Effects Of Couple Stresses Research Articles

Geometry of stress function surfaces for an asymmetric continuum

A two-dimensional stress field of dislocation or fault is geometrically studied for an asymmetric continuum. For geometric surfaces of the stress and couple-stress functions, the mean and Gaussian curvatures are derived. The mean curvature of couple-stress function surface is connected with the asymmetric of stress tensor. Moreover, the Gaussian curvature of stress function surface is characterized by both the stress and couple-stress. On the other hand, the mean curvature of stress function surface is not affected by the asymmetry of stress. Based on these geometric expressions, the Coulomb’s failure criterion and the friction coefficient are expressed by the curvatures of couple-stress function surface. Moreover, geometric structures of stress and couple stress function surfaces are shown for edge and wedge dislocations as faults. The curvatures of these surfaces show that the effect of couple-stress is constrained around the dislocations only.

Effect of Couple-Stresses on the Transient Dynamic Stress Intensity Factors for a Crack in an Infinite Elastic Medium Under an Impact Stress Wave

This study applies linearized couple-stress theory to evaluate the dynamic stresses around a crack in an infinite elastic medium that is subjected to an incoming shock stress wave impinging normal to the crack. The boundary conditions with respect to the crack are reduced to dual integral equations using a Fourier transform in the Laplace domain. To solve these equations, the differences in the displacement and rotation at the crack are expanded by a series of functions that are zero-valued outside the crack in the Laplace domain.

Analysis of Nanoparticle Additive Couple Stress Fluids in Three-layered Journal Bearing

The present theoretical study investigates the load capacity and friction coefficient in a three-layered journal bearing lubricated with nanoparticle additive couple stress fluids. The couple stresses effects are analyzed based on Stokes micro-continuum theory. The nondimensional pressure and shear stress expressions are derived using modified Reynolds equation. The nondimensional load capacity increases and the coefficient of friction decreases using nanoparticle additive lubricants with couple stress effects. The three-layered journal bearing performance characteristics are improved with increase in both (i) surface adsorbent fluid film layer thickness and (ii) dynamic viscosity ratio of surface to core layer.

Coupling effects of stress and ion irradiation on the mechanical behaviors of copper nanowires

By using molecular dynamics simulations, we studied the ion irradiation induced damage in mechanically strained Cu nanowires and evaluated the effects of damage on the mechanical properties of nanowires. The stresses in the pre-strained nanowires can be released significantly by the dislocation emission from the cascade core when the strain is greater than 1%. In addition, comparison of the stress-strain relationships between the defect-free nanowire and the irradiated ones indicates that ion irradiation reduces the yield strength of the Cu nanowires, and both the yield stress and strain decrease with the increase of irradiation energy. The results are consistent with the microscopic mechanism of damage production by ion irradiation and provide quantitative information required for accessing the stability of nanomaterials subjected to mechanical loading and irradiation coupling effects.

Effect of couple-stresses on the Mode I dynamic stress intensity factors for two equal collinear cracks in an infinite elastic medium during passage of time-harmonic stress waves

Dynamic stresses around two equal collinear cracks in an infinite elastic medium are evaluated based on linearized couple-stress theory while the medium is subjected to time-harmonic stress waves impinging normal to the cracks. The boundary conditions with respect to the cracks are reduced to dual integral equations using Fourier transformations. To solve these equations, the discontinuities in the displacement and in the rotation at the cracks are expanded in a series of functions that are zero-valued outside the cracks. The unknown coefficients in each series are solved using the Schmidt method to satisfy the boundary conditions along the crack faces. The stress intensity factors and the couple-stress intensity factors are determined, and they are calculated numerically for selected crack configurations.

Non‐Newtonian dynamic characteristics of wide composite slider bearings lubricated with couple stress fluids

PurposeThe purpose of this paper is to provide more information for fluid‐film bearing selection and designing. The present paper is mainly concerned with the dynamic characteristics of a wide composite slider bearing lubricated with non‐Newtonian couple stress fluids.Design/methodology/approachTaking into account the non‐Newtonian couple stress effects resulting from a Newtonian lubricant blended with additives, the non‐Newtonian dynamic coefficients are obtained for composite slider bearings.FindingsComparing with the non‐Newtonian inclined‐plane bearing, the non‐Newtonian composite bearing provides an improvement in the dynamic stiffness and damping coefficients; better bearing characteristics are achieved for the non‐Newtonian composite bearing under specific length‐ratio parameters.Originality/valueThe paper includes a numerical example to provide guidance for non‐Newtonian composite slider bearings.

1103 界面に接近して存在するき裂の応力拡大係数に及ぼすモーメント応力の影響について

1103 界面に接近して存在するき裂の応力拡大係数に及ぼすモーメント応力の影響について

Diffusion and Stress Coupling Effect during Oxidation at High Temperature

We report the diffusion and stress coupling effect during oxidation. An analytical model is developed for the stress and diffusion coupling effect based on equilibrium relationship and diffusion equation considering for the stress effect. Compressive stress will generate during the oxidation due to the growth strain. This growth stress can modify the diffusion coefficient; therefore, the oxidation kinetics is also affected. The coupling effect reduces both the oxidation rate and the stress. The proposed model is applied to predict the oxidation evolution for SiC and its consistence with the experimental data demonstrates the theoretical analysis.

Effects of Non-Newtonian Couple Stresses on the Dynamic Characteristics of Wide Rayleigh Step Slider Bearings

Based upon the micro-continuum theory developed by Stokes (1966), the present study investigates the non-Newtonian effects of couple stresses upon the dynamic characteristics of wide parabolic-shaped slider bearings. To account for the couple stress effects resulting from a Newtonian lubricant blended with various additives, the non- Newtonian dynamic Reynolds-type equation is derived using the Stokes motion equations together with the continuity equation. A closed-form solution for the bearing characteristics is obtained for engineering applications. Comparing with the parabolic-film Newtonian-lubricant case, the effects of couple stresses provide an increase in the dynamic stiffness and damping coefficients. Comparing with the inclinedplane bearings with couple stress fluids by Lin et al. (2003), the parabolic-film slider bearings signifies an improvement in the dynamic stiffness and dynamic characteristics; the improvement of bearing dynamics is more pronounced for lower squeezing-film heights and larger geometrical parameters and non-Newtonian couple stress parameters. The results of the present study provide engineers useful information in bearing selection and designing.

PERISTALTIC TRANSPORT OF A COUPLE STRESS FLUID: SOME APPLICATIONS TO HEMODYNAMICS

The paper deals with a theoretical investigation of the peristaltic transport of a couple stress fluid in a porous channel. The study is motivated toward investigating the physiological flow of blood in the micro-circulatory system, by taking account of the particle size effect. The velocity, pressure gradient, stream function, and frictional force of blood are investigated, when the Reynolds number is small and the wavelength is large, by using appropriate analytical and numerical methods. Effects of different physical parameters reflecting porosity, Darcy number, couple stress parameter, as well as amplitude ratio on velocity profiles, pumping action and frictional force, streamlines pattern, and trapping of blood are studied with particular emphasis. The computational results are presented in graphical form. The results are found to be in good agreement with those reported by Shapiro et al.52 that was carried out for a non-porous channel without consideration of couple stress effect. The present study puts forward an important observation that for peristaltic transport of a couple stress fluid during free pumping, flow reversal can be considerably controlled by suitably adjusting the couple stress effect of the fluid/Darcy permeability of the channel. It is also possible to avoid the occurrence of trapping, by reducing the permeability.

MATHEMATICAL MODELING OF OSCILLATORY MAGNETO-CONVECTION OF A COUPLE-STRESS BIOFLUID IN AN INCLINED ROTATING CHANNEL

A mathematical study is conducted of the oscillatory hydromagnetic flow of a viscous, incompressible, electrically conducting, non-Newtonian bio-fluid in an inclined, rotating channel with nonconducting walls, incorporating couple stress effects. The constitutive equations for a couple-stress fluid and the Maxwell electromagnetic field equations are presented and then reduced to a set of coupled partial differential equations for the primary and secondary flow. The model is then nondimensionalized with appropriate variables and shown to be controlled by the inverse Ekman number (K2= 1/Ek), the hydromagnetic body force parameter (M), channel inclination (α), Grashof number (Gr), Prandtl number (Pr), oscillation frequency (ω), and time variable (ωT). Analytical solutions are derived using complex variables. The influence of the governing parameters on the primary velocity (u), secondary velocity (w), temperature (θ), primary and secondary flow discharges per unit depth in the channel (Qx, Qz), and frictional shear stresses due to primary and secondary flow (τx, τz), are studied graphically and using tables. Applications of the study arise in the simulation of the manufacture of electrically conducting bio-polymeric liquids and magneto-physiological flow devices.

Finite element analysis of two- and three-dimensional static problems in the asymmetric theory of elasticity as a basis for the design of experiments

In this paper, the constitutive relations of the finite element method are constructed and used for solving two- and three-dimensional problems of the asymmetric theory of elasticity. Different variants of finite elements are considered. The numerical experiments are carried out to evaluate the reliability and computational efficiency of the finite element algorithm based on the comparison between the numerical and analytical solutions, numerical estimation of the convergence and checking of the degree of accuracy, to which the natural boundary conditions are satisfied. The obtained solutions to the two- and three-dimensional problems are interpreted from the viewpoint of their applicability to a design of experiments capable of revealing the facts of couple-stress effects in material under elastic deformation and identification of material constants for the asymmetric theory of elasticity. The capabilities of the finite element algorithm to interpret experimental data and estimate the errors occurring in real experiments have been tested by solving several example problems.

Combined Non-Newtonian and Viscous Shear Effects on Porous Squeeze Film Behavior

On the basis of the Stokes microcontinuum theory, a numerical study of the combined effects of non-Newtonian couple stress and viscous shear forces on porous squeeze film behavior for parallel circular plates is presented in this article. A modified Reynolds equation governing the film pressure is derived using the Stokes constitutive equations to account for lubricant couple stress effects due to the presence of additives or suspended particles. The Darcy-Brinkman equations describing the fluid flow within the porous plate are used to account for viscous shearing forces. Numerical solutions for the squeeze film characteristics including film pressure, radial velocity, squeeze velocity, and response time are calculated for various values of the couple stress and viscous shear parameters. The simulation results indicate that the combined effects of couple stresses and viscous shearing forces are considerable.

Effect of Couple Stresses on the Stress Intensity Factors for Two Parallel Cracks in an Infinite Elastic Medium under Tension

Stresses around two parallel cracks of equal length in an infinite elastic medium are evaluated based on the linearized couple‐stress theory under uniform tension normal to the cracks. Fourier transformations are used to reduce the boundary conditions with respect to the upper crack to dual integral equations. In order to solve these equations, the differences in the displacements and in the rotation at the upper crack are expanded through a series of functions that are zero valued outside the crack. The unknown coefficients in each series are solved in order to satisfy the boundary conditions inside the crack using the Schmidt method. The stresses are expressed in terms of infinite integrals, and the stress intensity factors can be determined using the characteristics of the integrands for an infinite value of the variable of integration. Numerical calculations are carried out for selected crack configurations, and the effect of the couple stresses on the stress intensity factors is revealed.

Couple-stress effects for the problem of a crack under concentrated shear loading

In this paper, we deal with the plane-strain problem of a semi-infinite crack under concentrated loading in an elastic body exhibiting couple-stress effects. The faces of the crack are subjected to a concentrated shear loading at a distance L from the crack tip. This type of loading is chosen since, in principle, shear effects are more pronounced in couple-stress elasticity. The problem involves two characteristic lengths, that is, the microstructural length ℓ and the distance L between the point of application of the concentrated shear forces and the crack tip. The presence of this second characteristic length introduces certain difficulties in the mathematical analysis of the problem: a non-standard Wiener–Hopf equation arises, one that contains a forcing term with unbounded behaviour at infinity in the transformed plane. Nevertheless, an analytic function method is employed that circumvents the aforementioned difficulty. For comparison purposes, the case of a semi-infinite crack subjected to a distributed shear load is also treated in the present study. Numerical results for the dependence of the stress intensity factor and the energy release rate upon the ratio of the characteristic lengths are presented.

Effect of turbulence on the static performance of a misaligned externally adjustable fluid film bearing lubricated with couple stress fluids

Static analysis of a misaligned externally adjustable fluid-film bearing is carried out thereby including turbulence and couple-stress effects in lubricants blended with polymer additives. A modified form of Reynolds equation, incorporated with the theory of micro-continuum and the concept of adjustability, is solved numerically, for various simulated operating conditions. The effects of turbulence and couple-stress on key performance parameters are presented. This study predicts that, an externally adjustable fluid-film journal bearing operating with negative adjustment configuration and lubricants with couple-stress, results in superior load carrying capacity with reduced friction and end leakage, as compared to a conventional partial arc bearing.

The problem of sharp notch in couple-stress elasticity

The problem of sharp notch in couple-stress elasticity is considered in this paper. The problem involves a sharp notch in a body of infinite extent. The body has microstructural properties, which are assumed to be characterized by couple-stress effects. Both symmetric and anti-symmetric loadings at remote regions are considered under plane-strain conditions. The faces of the notch are considered traction free. To determine the field around the tip of the notch, a boundary-layer approach is followed by considering an expansion of the displacements in a form of separated variables in a polar coordinate system. Our analysis is in the spirit of the Knein–Williams and Karp–Karal asymptotic techniques but it is much more involved than its corresponding analysis of standard elasticity due to the complicated boundary value problem (higher-order system of governing PDEs and additional boundary conditions as compared to the standard theory). Eventually, an eigenvalue problem is formulated and this, along with the restriction of a bounded potential energy, provides the asymptotic fields. The cases of a crack and a half-space are analyzed as limit cases of the general notch problem. Certain deviations from the standard classical elasticity results are noted.

On material velocities and non-locality in the thermo-mechanics of continua

Following is a discussion of several issues surrounding the continuum modeling of discrete particulate systems, particularly the uncertainty in the definition of continuum-level material particles and velocities. The work is motivated in part by various proposals for the introduction of supplemental velocity fields into the thermo-mechanics of single-component fluids. A review and modification are given of the relevant continuum field equations, based on the Eulerian rather than the conventional Lagrangian description, and a connection is made to the well-known statistical mechanics of Kirkwood and coworkers for point-particles. The Noetherian technique of Green and Naghdi is employed to derive the momentum balance directly from the particle-level energy balance, and it is shown that non-barycentric effects in particle motion engender stress asymmetry. It is conjectured that this and related effects are generally bound up with higher-gradient effects and the breakdown of the simple-material model for continuum thermo-mechanics. To illustrate this, a theory of non-local linear viscoelasticity is presented and compared with Brenner’s “bi-velocity hydrodynamics” and Müller’s “extended thermodynamics” for heat flux and stress. These models are shown to represent expansions in spatial wave vector, representing a Knudsen number, and temporal frequency, representing a Deborah number. Suggestions are made for further work to explore the associated effects of couple-stress and the consequences of departures of entropy flux from heat flux.

Effects of Couple Stress on the Growth Rate of Rayleigh- Taylor Instability at the Interface in a Finite Thickness Couple Stress Fluid

In this paper the effects of couple stress fluid on the control of Rayleigh-Taylor instability at the interface between a dense fluid accelerated by a lighter fluid is studied. A simple theory, based on fully developed approximations, is used to derive the growth rate of Rayleigh-Taylor instability. The cutoff and maximum wave numbers and the corresponding maximum frequency are obtained. It is shown that the effect of couple stress parameter reduces the growth rate considerably compare to the classical growth rate in the absence of couple-stress and hence favorable to control the growth rate of surface instabilities in many practical problems.

Couple-stress effect on the effective viscosity of magnetic fluids

The presence of nanostructure in a fluid causes the collision and friction between nanoparticles and between nanoparticles and walls when it is flowing; that is, the couple stresses in a fluid are present. It is desirable to understand the effect of couple stresses on the effective viscosity of magnetic fluids. In this study, we propose the modifications in momentum balance of magnetic fluids with nanostructure and derive a magnetoviscosity expression coming from the effective-field method, which describes the nonNewtonian behaviour of magnetic fluids. Results reveal that the effective viscosity is greater than the viscosity of non-couplestress fluids. However, the magnetic response and the shear-thinning non-Newtonian behavior are reduced.