Effects Of Couple Stresses Research Articles

Microbeam Model and Related Differential Quadrature Finite Elements

A size-dependent quasi-3D functionally graded (FG) microbeam model was presented within the combined framework of the modified couple stress theory and a 4-unknown higher-order shear and normal deformation theory. Then the model was applied to analyze the static bending and free vibration of FG microbeams. With the 2nd Lagrange equation, the corresponding motion equations and the appropriate boundary conditions were obtained. A 2-node 16DOF differential quadrature finite element combining the Gauss-Lobatto quadrature rule with the differential quadrature rule was constructed to handle the general static/dynamic boundary value problems of FG microbeams. A comparison study was performed to show the efficacy of the proposed theoretical model and solution method. Finally, the effects of the gradient index, the intrinsic length scale parameter, the geometrical parameters and the boundary conditions on the static and dynamic characteristics of FG microbeams were examined. Numerical results reveal that the developed beam model and element are applicable to the analysis of mechanical behaviors of FG microbeams with various slenderness ratios. Besides, introduction of the couple stress effect can significantly change the static and dynamic characteristics of FG microbeams.

A microstructure-dependent Kirchhoff plate model based on a reformulated strain gradient elasticity theory

A new microstructure-dependent non-classical model for Kirchhoff plates is developed by using a reformulated strain gradient elasticity theory that incorporates both the strain gradient and couple stress effects. The equation of motion and the boundary conditions are simultaneously obtained through a variational formulation based on Hamilton’s principle. The new plate model contains one material constant to account for the strain gradient effect and one material length scale parameter to capture the couple stress effect. The newly developed non-classical plate model includes the plate model incorporating the couple stress effect alone and the plate model based on the classical elasticity as two special cases. To illustrate the new model, the buckling, static bending and free vibration problems of a simply supported rectangular plate are analytically solved by directly applying the general formulas derived. The numerical results reveal that the presence of the strain gradient and couple stress effects leads to reduced plate deflections, enlarged critical buckling loads and increased natural frequencies. These microstructure effects are significant when the plate is very thin, but they are diminishing as the plate thickness increases. These predicted trends of the size effects at the micron scale agree with those observed experimentally.

Couple stress effects on the stability of three‐component convection‐diffusion in a porous layer

AbstractIn this study, the stability (linear and weak nonlinear) of triple‐diffusive convection in a couple stress fluid‐saturated porous layer has been studied. A normal mode analysis yields an exact dispersion equation of fourth degree, and the criterion for the onset of stationary and oscillatory convection is obtained accordingly. The numerical computations are carried out for diffusivity elements experimentally determined for an aqueousNaCl‐KCl‐Sucrosesystem. Contrary to the double‐diffusive couple stress fluid system, it is found that (i) oscillatory convection occurs even if the diffusivity ratios are greater than unity and (ii) a disconnected heart‐shaped oscillatory neutral curve exists for certain choices of physical parameters, demonstrating the requirement of three critical values of Darcy‐Rayleigh number to specify the linear instability criteria. The impact of a couple stress parameter on some of these unusual behaviors is emphasized. The cubic Landau equations are derived by performing a weak nonlinear stability analysis and the stability of stationary and oscillatory bifurcating solutions is discussed. The heat and mass transfer for stationary and oscillatory convection modes is presented, and the influence of the couple stress parameter on the same is analyzed.

Electrothermal analysis in two-layered couple stress fluid flow in an asymmetric microchannel via peristaltic pumping

Being motivated from the recent developments in biomicrofluidics, a mathematical model is presented to analyze the two-layered electrothermal flow via peristaltic propulsion of couple stress fluids caused by velocity and thermal slip conditions. An asymmetric microchannel is considered for the flow regime with different zeta potential moving with wave velocity. Couple stress fluid has been taken for aqueous solution to represent the non-Newtonian characteristics of physiological fluids. A lubrication approach with Debye H $$\ddot{u}$$ ckel linearization is taken to obtain the analytical solution. Furthermore, heat transfer analysis is performed to analyze the thermal characteristics and variations in Nusselt number in the presence of thermal radiation. The study shows that the temperature reduces with increasing the electrical double layer thickness, thermal radiation, couple stress parameter, and magnitude of Brinkman number, however, it enhances with increasing the Joule heating and thermal slip effects. The rate of heat transfer enhances with Joule heating effects, while the trend is reversed due to the presence of two-layered electroosmotic flow and couple stress effect.

Fracture Propagation of Rock like Material with a Fluid-Infiltrated Pre-existing Flaw Under Uniaxial Compression

Crack propagation can gradually reduce the strength of the rock and eventually result in rock failure. Coupling effect of stress and seepage in fracture could accelerate the rock failure process. In this work, a set of water sealing device is developed to apply different fluid pressures in the pre-existing fracture in specimens made of rock-like material. We have carried out uniaxial compression tests on specimens at different pre-existing flaw dip angles (30°, 45°, and 60°) coupled with fluid pressures in the fracture. Through laboratory experiments and numerical simulations, we find that without fluid pressure in the pre-existing flaw, wing cracks and secondary cracks appear at the pre-existing flaw tips. With the increase of the fluid pressure in the flaw, the propagation of secondary cracks is restrained, no secondary cracks appear at the flaw tips. The increase of fluid pressure accelerates the wing crack propagation, inhibits the secondary cracks, and causes the specimen to undergo tensile failure. Compared with the specimen without the fluid pressure in the flaw, the fluid pressure in the flaw promotes wing crack initiation and propagation, and causes the initiation stress of the wing cracks and the peak strength of the specimens to decrease gradually. With or without fluid pressure in the fracture with the increase of the flaw dip angle, the initiation stress of wing cracks and peak strength of the specimen first decrease and then increase. When the pre-existing flaw dip angle is 45°, the peak strength and the initiation stress are the lowest.

Chemo-mechanical response of composite electrode systems with multiple binder connections

In Li-ion batteries, the feature of inter-particle connection of a non-active binder can affect lithium diffusion inside the particle and stress development due to the diffusion–stress coupling effect, leading to change in the failure mechanisms of the electrode. In this study, to investigate the effect of binder connection feature on mechanical response, a series of simulations is carried out by changing the particle radius for three cases of single, double, and triple binder connections. The effects of C-rates, lithium flux at the particle–binder interface, level of mechanical constraint, and binder content on the stress development in the particle, binder, and interface domains are explored. We find that two effects of binder confinement and concentration gradients compete in the stress development. For small particles, the binder confinement effect is dominant; while for large particles, the concentration gradients effect is dominant. In addition, the single binder model shows a different stress trend, compared to the multiple binder models, due to asymmetric constraint from the binder. The insights obtained from this study help in the design of composite electrode materials for enhanced battery performance by optimizing parameters.

Experimental Investigation on Mechanics and Seepage Characteristics of Tectonic and Intact Coal Containing Gas

Coalbed methane is a double-edged sword with two attributes of energy and hazard in coal mines. Gas drainage is the most direct and effective measure for gas recovery and disaster prevention in coal mines, which is seriously affected by the mechanics and seepage characteristics of coal. In this work, we experimentally simulated the triaxial compression and gas depletion processes using both tectonic coal and intact coal. The mechanics and seepage characteristics of tectonic and intact coal under the coupling effect of stress and gas pressure were analyzed and compared. The results show that during the triaxial compression, the damage stress and peak stress of tectonic coal is only half that of intact coal, while their compaction stress or residual stress are almost the same. Meanwhile, the permeability recovery value after tectonic coal failure is very limited, even smaller than that of intact coal, although its primary permeability is much larger than that of intact coal. On the contrary, the permeability recovery value after intact coal failure is more than twice of its primary permeability. During the gas depletion, the rebound gas pressure of tectonic coal is smaller than that of intact coal, and the permeability of tectonic coal is one order of magnitude larger than that of intact coal before the gas pressure drops to 2 MPa. The broken of tectonic coal and the low permeability of intact coal may be the two principal reasons. Therefore, in the tectonic coal area, the gas extraction time at high gas pressure stage should be stabilized, while in the intact coal area, the gas extraction time at low gas pressure stage should be increased, and the coal permeability enhancement measures should be combined to achieve the goal of high and stable production of coalbed methane.

Investigation of thermal enhancement in non-Newtonian fluid with hybrid micro-structures in an enclosure

Enhancement in the thermal performance of the fluids with micro-structures via hybrid nanoparticles is highly appreciated since the efficiency of the thermal system depends upon the thermal conductivity of the fluid being used as coolant or working fluid. Dispersion ofCuO and Al2O3in the fluid exhibiting micro- inertia, vortex viscosity and couple stress effects is studied. The main motivation behind investigation of this fluid with enhanced properties is that these fluids are encountered at industry and engineering processes. Hybrid thermo-physical relations and conservation of momenta, energy and mass are simultaneously used for the development of models to investigate the effectiveness of thermal conductivity of fluid with micro-structures (such fluids are called micropolar fluid). Two-dimensional models are set into their dimensionless forms in view of the importance of dimensional analysis. Further, finite volume method (FVM) is implemented to find numerical solution. The simulations are recorded in the form of graphical data and their outcomes are discussed. The performed study concludes a significant rise in thermal performance of the working fluid via hybrid micro-structure constituents. The behavior of vortex viscosity on fluid velocity and angular motion is investigated under various parametric values.

Theoretical Analysis of Roll-Over-Web Surface Thin Layer Coating

This study presents the theoretical investigation of a roll-over thin layer formation under the lubrication approximation theory. The set of differential equations derived by lubrication approximation is solved by the optimal homotopy asymptotic method (OHAM) to obtain precise expressions for pressure and velocity gradients. Critical quantities such as velocity, pressure gradient, and coating layer depth are numerically estimated. The impact of parameters affecting the coating and layer formation is revealed in detail. Results indicate that the transport properties of the higher-grade fluid play an essential role in regulating velocity, pressure, and the final coated region. Moreover, couple stress effects on the properties of fluid particles to be coated on roller-surface have also been studied.

EFFECT OF COUPLE STRESS AND IMPACT OF CHEMICAL REACTION ON THE BEHAVIOUR OF ATMOSPHERIC AEROSOLS

Adv. Math. Sci. J. Vol. 9, No. 4 Open Access EFFECT OF COUPLE STRESS AND IMPACT OF CHEMICAL REACTION ON THE BEHAVIOUR OF ATMOSPHERIC AEROSOLS P. Meenapriya DOI: https://doi.org/10.37418/amsj.9.4.84 Full Text Abstract Abstract The model is developed as a course of improved understanding of interactions between aerosols in the couple stress fluid. … page AMSJ9-N4-84 Read More »

A general dynamic model based on Mindlin’s high-frequency theory and the microstructure effect

Based on Hamilton’s principle, a general three-dimensional mechanical model with consideration of the consistent couple stress theory is established in this paper, and the dynamic governing equations and boundary conditions are derived strictly. After that, inspired by the high-frequency theory established by Mindlin, a novel two-dimensional theory of micro-plates is proposed. Governing equations and boundary conditions are simplified and further validated via some reductions and comparisons with the traditional Mindlin plate and the Timoshenko beam. As an application, the propagation property of straight-crested waves in a micro-plate is investigated, and the effect of couple stress is revealed. Then, the static bending and free vibration of a simply supported rectangular micro-plate is investigated with the aid of the double Fourier series. It is demonstrated that the couple stress has significant influence on the mechanical behaviors, including the static deflection and natural frequency, as the plate thickness shrinks. Physically, the couple stress effect is equivalent to an increase in structural stiffness. In order to illustrate the effect of the couple stress, a general criterion for quantifying the critical size that distinguishes microscale from macroscale is proposed numerically. To some extent, it can also be viewed as a criterion for distinguishing the consistent couple stress theory of micro-structures from the classical continuum mechanics theory of macro-structures.

NEURINGER-ROSEINWEIG MODEL BASED LONGITUDINALLY ROUGH POROUS CIRCULAR STEPPED PLATES IN THE EXISTENCE OF COUPLE STRESS

This study intents to scrutinize the impact of ferrofluid in the presence of couple stress for longitudinally rough porous circular stepped plates. The influence of longitudinal surface roughness is developed using the stochastic model of Christensen and Tonder for nonzero mean, variance and skewness. Neuringer-Roseinweig model is adopted for the influence of ferrofluid. The couple stress effect is characterized by Stoke’s micro continuum theory. The modified Reynolds’ type equation is stochastically averaged and solved by no-slip boundary conditions. The closed form solutions for load bearing capacity and film pressure are obtained as a function of different parameters and plotted graphically. It is perceived that the load capacity gets elevated owing to the combined influence of magnetization and couple stress when the proper choice of roughness parameters (negatively skewed, standard deviation) is in place. Porosity and roughness (positively skewed) adversely affect bearing’s performance. The graphical and tabular analysis shows that there is a significant growth in load bearing capacity compared to the conventional lubricant case.

Experimental Investigation of Gas Transfer Properties and Stress Coupling Effects of Salt Rocks

This experimental study is dedicated to the measurements of gas permeability under confinement and to preliminary characterizations of salt rock poromechanical behavior. Salt porosity and permeability under loading are recorded either with argon or hydrogen gas. Permeability measurements carried out with both gases led to similar values. Poromechanical effects occur but they are weak and strongly dependent on the level of confining pressure. Furthermore, triaxial tests have been used to investigate the evolution of permeability of damaged salt samples with time and confinement. These experimental characterizations are finally analysed in the context of gas storage applications.

Combined effects of surface energy and couple stress on the nonlinear bending of FG-CNTR nanobeams

This paper investigates the size-dependent nonlinear bending of functionally graded carbon nanotube-reinforced (FG-CNTR) nanobeams. Chen–Yao’s surface elasticity and modified couple stress theories are adopted to describe surface effects and couple stress effects, respectively. These nanobeams, in which the carbon nanotube (CNT)-reinforced phases are assumed to be distributed in a gradient along the thickness, are subjected to a uniform pressure and rest on a nonlinear elastic foundation. In accordance with the Euler–Lagrange variational principle, the governing equations and boundary conditions for the FG-CNTR nanobeams, which involve geometric nonlinearity due to the von Kármán strain relations, are obtained. Then, with the assistance of the two-step perturbation technique, the load-deflection relationship is determined for nanobeams subjected to simply supported (SS) and clamped–clamped (CC) boundary conditions. Finally, the impacts of various factors, including surface properties, characteristic material length, elastic foundation, geometric factors, layout type and volume fraction of CNTs, on the mechanical behaviors of CNT-based nanobeams are examined. The numerical results reveal that the combination of surface effects and couple stress helps to enhanceq the stiffness of the nanobeams. Furthermore, the size-dependent nonlinear bending of the FG-CNTR nanobeam is markedly affected by the content and layout type of the reinforcements.

Size-dependent vibrations of thermally pre/post-buckled FG porous micro-tubes based on modified couple stress theory

Based on the modified couple stress theory, an analytical approach is presented to study vibrations of thermally pre/post-buckled functionally graded (FG) tubes. The case of simply supported FG micro-tubes with uniform distributed porosity surrounded by nonlinear elastic medium in uniform temperature field is analyzed. Thermomechanical properties are functionally graded across the radius of cross-section of the tube by means of a power law function. The traction free boundary conditions on the inner and outer surfaces of the structure are satisfied. Basic formulations are constructed using the higher-order shear deformation tube theory and the von Kármán type of nonlinear strain-displacement relationships. The governing equations of motion are derived using the Hamilton principle. The dimensionless equations of motion are solved analytically by employing the two-step perturbation technique and the Galerkin procedure. An explicit closed-form solution is obtained to analyze the size-dependent linear and nonlinear free vibrations of micro-tubes in thermal environment. The numerical results are verified by comparison with the existing data in literature for tubes without couple stress effect. Novel numerical results are revealed in the parametric studies to show the large amplitude vibration responses of thermally pre/post-buckled FG porous micro-tubes. The effects of microstructural length scale parameter, functionally graded patterns, porosity distribution parameter, nonlinear elastic foundation, temperature dependence, and geometrical properties of the structure are investigated.

Free and forced vibration of layered one-dimensional quasicrystal nanoplates with modified couple-stress effect

Free and forced vibration of layered one-dimensional quasicrystal nanoplates with modified couple-stress effect

Theoretical study of elastic wave propagation through a functionally graded micro-structured plate base on the modified couple-stress theory

In this paper, two different methods, Legendre orthogonal polynomial method (LOPM) and Global matrix method (GMM), are combined with the couple-stress theory to investigate the reflection and transmission of P wave in a functionally graded (FG) couple-stressed plate immersed in liquid. The GMM needs to divide the FG plate into the multilayered model, with each layer containing six partial waves. However, the LOPM only expands the displacement vectors in the FG couple-stressed plate into the Legendre orthogonal polynomial series. The paper shows that both methods are in good agreement. Nevertheless, the proposed LOPM is more efficient for the FG microstructure because it does not require plate delamination and calculation of the displacements of each partial wave. It also shows that the couple-stress effect affects the resonant frequencies of the FG plate, decreasing the number of resonant frequencies. By controlling the gradient field, some resonances can be avoided.

Convective instability analysis of couple-stress dielectric fluid saturated anisotropic porous medium with radiation effect

PurposeThe effects of anisotropy and radiation cannot be considered negligible while investigating the stability of the fluid in convection. Hence, the purpose of this paper is to analyze how these effects could affect the system while considering a couple-stress dielectric fluid. Therefore, the study establishes the effect of thermal radiation in a couple-stress dielectric fluid with an anisotropic porous medium using Goody's approach (Goody, 1956).Design/methodology/approachTo analyze the effect of radiation on the onset of convection, the Milne–Eddington approximation is employed to convert radiative heat flux to thermal heat flux. The equations are further developed to approximate for transparent and opaque medium. Stability of the quiescent state within the framework of linear theory is performed. The principle of exchange of stabilities is shown to be valid by means of single-term Galerkin method. Large values of conduction–radiation and absorptivity parameters are avoided as fluid is considered as liquid rather than gas.FindingsThe radiative heat transfer effect on a couple-stress dielectric fluid saturated anisotropic porous medium is examined in terms of Milne–Eddington approximation. The effect of couple-stress, dielectric, anisotropy and radiation parameters are analyzed graphically for both transparent and opaque medium. It is observed that the conduction–radiation parameter stabilizes the system; in addition, the critical Darcy–Rayleigh number also shows a stabilizing effect in the absence of couple-stress, dielectric and anisotropy parameters, for both transparent and opaque medium. Furthermore, the absorptivity parameter stabilizes the system in the transparent medium, whereas it exhibits a dual effect in the case of an opaque medium. It was also found that an increase in thermal and mechanical anisotropy parameters shows an increase in the cell size, whereas the increase in Darcy–Roberts number and conduction–radiation parameter decreases the cell size. The validity of principle of exchange of stability is performed and concluded that marginal stability is the preferred mode than oscillatory.Originality/valueThe effects of anisotropy and radiation on Rayleigh–Bénard convection by considering a couple-stress dielectric fluid has been analyzed for the first time.

Effects of oil film thickness and viscosity on the performance of misaligned journal bearings with couple stress lubricants

This paper investigated the performance characteristics of misaligned journal bearing lubricated using couple stress fluids. Based on micro-continuum theory, the modified Reynolds equation for couple stress lubricants was developed, in which viscosity-pressure effect was considered. By setting the critical oil film thickness, the region with couple stress effect can be recognized. The ratio of the critical oil film thickness to couple stress parameter was referred to as film thickness coefficient. It was found from results that increase of film thickness coefficient can significantly improve the maximum film pressure and high-pressure area, when film thickness coefficient was smaller than 4. Viscosity-pressure effect was capable of enhancing viscosity, friction coefficient and the maximum film pressure, and reducing couple stress parameter, especially for large misalignment angle.

Experimental Study on Lateral Permeability Evolution of Sandstone under Seepage‐Damage Coupling

To analyze the internal pore evolution law of aquifer rock in a coal mining front under the coupling effect of stress and seepage and the influence on the water inrush performance of the working face, research on the working face was conducted to improve the RTR‐1000 high‐temperature and high‐pressure rock triaxial mechanical testing system, using hollow cylindrical and complete sandstone samples and by considering the stress change law in the actual mining process as the reference loading path. At the initial stage of loading, the permeability of sandstone demonstrates a rapid downward trend within a small range of stress change, with a decline rate of 50%. At lower permeabilities, the fluctuation is small; the plastic and failure stages are transient, and the relationship curve between the horizontal permeability and the axial confining pressure of sandstone is divided into compaction, multiple fluctuations, surrender, and failure. In several stages, the sandstone lateral permeability experiment under the coupling effect of stress and seepage demonstrates that the permeability of the aquifer in the coal mining front is significantly reduced after the original rock stress is disturbed by mining, suggesting that the water inrush calculation of the traditional water‐flowing fractured zone and caving zone aquifer rock permeability experiment is inaccurate. Further research can deepen the stress and seepage coupling evolution process under the action of working face water inrush.