Length Scale Effects Research Articles

Asperity level characterization of abrasive wear using atomic force microscopy.

Using an atomic force microscope, a nanoscale wear characterization method has been applied to a commercial steel substrate AISI 52100, a common bearing material. Two wear mechanisms were observed by the presented method: atom attrition and elastoplastic ploughing. It is shown that not only friction can be used to classify the difference between these two mechanisms, but also the ‘degree of wear’. Archard's Law of adhesion shows good conformity to experimental data at the nanoscale for the elastoplastic ploughing mechanism. However, there is a distinct discontinuity between the two identified mechanisms of wear and their relation to the load and the removed volume. The length-scale effect of the material's hardness property plays an integral role in the relationship between the ‘degree of wear’ and load. The transition between wear mechanisms is hardness-dependent, as below a load threshold limited plastic deformation in the form of pile up is exhibited. It is revealed that the presented method can be used as a rapid wear characterization technique, but additional work is necessary to project individual asperity interaction observations to macroscale contacts.

Exact and approximate analytical solutions for nonlocal nanoplates of arbitrary shapes in bending using the line element-less method

In this study, an innovative procedure is presented for the analysis of the static behavior of plates at the micro and nano scale, with arbitrary shape and various boundary conditions. In this regard, the well-known Eringen’s nonlocal elasticity theory is used to appropriately model small length scale effects. The proposed mesh-free procedure, namely the Line Element-Less Method (LEM), only requires the evaluation of simple line integrals along the plate boundary parametric equation. Further, variations of appropriately introduced functionals eventually lead to a linear system of algebraic equations in terms of the expansion coefficients of the deflection function. Notably, the proposed procedure yields approximate analytical solutions for general shapes and boundary conditions, and even exact solutions for some plate geometries. In addition, several applications are discussed to show the simplicity and applicability of the procedure, and comparison with pertinent data in the literature assesses the accuracy of the proposed approach.

A real-time TEM study of the deformation mechanisms in β-Ti reinforced bulk metallic glass composites

The deformation mechanisms in a β-Ti reinforced Zr-based bulk metallic glass composite (BMGC) are studied by extracting submicron sized tensile coupons of the crystalline and amorphous phase in their monolithic and bilaminate composite forms and tensile testing them inside a TEM. Results show that the monolithic BCC crystalline phase and amorphous phase have high yield strains, owing to small length scale effects, but undergo negligible post-yield elongation before failure. However, the ductility of the bilaminate composite is significantly higher (~12.4%), provided the thickness of its amorphous portion is < 100 nm. Real time videos, which are supplemented by molecular dynamics simulations, show that the negligible post yield elongation of the monolithic BCC crystalline phase is caused by planar slip on one of the {110} planes. However, the bilaminate composite form exhibits strain hardening, despite the occurrence of planar slip, as dislocations pile up at the impervious amorphous/crystalline interface, which in turn, activates slip on other {110} planes. Strain hardening in the crystalline phase ceases when a shear band nucleated in the amorphous phase penetrates the dendrite along one of the slip planes. These mechanisms are extended to explain the flow behavior of β-Ti reinforced BMGCs and strategies to improve the ductility are discussed.

Hierarchical kirigami-inspired graphene and carbon nanotube metamaterials: Tunability of thermo-mechanic properties

Tuning and programming the multiphysical properties of advanced materials are of critical importance for developing the next generation of adaptable multifunctional metamaterials. This study demonstrates the tunability of thermo-mechanical properties of graphene sheets and carbon nanotubes by inspiring from hierarchical kirigami mechanical metamaterials. The theoretical investigation, multiscale simulation, and experimentation show that the thermo-mechanical properties of nano-architected kirigami metamaterials can be tuned by altering geometrical parameters and introducing the hierarchical cutting patterns. Additionally, the thermal conductivity of kirigami-inspired graphene and carbon nanotube metamaterials can be regulated by an external mechanical tension. We develop closed-form formulations for predicting the mechanical behavior of kirigami graphene sheets and carbon nanotubes. Molecular dynamics and finite element simulations are conducted to evaluate theoretical predictions. By analyzing and comparing the results from atomistic and continuum-based simulations, the effect of length scale on the thermo-mechanical properties is explored. We realize that the stress–strain response, thermal conductivity, and buckling-induced 3D patterns of nano-architected graphenes can be programmed by utilizing kirigami building blocks, nano-architectural hierarchy, and heterogeneous material design.

Length-Scale Effects in Hydrophobic Polymer Collapse Transitions.

The study of molecular mechanisms for cosolvent-driven hydrophobic polymer collapse transitions in water is of pivotal importance in the field of smart responsive materials. Computational studies together with complementary experimental data have led to the discovery and understanding of new phenomena in recent years. However, elementary mechanisms, generally contributing to polymer coil-globule transitions in different classes of cosolvent-water systems, remain elusive due to compensating energy-entropy effects. Herein, I discuss the role of length scales in polymer solubility problems. New ideas on surfactant mechanisms are discussed based on examples in which these mechanisms drive polymer swelling or collapse.

A novel size-dependent nonlocal strain gradient isogeometric model for functionally graded carbon nanotube-reinforced composite nanoplates

The paper presents a novel nonlocal strain gradient isogeometric model for functionally graded carbon nanotube-reinforced composite (FG-CNTRC) nanoplates. To observe the length scale and size-dependency effects of nanostructures, the nonlocal strain gradient theory (NSGT) is considered. The present model is efficient to capture both nonlocal effects and strain gradient effects in nanoplate structures. In addition, the material properties of the FG-CNTRC are assumed to be graded in the plate thickness direction. Based on the higher order shear deformation theory (HSDT), the weak form of the governing equations of motion of the nanoplates is presented using the principle of virtual work. Afterward, the natural frequency and deflection of the nanoplates are made out of isogeometric analysis (IGA). Thanks to higher order derivatives and continuity of NURBS basic function, IGA is suitable for the weak form of NSGT which requires at least the third-order derivatives in approximate formulations. Effects of nonlocal parameter, strain gradient parameter, carbon nanotube (CNT) volume fraction, distributions of CNTs and length-to-thickness ratios on deflection and natural frequency of the nanoplates are examined and discussed in detail. Numerical results are developed to show the phenomenon of stiffness-softening and stiffness-hardening mechanisms of the present model.

Analytical solutions of the cylindrical bending problem for the relaxed micromorphic continuum and other generalized continua

We consider the cylindrical bending problem for an infinite plate as modelled with a family of generalized continuum models, including the micromorphic approach. The models allow to describe length scale effects in the sense that thinner specimens are comparatively stiffer. We provide the analytical solution for each case and exhibit the predicted bending stiffness. The relaxed micromorphic continuum shows bounded bending stiffness for arbitrary thin specimens, while classical micromorphic continuum or gradient elasticity as well as Cosserat models [35] exhibit unphysical unbounded bending stiffness for arbitrary thin specimens. This finding highlights the advantage of using the relaxed micromorphic model, which has a definite limit stiffness for small samples and which aids in identifying the relevant material parameters.

Dynamics of nonlocal strain gradient nanobeams with longitudinal magnetic field

Flexural dynamics of carbon nanotubes under the longitudinal magnetic field have been investigated in the paper. Carbon nanotube has been assumed as a hollow beam with circular cross section. Nonlocal strain gradient model has been employed in the modeling of nanobeam. Transverse component of Lorentz force, which occurs with longitudinal magnetic field, has been considered as an external force on nanobeam. Stress and strain energy functionals have been defined for the nonlocal strain gradient model using Hamilton principle. Higher‐order governing differential equation of motion for the present problem has been solved with Differential Quadrature Method. Lorentz force and nonlocal strain gradient parameters have been considered in the standard and nonstandard boundary conditions in the present model formulation. Length scale and magnetic field parameters effect on the flexural vibration response of nanobeam have been investigated. Mode shapes of nonlocal strain gradient nanobeam have been depicted on various cases. Softening nonlocal strain gradient model gives physically consistent results and should be used in the analysis. Magnetic field effect shifts the mode shapes of clamped‐free nanobeam. Present study could give useful results for designing of magnetically actuated nanomotors.

Mechanics of cellulose nanopaper using a scalable coarse-grained modeling scheme

Cellulose, the abundantly available and sustainable biopolymer, exhibits intrinsic mechanical properties superior to many high-performance structural materials. The exceptional mechanical properties of cellulose-based materials inherently hinge upon their bottom-up hierarchical material structure starting from cellulose molecular chains to large scale fibers. However, fully atomistic simulation of such materials at experimental sample dimension becomes computationally prohibitive for the exploration of mechanics involving length scale effects. To address this challenge, here we develop a bottom-up, scalable coarse-grained (CG) modeling scheme of cellulose materials to study the deformation and failure mechanism of cellulose-based materials with insight of the interplay among cellulose building blocks at different length scales, starting from molecular chain, to nanofiber, and finally to microfiber scales. After studying the response of cellulose fibers under different loadings such as shearing and opening, this CG scheme is applied to study the deformation process of a cellulose nanopaper under tension, thus revealing the nanoscale failure mechanism otherwise impossible by atomistic simulations. In addition, the CG model also predicts the strength and stiffness of the nanopaper with respect to varying fiber lengths. Given its scalable nature, such a CG modeling scheme can be readily adapted to study the mechanical behaviors of other cellulose-based materials with mechanistic insight from molecular scale, and thus holds promise to foster the design of cellulose-based high-performance materials.

Droplet Interfacial Tensions and Phase Transitions Measured in Microfluidic Channels

Measurements of droplet phase and interfacial tension (IFT) are important in the fields of atmospheric aerosols and emulsion science. Bulk macroscale property measurements with similar constituents cannot capture the effect of microscopic length scales and highly curved surfaces on the transport characteristics and heterogeneous chemistry typical in these applications. Instead, microscale droplet measurements ensure properties are measured at the relevant length scale. With recent advances in microfluidics, customized multiphase fluid flows can be created in channels for the manipulation and observation of microscale droplets in an enclosed setting without the need for large and expensive control systems. In this review, we discuss the applications of different physical principles at the microscale and corresponding microfluidic approaches for the measurement of droplet phase state, viscosity, and IFT.

Applying nonlocal strain gradient theory to size-dependent analysis of functionally graded carbon nanotube-reinforced composite nanoplates

In this research paper, as initial endeavors, the vibrational responses of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) nanoplates taking into account the effect of nonlocal parameter and strain gradient coefficient are investigated. The study aims at developing mathematical modeling via an analytical solution to FG-CNTRC nanoplate structure with allowance for the nonlocal strain gradient effect. The four types of CNT distribution are used and compared in the context of the vibration of nanoplate in the presence of the small length scale effects, namely the (a) UD, (b) FG-V, (c) FG-O, and (d) FG-X. Some theoretical equations based on the first-order shear deformation plate theory (FSDT) are presented to provide a lucid understanding of how the small length-scale influences the FG-CNTRC nanoplate. For the vibrational analysis of a nanoplate, which is simply supported boundary condition, Navier solutions are obtained. Also, in contrast to earlier studies, an analytical approach is used to establish the governing equations of the FG-CNTRC nanoplate. Some specific numerical examples are given and compared with the results presented in the literature. In the section of numerical results, the influence of the nonlocal parameter, strain gradient coefficient, geometric parameters and vibrational modes on the non-dimensional natural frequency are investigated and discussed in detail. These could be useful to analysts and designers to estimate the fundamental natural frequencies in each of the four CNT distributions that the FG-CNTRC nanoplate possesses.

A couple stress model in non-polynomial framework to examine structural responses of laminated composite micro-plates: An analytical solution

In the present article, the couple stress models in the non-polynomial framework are developed and employed to examine the structural response characteristics of composite micro-plates. The length scale effects in the micro-laminates are considered using the couple stress theory. The trigonometric, inverse-trigonometric, hyperbolic, inverse-hyperbolic and exponential shear shape functions are considered to model transverse shear deformation effects in micro-plates. The Hamilton principle is employed to formulate the governing equations assuming linear structural kinematics. The governing equations are solved for simply supported micro-plates using the Navier solution for the prediction of analytical results. The structural responses of the composite micro-plates are examined for bending, free vibration, and buckling responses. The nondimensionalized deflection, stresses, frequencies, and axial buckling loads are evaluated using the present methodology. The higher buckling modes and free vibration modes are also obtained. The response characteristics due to five plate theories are compared and the applicability of the considered transverse shear deformation theories to model and analyze composite micro-plates is assessed. The effects of various parameters on the structural responses of micro-laminates are examined.

Transverse wave propagation in viscoelastic single-walled carbon nanotubes with surface effect based on nonlocal second-order strain gradient elasticity theory

Nowadays, the viscoelastic carbon nanotubes (CNTs) have been used as one of the most promising candidates for nanodevices (or nanoelectronics) and super-strong reinforcement fibers in polymer nanocomposites. In recent years there have been many papers that considered the effects of material length scales in the investigations of the material constants related on the structural parameters on the wave propagation in the viscoelastic CNTs. By using different approaches, for examples, Eringen’s differential nonlocal model, modified couple stress theory, and strain gradient theories, the stiffness softening or strengthening effect can be well predicted. However, the influence of the rapid stiffness enhancing effect on the wave characteristics of the viscoelastic CNTs is still not reported. To deal with such problem, this work aims to investigate the transverse wave propagation in viscoelastic single-walled carbon nanotubes (SWCNTs) adhered by surface material based on the nonlocal second-order strain gradient elasticity theory. The characteristic equation of wave motion of the viscoelastic SWCNTs with surface effect is systematically formulated to achieve the analytical dispersion relation between the wave frequency (or phase velocity) and the wave number. In the end, some most important conclusions are concluded.

LOCAL THERMAL NONEQUILIBRIUM VISCOUS DISSIPATIVE COUETTE FLOW IN A POROUS MEDIUM

A local thermal nonequilibrium Couette flow in a saturated porous medium, subjected to uniform heat flux, is investigated, where concern is focused on the effects of viscous dissipation. The temperature field is derived analytically in terms of Brinkman number (Br) and porous medium shape factor applied to conditions where the local thermal nonequilibrium effect is profound. Contrary to pressure-driven flow in porous medium, viscous dissipation has a more significant effect on the transverse temperature variation of a porous medium with high porous medium shape factor due to the shearing force on the moving wall. A comparison with the local thermal equilibrium model reveals that such an effect is heightened as the thermal resistance to heat conduction in fluid at the heated boundary becomes greater. The computed Nusselt number (Nu) indicates a reversal in the trend of declining Nu with increasing Br as the porous medium shape factor drops below one. As Br is a function of characteristic gap size, this study also gauges the effect of characteristic length scale of the parallel channel on the temperature field. The resulting fluid and solid temperature fields depend strongly on the characteristic gap size between parallel plates, while viscous dissipation intensification overrides the convection enhancement effect in microscale applications.

Size-dependent thermoelastic initially stressed micro-beam due to a varying temperature in the light of the modified couple stress theory

The bending of the Euler-Bernoulli micro-beam has been extensively modeled based on the modified couple stress (MCS) theory. Although many models have been incorporated into the literature, there is still room for introducing an improved model in this context. In this work, we investigate the thermoelastic vibration of a micro-beam exposed to a varying temperature due to the application of the initial stress employing the MCS theory and generalized thermoelasticity. The MCS theory is used to investigate the material length scale effects. Using the Laplace transform, the temperature, deflection, displacement, flexure moment, and stress field variables of the micro-beam are derived. The effects of the temperature pulse and couple stress on the field distributions of the micro-beam are obtained numerically and graphically introduced. The numerical results indicate that the temperature pulse and couple stress have a significant effect on all field variables.

Length Scale Effect in Frictional Aging of Silica Contacts.

Friction between two solid surfaces often exhibits strong rate and slip-history dependence, which critically determines the dynamic stability of frictional sliding. Empirically, such an evolutional effect has been captured by the rate-and-state friction (RSF) law based on laboratory-scale experiments; but its applicability for generic sliding interfaces under different length scales remains unclear. In this Letter, frictional aging, the key manifestation of the evolutional behavior, of silica-silica contacts is studied via slide-hold-slide tests with apparent contact size spanning across 3 orders of magnitude. The experimental results demonstrate a clear and strong length scale dependency in frictional aging characteristics. Assisted by a multiasperity RSF model, we attribute the length scale effect to roughness-dependent true contact area evolution as well as scale-dependent friction stress due to nonconcurrent slip.

Plate reader microrheology

In this work, we report the development of a simplified method to perform microrheology to rapidly assess soft materials. This approach uses fluorescence polarization and a plate reader format to measure the rotational diffusion of nanoparticles within a sample of interest. We have established that this technique can be used to characterize a range of soft materials based on the rotational diffusion of nanoparticles in materials with viscosities exceeding 100 cP. Using these fluorescence polarization-based measurements, we describe formalism that enables the estimation of viscosity in polymer solutions and gels composed of polyethylene glycol, hyaluronic acid, and Matrigel after accounting for the length-scale dependent effects of the polymer environment on the nanoparticle rotational diffusion. Using this analysis, we show that the plate reader microrheology measurements of viscosity are in reasonable agreement with traditional particle tracking microrheology. The use of a plate reader format allows this approach to be higher throughput, less technically challenging, and more widely accessible than standard macro- and micro-rheological methods, making it available to non-experts. This approach has potential applications in clinical settings where conventional rheological equipment may not be available to rapidly characterize patient-derived samples.

Static finite element analysis of thin laminated strain gradient nanoplates in hygro-thermal environment

The manuscript aims to investigate the static behavior of laminated nanoplates in hygro-thermal environment. The theoretical framework is based on the Kirchhoff hypothesis for thin structures including the effect of material length scales, which is described by a nonlocal model. For this purpose, the plane stress constitutive laws for laminates are enriched by a size-dependent parameter according to the principles of strain gradient theory. The variational form of such a peculiar theoretical formulation is developed to obtain the corresponding finite element (FE) model, due to the lack of similar numerical approaches in the literature. The difficulties arisen by the presence of higher-order derivatives of the displacements are overcome by using Hermite interpolating polynomials. Conforming and nonconforming FE formulations are presented to this aim. A broad validation procedure is carried out in terms of displacement and stress analysis to verify the accuracy of the approach. The comparison is accomplished taking into account the analytical solution given by the Navier methodology for cross-ply and angle-ply simply supported plates in hygro-thermal environment. The general model allows to extend the analysis to various boundary conditions and lamination schemes.

An Experimental Study of Turbulent Mixing in Channel Flow Past a Grid

Grid turbulence is considered to be a canonical case of turbulent flow. In the presented paper, the flow structure is analyzed from the point of view of mixing properties, where vortical structures and their properties play a significant role. That is why the effect of various length-scales in turbulence is studied separately. The experimental study uses the Particle Image Velocimetry (PIV) method. The original method for spatial spectrum evaluation is applied. Results on vortex spatial spectrum and isotropy are presented. The scaling of turbulent kinetic energy (TKE) is measured; furthermore, the TKE is decomposed according to the length-scales of the fluctuations. By this method, we found that the decay of TKE associated with the smallest length-scales is more sensitive to the Reynolds number than that at larger length-scales. The TKE at the largest investigated length-scales decays more slowly. The turbulence decay-law is studied for various Reynolds numbers. The second and fourth statistical moments of vorticity are evaluated at various Reynolds numbers and distances from the grid. The isotropy is investigated in the sense of ratio of fluctuations in stream-wise to span-wise directions as the used data are captured using the planar PIV method. The full 3D fluctuation invariants were investigated in a representative position by means of the Stereo-PIV method.

A source-term formulation for injecting wind gusts in CFD simulations

The objective of the present paper is to develop a methodology to inject strong wind gusts into the computational domain in order to efficiently simulate their effect on the fluid flow. The design of the methodology based on a source-term formulation takes the feedback effect of the resulting turbulent flow (and, if present, the impacted structure) on the wind gust itself into account. Since the injection of the wind gusts can be carried out close to the region of main interest, CPU-time intensive methods to ensure a proper transport of the gust through the flow field can be avoided. The methodology is mainly intended for the application within eddy-resolving simulations (e.g., LES), but it is not restricted to this class of simulation approaches. For the description of the gusts classical shape functions such as the Extreme Coherent Gust (ECG) and the Extreme Operating Gust (EOG) as well as a newly derived C2-”1-cosine” shape are applied. Two scenarios are taken into account to assess the proposed gust injection technique. On the one hand a (laminar) undisturbed flow field is considered and the effect of different time and length scales of the gusts on their evolution and propagation through the flow field is studied in detail. On the other hand a turbulent background flow is assumed demonstrating that the methodology suggested is also applicable for practically relevant turbulent flows.