DIR. This study revealed that taking into account the smart foundation reduces the area of dynamic instability region by more than 60% for a constant intensity of magnetic field. The stability responses are also more convergent with the smart foundation. Additionally, the range is moved toward higher excitation frequencies and greater system stability. Validation of answers based on reliable scientific articles is one of the final stages of this research. These results can be used to design nano/micro electromechanical systems.

Surface effects and symmetry lowering effect on the anisotropic bending and equilibrium of freestanding nanofilms

A self-consistent theory for describing self bending, self equilibrium and symmetry lowering of nanofilms was proposed in this paper. The lowered symmetry and corresponding additional elastic parameter were considered to describe the mechanical properties of nanofilms. A freestanding nanofilm may spontaneously roll into a nanotube due to intrinsic surface stress imbalance. It is not necessarily isotropic for surface stress. The anisotropic surface stress is possible, Si nanofilm with (001) surface may behave (2 × 1) reconstruction, for example. The anisotropic surface stress induces anisotropic bending. And then, the isotropic Stoney formular should be modified to suit the anisotropic surface stress effect. A theory for anisotropic bending should be established. On the other hand, intrinsic surface stress balance induces uniform in-plane deformation of nanofilms. The theory in this paper was used to predict equilibrium strains of Cu, Ni, Ag, Au, Pd and Pt nanofilms, and was used to research Si nanofilm rolling behavior.

Atomistic Wear Mechanisms in Diamond: Effects of Surface Orientation, Stress, and Interaction with Adsorbed Molecules.

Despite its unrivaled hardness, diamond can be severely worn during the interaction with others, even softer materials. In this work, we calculate from first-principles the energy and forces necessary to induce the atomistic wear of diamond and compare them for different surface orientations and passivation by oxygen, hydrogen, and water fragments. The primary mechanism of wear is identified as the detachment of the carbon chains. This is particularly true for oxidized diamond and diamonds interacting with silica. A very interesting result concerns the role of stress, which reveals that compressive stresses can highly favor wear, making it even energetically favorable.

Dynamic analysis of 2DFGM porous nanobeams under moving load with surface stress and microstructure effects using Ritz method

This paper investigates the dynamic behavior of micro/nanobeams made of two-dimensional functionally graded porous material (2DFGPM) under accelerated, decelerated, and uniform moving harmonic load, using surface elasticity and modified couple stress theories. The key feature of this formulation is that it deals with a higher order shear deformation beam theory. The non-classical equilibrium equations are developed using Lagrange's equation and the concept of physical neutral surface. The equations of motion are derived using the same approach, accounting for the porosity effect and the modified power-law distribution of material properties. The trigonometric Ritz method is used with sinusoidal trial functions for the displacement field, and the Newmark method is applied to obtain the dynamical response of 2DFGPM nanobeams. The results are compared with previous studies, and the impact of critical parameters such as gradation indices, volume fraction ratio, pattern of porosity, velocity, frequency, and motion type of the applied force are explored. This study highlights the importance of considering the porosity effect, as neglecting it can lead to significant errors in the predicted results. Additionally, the study found that the accelerated and decelerated motions of the applied load have a greater impact on the dynamical deflection of 2DFGPM nanobeams than the uniform motion. The findings of this study can provide guidance for the optimal design of micro/nanobeams subjected to a moving force with multifunctional properties.

Bending, vibration and buckling isogeometric analysis of functionally graded porous microplates based on the TSDT incorporating size and surface effects

This paper presents a new microplate model for the static bending, free vibration, and buckling analysis of functionally graded (FG) porous plates. The model is based on the third-order shear deformation theory (TSDT) and incorporates the microstructural effect using the modified couple stress theory (MCST), as well as the surface stress effect using the Gurtin–Murdoch theory. The accuracy and reliability of the proposed model are evaluated using NURBS-based isogeometric analysis (IGA), which demonstrates excellent validation results. Furthermore, this study provides new insights into the mechanical behavior of FG porous microplates, investigating the influences of boundary conditions, surface effects, length scale parameters, porosity coefficients, plate aspect ratios, and buckling load conditions. Novel conclusions are drawn based on the analysis of deflection, stress, natural frequency, and buckling load.

Rolling structure from bilayer nanofilm by mismatch

A continuum theoretical scheme for self-rolling nanotubes from bilayers by mismatch is obtained by considering surface elasticity, surface stress, and symmetry lowering effects. For an ultrathin nanofilm with only several nanometers in thickness, isotropic mismatch, and isotropic surface stress usually induce anisotropic rolling behavior. The isotropic Timoshenko formula should be modified anisotropically to explain the mechanical behavior of anisotropic rolling structure of nanotubes accurately. The nanofilm rolls up in tangential direction while remaining straight in cylindrical direction theoretically. Therefore, in this paper the anisotropic shape of nanotubes is taken into consideration. Along the cylindrical direction, although it maintains straight and its residual strain is uniform, the stress varies in the radial direction due to the Poisson’s effect of tangential strain. The results of the current theory applied to Si–Si nanotube, InAs–GaAs nanotube, and InGaAs–Cr nanotube systems show good agreement with the experimental data. Beside the surface elasticity effect and surface stress effect, the symmetry breaking and the anisotropic rolling structure are of great importance in theoretically describing the mechanical behavior of rolling-up of nanotubes.

Nonlinear three-dimensional stability characteristics of geometrically imperfect nanoshells under axial compression and surface residual stress

Abstract Through reduction of thickness value in nanostructures, the features of surface elasticity become more prominent due to having a high surface-to-volume ratio. The main aim of this research work was to examine the surface residual stress effect on the three-dimensional nonlinear stability characteristics of geometrically perfect and imperfect cylindrical shells at nanoscale under axial compression. To do so, an unconventional three-dimensional shell model was established via combination of the three-dimensional shell formulations and the Gurtin–Murdoch theory of elasticity. The silicon material is selected as a case study, which is the most utilized material in the design of micro-electromechanically systems. Then, the moving Kriging meshfree approach was applied to take numerically into account the surface free energy effects and the initial geometrical imperfection in the three-dimensional nonlinear stability curves. Accordingly, the considered cylindrical shell domain was discretized via a set of nodes together using the quadratic polynomial type of basis shape functions and an appropriate correlation function. It was found that the surface stress effects lead to an increase the critical axial buckling load of a perfect silicon nanoshell about 82.4 % 82.4 \% for the shell thickness of 2 nm 2{\rm{nm}} , about 32.4 % 32.4 \% for the shell thickness of 5 nm 5{\rm{nm}} , about 15.8 % 15.8 \% for the shell thickness of 10 nm 10{\rm{nm}} , and about 7.5 % 7.5 \% for the shell thickness of 20 nm 20{\rm{nm}} . These enhancements in the value of the critical axial buckling load for a geometrically imperfect silicon nanoshell become about 92.9 % 92.9 \% for the shell thickness of 2 nm 2{\rm{nm}} , about 36.5 % 36.5 \% for the shell thickness of 5 nm 5{\rm{nm}} , about 17.7 % 17.7 \% for the shell thickness of 10 nm 10{\rm{nm}} , and about 8.8 % 8.8 \% for the shell thickness of 20 nm 20{\rm{nm}} .

On the vibrations of FG GNPs-RPN annular plates with piezoelectric/metallic coatings on Kerr elastic substrate considering size dependency and surface stress effects

On the vibrations of FG GNPs-RPN annular plates with piezoelectric/metallic coatings on Kerr elastic substrate considering size dependency and surface stress effects

Surface stress effect on nonlinear dynamical performance of nanobeam-type piezoelectric energy harvesters via meshless collocation technique

The chief point of the present study is to analyze numerically the surface stress effects on the nonlinear dynamic performance of nanosized lightweight piezoelectric bridge-type energy harvesters having agglomerated nanocomposite passive bulk. In this regard, the Gurtin-Murdoch continuum elasticity is formulated based upon the quasi-3D beam theory incorporating the relevant surface elastic constants as well as the surface residual stress. Afterwards, an effective numerical solving procedure employing the meshless collocation technique is developed to discretize the nonlinear governing equations via a combination of the polynomial as well as multiquadric basis functions to avoid any possible singularity. It is indicated that the surface stress effects result in to decrease the peaks of achieved voltage from the nonlinear dynamical response of nanobeam-type energy harvesters, but the associated frequency increases. Accordingly, for simply supported nanosized energy harvesters having the thickness of 50 nm, 20 nm, and 10 nm, the reductions in the average achieved voltage in order are about 7.79%, 25.57%, and 37.98%, but the required time decreases from 40.41 μs to 39.78 μs, from 35.17 μs to 33.57 μs, and from 28.37 μs to 26.46 μs, respectively. On the other hand, for clamped nanosized energy harvesters having the thickness of 50 nm, 20 nm, and 10 nm, the reductions in the average achieved voltage due to the surface stress effects are, respectively, about 8.33%, 27.35%, and 48.85%, but the required time decreases from 38.92 μs to 38.43 μs, from 33.42 μs to 32.04 μs, and from 26.58 μs to 24.62 μs, respectively.

Surface stress size dependency in nonlinear thermomechanical in-plane stability characteristics of FG laminated curved nanobeams

In the present exploration, the effect of surface stress type of size dependency on the nonlinear in-plane stability characteristics of functionally graded (FG) laminated composite curved nanobeams subjected to uniform radial pressure together with a temperature rise is examined. To accomplish this motivation, the Gurtin-Murdoch continuum elasticity is applied within a higher-order shear flexible curved beam theory in the presence of geometric type of nonlinearity. The effective properties of the employed nanocomposites are approximated via the Halpin-Tsai homogenization scheme corresponding to different lamination patterns and are considered in the principle of virtual work to establish the surface elastic-based nonlinear differential equations of the stability problem. It is found that by taking the surface stress effect into account, the values of the radial load related to the first and second bifurcation points get larger. Also, it causes to increase the curved beam deflection associated with the first bifurcation point, while it leads to decrease the radial deflection at the second bifurcation point. Accordingly, the effect of surface stress type of size dependency resulted in a reduction in the slope of bifurcation path related to the nonlinear radial load–deflection equilibrium curve of a curved nanobeam. It can be also observed that the temperature rise causes to increase the radial loads associated with the upper limit and the first bifurcation points, while it leads to reduce the values of radial load related to the lower limit and the second bifurcation points. In this regard, there is a unique intersection point as all equilibrium curves traced for different temperature rises pass through that.

Investigating the effect of nanovoid inelastic surface stress and the austenite–martensite interface inelastic stress on the martensitic growth at the nanovoid surface

Investigating the effect of nanovoid inelastic surface stress and the austenite–martensite interface inelastic stress on the martensitic growth at the nanovoid surface

Elastic solution of surface loaded layer with couple and surface stress effects

In this study, an elastic solution of an axisymmetrically surface-loaded thin layer resting on a rigid substrate is established by taking the surface stress and material microstructural effects into account. Derived solutions provide not only a means to investigate the size effects on the mechanical response but also a set of fundamental solutions essential for tackling contact problems in a micro/nano scale. In the formulation, the couple stress and surface elasticity theories are adopted to simulate the microstructured bulk layer and the surface material, respectively. A general solution of an elastic field within the bulk layer is obtained first by Hankel transform method and subsequently used together with the surface equations and boundary conditions to form a set of conditions essential for determining all unknown constants. After being fully tested with available benchmark solutions, results are used to study the role of surface and couple stresses on the load transferring mechanism to the substrate and its size-dependent characteristic for a wide range of external length scales relative to the internal length scales.

Anti-plane shear waves in an elastic strip rigidly attached to an elastic half-space

We consider the anti-plane shear waves in a domain consisting of an infinite layer with a thin coating lying on an elastic half-space. The elastic properties of the coating, layer, and half-space are assumed to be different. On the free upper surface we assume the compatibility condition within the Gurtin–Murdoch surface elasticity, whereas at the plane interface we consider perfect contact. For this problem there exist two possible regimes related to waves exponentially decaying in the half-space. The first one, called transversely exponential–transversely exponential (TE–TE) regime, is related to waves described by exponential in transverse direction functions; the second, transversely harmonic–transversely exponential (TH–TE) regime, corresponds to waves in the upper layer which have the harmonic behaviour in the transverse direction. Detailed analysis of the derived dispersion equations for both regimes is provided. In particular, the effects of surface stresses, the layer thickness as well as of the ratio of shear moduli of the upper layer and half-space on the dispersion curves is analysed.

Effects of residual stress caused by abrasion on the flexoelectric response of BaTiO<sub>3</sub> ceramics

The spontaneously polarized surface layer, which originates from stress relaxation, has been proposed for the unexpectedly large flexoelectric response measured in ferroelectric ceramics. However, the source of the stress that led to the polarized surface layer is still not completely known. In this work, the effect of surface stress on the microstructure, dielectric properties and flexoelectric response of BaTiO<sub>3</sub> ceramics abraded by abrasive papers of various grit sizes was systematically studied. Compared with the as-prepared sample, the flexoelectric coefficients of abraded BaTiO<sub>3</sub> ceramics decreased from ~600 μC/m to less than 200 μC/m. The flexoelectric coefficients of all the samples, however, recovered to ~500 μC/m following heat treatment at 200 °C and a subsequent slow cooling process. The results indicate that abrasion can introduce stress on the surface layers and affect the flexoelectric response of ferroelectric ceramics to some extent, but the stress is not the main reason for the formation of polarized surface layers.