Effects Of Couple Stresses Research Articles

Theoretical Study of the Effect of Magneto-Hydrodynamics and Couple Stress on Squeeze Film Lubrication of Rough Triangular Plates

Theoretical Study of the Effect of Magneto-Hydrodynamics and Couple Stress on Squeeze Film Lubrication of Rough Triangular Plates

Vertical shortening prediction for super‐tall buildings considering enclosure effect and coupling effect

SummaryIn this paper, the time‐dependent vertical shortening behavior of the super‐tall building is studied considering the enclosure effect and the coupling effect. A combined method to predict the overall strain of the mega section is firstly proposed by combining the B3 model and the fiber modeling approach to consider the enclosure effect of mega steel and validated by a series of in‐house experiments. An iteration method is then proposed based on the construction sequence method to consider the coupling effect of stress and strain in the vertical shortening prediction and illustrated by a super‐tall building project. Finally, the vertical shortening predictions of the super‐tall building project are compared with the field monitoring records. The results show that the strain predictions by the combined method show good agreement with experiments. Without considering the enclosure effect, the overall strain of mega section is overestimated. The coupling effect affects more on the vertical shortening of the mega column than on that of the shear wall and more on the elastic shortening than on the inelastic shortening. Without considering the coupling effect, the elastic shortening is significantly underestimated in the mega column but slightly overestimated in the shear wall. The predictions of vertical shortening in the shear wall show reasonable agreement with the measurements, whereas those in the mega column show large disagreement with the measurements, which enlightens the necessity to improve the prediction method further.

A new Bernoulli–Euler beam model based on a reformulated strain gradient elasticity theory

A new non-classical Bernoulli–Euler beam model is developed using a reformulated strain gradient elasticity theory that incorporates both couple stress and strain gradient effects. This reformulated theory is first derived from Form I of Mindlin’s general strain gradient elasticity theory. It is then applied to develop the model for Bernoulli–Euler beams through a variational formulation based on Hamilton’s principle, which leads to the simultaneous determination of the equation of motion and the complete boundary conditions and provides a unified treatment of the strain gradient, couple stress and velocity gradient effects. The new beam model contains one material constant to account for the strain gradient effect, one material length scale parameter to describe the couple stress effect and one coefficient to represent the velocity gradient effect. The current non-classical beam model reduces to its classical elasticity-based counterpart when the strain gradient, couple stress and velocity gradient effects are all suppressed. In addition, the newly developed beam model includes the models considering the strain gradient effect only or the couple stress effect alone as special cases. To illustrate the new model, the static bending and free vibration problems of a simply supported beam are analytically solved by directly applying the general formulas derived. The numerical results reveal that the beam deflection predicted by the current model is always smaller than that by the classical model, with the difference being large for very thin beams but diminishing with the increase of the beam thickness. Also, the natural frequency based on the new beam model is found to be always higher than that based on the classical model.

Investigation on mechanism of oxide removal and plasma behavior during laser cleaning on aluminum alloy

Through comparing the cleaning effect of aluminum alloy at different energy densities, the model of materials thermodynamics was established, illuminating the cleaning mechanism and plasma behavior. The research showed laser cleaning could remove oxide layer completely. The initial cleaning threshold was 12.7 J/cm2 and complete cleaning threshold was 25.5 J/cm2. At low energy density, phase explosion caused by laser ablation was the main cleaning mechanism. At high energy density, besides phase explosion, impact effect induced by evaporation pressure caused the splattering and removal of oxide layer. Plasma lifespan had positive correlation with energy density. Its lifespan in 25.5 J/cm2 and 51.0 J/cm2 were about 6 μs and above 10 μs, respectively. The model of materials thermodynamics showed that at low energy density, substrate evaporation pushed out molten oxide layer and formed pulse craters. At high energy density, transient energy absorption caused thermal stress coupling effect and separated substrate with oxide layer. The impact effect induced by evaporation pressure resulted in the removal of oxide layer. The vapor of Al absorbed laser energy and formed plasma. The high energy density enhanced the laser-plasma coupling. It caused high temperature and intensive electron density. The time of plasma cooling and atomization became longer.

A general dynamic theoretical model of elastic micro-structures with consideration of couple stress effects and its application in mechanical analysis of size-dependent properties

A general and systematic theoretical framework of elastic micro-structures is established with the aid of modified couple stress theory for investigating the size-dependent property in small scale, in which the size-dependence is considered by introducing a material length scale parameter. Mathematically, dynamic governing equations and corresponding boundary conditions are derived and simplified by using single power series expansion for a micro-plate and double power series expansion for a micro-beam. It is demonstrated that this method exhibits extraordinary superiority, i.e., different vibration modes can be extracted easily from artificial truncations. This theoretical model can be reduced to some classical cases, including the Bernoulli–Euler beam, Timoshenko beam, Kirchhoff plate and Mindlin plate, if some specific assumptions are made. After validation, a systematic numerical investigation is carried out, which focuses on the couple stress effect on shear resonance of a cantilever micro-plate. Finally, a methodology for proposing the critical size that distinguishes micro-scale from macro-scale is illustrated in detail.

Quantifying viscoelastic, piezoelectric and couple stress effects on Love-type wave propagation

The propagation of Love-type wave in multilayered structures plays a vital role for designing of Love wave-based devices. In this present paper, we have considered a theoretical model consisting of a heterogeneous viscoelastic layer lying under a finite layer of piezoelectric medium and lying over size-dependent couple stress substrate. The traction free surface is considered on the top layer of the considered geometry of the problem. The closed form of secular equations are derived for electrically open and short circuits. The impacts of heterogeneity, internal friction related to viscoelastic layer, together with the internal microstructures of couple stress substrate are demonstrated graphically. The effect of piezoelectric medium is displayed by taking or BaTiO3 materials of the piezoelectric layer. The validation has been carried out for the study, which is in close agreement with the already established results.

Analyzing nonlinear mechanical-thermal buckling of imperfect micro-scale beam made of graded graphene reinforced composites

This research is devoted to analyzing mechanical-thermal post-buckling behavior of a micro-size beam reinforced with graphene platelets (GPLs) based on geometric imperfection effects. Graphene platelets have three types of dispersion within the structure including uniform-type, linear-type and nonlinear-type. The micro-size beam is considered to be perfect (ideal) or imperfect. Buckling mode shape of the micro-size beam has been assumed as geometric imperfection. Modified couple stress theory has been used for describing scale-dependent character of the beam having micro dimension. Via an analytical procedure, post-buckling path of the micro-size beam has been derived. It will be demonstrated that nonlinear buckling characteristics of the micro-size beam are dependent on geometric imperfection amplitude, thermal loading, graphene distribution and couple stress effects.

Invariance of conveying capacity for drilling into lunar soil simulant

In this paper, we study the conveying dynamics in the helical groove of an auger drilling into lunar simulant. We demonstrate that the stress-coupling effect of the conveyed granules by the groove of a drill auger plays a significant role on the dynamics of conveyance. For this, a discrete element method (DEM) is adopted first to uncover the motion and the stress characteristics of conveyed granules in a working auger. Then, a simplified dynamic model following the stress characteristics of DEM is established. The simplified model can not only reflect the results by the discrete element method, but can also explain well the proportional relationship between the maximum conveying rate and the rotating speed of the auger in the experiment (Zhao et al., 2019).

Understanding the effects of stress on the coefficient of thermal expansion

Important coupled effects of stress and temperature change have long been recognised and taken into account in models assessing the performance of solid materials. However, due to incomplete understanding, existing models used for concrete are essentially empirical and lack rational basis. This limits their predictive capability and applicability range. In this paper, fundamental thermodynamics and continuum mechanics laws are used to obtain an expression that quantitatively predicts the effects of stress on the coefficient of thermal expansion. The newly-defined thermal expansion coefficient is then used to develop a rational model, which is shown to be capable of reliably quantifying the coupling effects of stress and temperature change. Good agreement between the model predictions, available data and observations is obtained. Equally important, all parameters of the developed model can be determined using simple tests. This enables a wide adoption of the model in practical engineering applications. While this paper uses data for concrete, the proposed model is developed from first principles and using fundamental physical laws. The model should thus be applicable to a wide range of solid materials.

Experimental and numerical study on the non-planar propagation of hydraulic fractures in shale

To better understand the non-planar propagation and geometry of fracture networks, hydraulic fracturing simulation tests on shale specimens were conducted using an established true triaxial hydraulic fracturing simulation test system. A two-dimensional numerical model of hydraulic fracturing was developed to clarify the evolution of hydraulic fractures and their non-planar behaviour at bedding planes. The numerical model with the alternating rock matrix and bedding planes considered the coupling effect of stress, fluid flow, and damage. The mechanisms by which hydraulic fractures penetrate or become arrested/deflected at bedding planes were then revealed as per the physical and numerical simulation results. The results revealed that the typical severe fluctuation of the injection pressure, which is closely related to the growth of sub-fractures along bedding planes or natural fractures, is a clear characteristic of the non-planar propagation of hydraulic fractures. The mechanical properties of the bedding primarily determine whether a hydraulic fracture penetrates or is deflected at the bedding. Strong beddings favour hydraulic fracture penetration; whereas, weak beddings favour hydraulic fracture deflection along the beddings. The hydraulic fractures typically extend along the path of least resistance, and therefore, induce the non-planar propagation behaviour at bedding planes. Tensile failure is a major fracture mechanism of the hydraulic fractures that penetrate or deviate at bedding planes. The experimental and numerical findings provide a basis for the optimum design of hydraulic fracturing and control of the fracture growth geometry in shale gas reservoirs.

Lithium redistribution around the crack tip of lithium-ion battery electrodes

Silicon film with pre-crack was used to study the coupling effect of stress and electrochemical field around the crack tip. The in-situ experiments were established to monitor the crack to realize the stress concentration around the crack and simultaneously prevent the crack initiation. The ex-situ Auger electron spectroscopy experiments shown the remarkably Li redistributed phenomenon around the crack tip. Furthermore, the fully coupled finite element method was used to reveal the fundamental mechanisms of the Li gathering effect and the stress relaxation phenomenon around the crack tip.

Dispersion feature of elastic waves in a 1-D phononic crystal with consideration of couple stress effects

The couple stress effects upon the propagation behavior and the dispersive feature of Bloch waves in the periodically laminated structure are studied in this paper. First, the various modes of wave motion in the elastic solid with consideration of the couple stress are formulated. Apart from the dispersive P wave, SV wave, and SH wave, there are two evanescent waves, namely SS wave and SSH wave. These modes of wave motion are considered to formulate the state vector and further the transfer matrix in each layer. Then, the non-classic interface continuity conditions with consideration of couple stress effects are used to derive the transfer matrix of the state vector in a typical single cell. At last, the Bloch theorem is used to give the dispersive equations of Bloch waves in the periodical structure. The in-plane Bloch waves and the anti-plane Bloch waves which propagate either obliquely or vertically are both considered in the present work. The numerical results are obtained by solving the dispersive equations and shown graphically. The influences of the couple stress effects on the propagation and the dispersive feature of Bloch waves are discussed based on the numerical results.

Magnetohydrodynamic effects on finite and infinite slider bearings

This paper presents a numerical investigation of lubricating slider bearings with conducting couple stress fluids using externally applied magnetics fields. The modified two-dimensional magnetohydrodynamic couple stress Reynolds-type equation is obtained. This governing equation is resolved numerically by using finite difference scheme, which involves the Gauss–Seidel method to compute the bearing characteristics. Numerical results using different considered values of the couple stress and Hartman number are presented. These results demonstrate that the transverse magnetic field and couple stress effects are significant.

Squeeze Film Analysis of Three-layered Parallel Plate and Partial Journal Bearing Lubricated with Couple Stress Fluids for Skeletal Joint Applications

Abstract Squeeze film lubrication in surfaces approaching each other with a normal velocity, play an important role in skeletal joints. The objective of this study is to analyse the squeeze film load capacity characteristics of three-layered parallel plate and partial journal bearing lubricated with couple stress fluids for skeletal joint applications using one-dimensional analysis. The nondimensional squeeze film pressure is derived based on modified Reynolds equation. The couple stress fluids take into account of lubricant properties with additives are analyzed based on Stokes micro-continuum theory. The Brinkman model is utilized to model the flow in the porous region. In this work, bearing performance improvement under the influence of lubricants with additives are evaluated using surface (or porous) adsorbent layer on stationary plate (or bearing), couple stress fluid film core region, and surface adsorbent layer on moving plate (or journal). The nondimensional squeeze film load capacity increases with (i) increase in couple stress effects, (ii) increase in dynamic viscosity ratio of surface to core layer, and (iii) decrease in permeability of porous layer. The surface (or porous) adsorbent layer and couple stress fluid film core layer improve the squeeze film bearing characteristics for skeletal joints.

Analysis of Piston-cylinder Dashpot Damping Constant with Slip and Couple Stress Fluid

An analytical model for damping constant calculation of piston-cylinder dashpot filled with couple stress fluid considering slip on piston and cylinder surfaces is presented. The damping constant of dashpot is determined using shear stress equation for couple stress fluids. Governing equations of fluid flow are derived from force on piston and viscous friction force. The influence of (i) couple stress parameter, (ii) nondimensional slip coefficients of piston and cylinder surfaces, (iii) nondimensional piston-cylinder clearance and (iv) reference piston-cylinder clearance to piston radius ratio on damping constant ratio of piston-cylinder dashpot are investigated. The damping constant ratio increases with (i) increase in couple stress effects, and (ii) decreases with slip on piston and cylinder surfaces. The couple stress fluid increases shearing force of film in piston-cylinder clearance space and enhances damping constant.

A displacement-based formulation for interaction problems between cracks and dislocation dipoles in couple-stress elasticity

Interaction problems of a finite-length crack with plane and antiplane dislocation dipoles in the context of couple-stress elasticity are presented in this study. The analysis is based on the distributed dislocation technique where infinitesimal dislocation dipoles are used as strain nuclei. The stress fields of these area defects are provided for the first time in the framework of couple-stress elasticity theory. In addition, a new rotational defect is introduced to satisfy the boundary conditions of the opening mode problem. This formulation leads to displacement-based hyper-singular integral equations that govern the crack problems, which are solved numerically. It is further shown that this method has several advantages over the slope formulation. Based on the obtained results, it is deduced that in all cases the cracked body behaves in a more rigid way when couple-stresses are considered. The effect of couple-stresses is highlighted in a small zone ahead of the crack-tip and around the dislocation dipole, where the stress level is significantly higher than the classical elasticity prediction. Further, the dependence of the energy release rate and the configurational force exerted on the defect on the characteristic material length and the distance between the defect and the crack-tip is discussed. In the plane problems, couple-stress theory predicts either strengthening or weakening effects while in the antiplane mode a strengthening effect is predicted.

Research on the creep mechanism of Huangniba landslide in the Three Gorges Reservoir Area of China considering the seepage–stress coupling effect

The impoundment of China’s Three Gorges Reservoir has led to the revival of many old landslides along the bank, and the annual fluctuation in water level of 30 m is likely to affect the creep deformation of these landslides. Through a field investigation of Huangniba landslide in the Three Gorges Reservoir Area, the local deformation signs and field monitoring data were analyzed. It was preliminarily considered that this landslide was currently at the creep stage and the creep rate was affected by the reservoir level variation. In order to carry out further research on the effect of reservoir level variation on the landslide movement, the finite element method was used to establish the seepage–stress coupling model of Huangniba landslide based on the seepage–stress coupling theory and taking into account the creep behavior of landslide material. The model was used to simulate the variation characteristics of the seepage field, stress field, and displacement field in the landslide during 6 years of cycles of reservoir level variation. Based on the numerical simulation results and field monitoring data, the deformation mechanism of the landslide was discussed. Finally, the sensitivity of the parameters in the creep model to the simulation results was discussed. The results show that creep deformation is the main deformation mechanism of Huangniba landslide, and it is obviously affected by the drawdown of the reservoir water level. During drawdown of the reservoir level, the pore water pressure inside the landslide decreases, resulting in an increase in effective creep stress and creep strain rate, thus accelerating creep deformation. The results of this study will provide a reference for the deformation mechanism of such creeping landslides subjecting to reservoir water level fluctuation.

Dampening of Submesoscale Currents by Air-Sea Stress Coupling in the Californian Upwelling System

Oceanic submesoscale currents (SMCs) occur on an scale of 0.1–10 km horizontally and have a large influence on the oceanic variability and on ecosystems. At the mesoscale (10–250 km), oceanic thermal and current feedbacks are known to have a significant influence on the atmosphere and on oceanic dynamics. However, air-sea interactions at the submesoscale are not well known because the small size of SMCs presents observational and simulation barriers. Using high-resolution coupled oceanic and atmospheric models for the Central California region during the upwelling season, we show that the current feedback acting through the surface stress dominates the thermal feedback effect on the ocean and dampens the SMC variability by ≈17% ± 4%. As for the mesoscale, the current feedback induces an ocean sink of energy at the SMCs and a source of atmospheric energy that is related to induced Ekman pumping velocities. However, those additional vertical velocities also cause an increase of the injection of energy by baroclinic conversion into the SMCs, partially counteracting the sink of energy by the stress coupling. These stress coupling effects have important implications in understanding SMC variability and its links with the atmosphere and should be tested in other regions.

Interaction of shear cracks in microstructured materials modeled by couple-stress elasticity

The interaction of two colinear in-plane shear cracks is investigated within the context of couple-stress elasticity. This theory introduces characteristic material length scales that emerge from the underlying microstructure and has proved to be very effective for modeling complex microstructured materials. An exact solution of the boundary value problem is obtained through integral transforms and singular integral equations. The main goal is to explain the size effects that are experimentally observed in fracture of brittle microstructured materials. Two basic configurations are considered: a micro-macrocrack interaction, and a micro-microcrack interaction. Numerical results are presented illustrating the effects of couple-stresses on the stress intensity factor and the energy release rate. It is shown that significant deviations from the predictions of the standard LEFM occur when the geometrical lengths of the problem become comparable to the characteristic material length of the couple-stress theory revealing that in such cases it is inadequate to analyze fracture problems employing only classical elasticity considerations.

A Three-Dimensional Size-Dependent Layered Model for Simply-Supported and Functionally Graded Magnetoelectroelastic Plates

A three-dimensional size-dependent layered model for simply-supported and functionally graded magnetoelectroelastic plates is presented based on the modified couple-stress theory. The functionally graded material is assumed to be exponential in the thickness direction of the plate. The final governing equations are reduced to an eigensystem by expressing the extended displacements in terms of two-dimensional Fourier series. Using the propagator matrix method, the exact solutions of the magnetic, electric and mechanical fields of sandwich nanoplates with couple-stress effect and under the surface loads are derived. Numerical examples for two functionally graded sandwich plates made of piezoelectric $$\hbox {BaTiO}_{{3}}$$ and magnetostrictive $$\hbox {CoFe}_{{2}}\hbox {O}_{{4}}$$ materials are presented to demonstrate the effect of the functional gradient factor and material length-scale parameter on the induced fields. The exact solutions presented in this work can also serve as benchmarks to various numerical methods for analyzing the size-dependent features in layered systems.