Showing papers in "Acta Mechanica in 1996"
TL;DR: In this article, the steady flow of an electrically conducting, viscous, incompressible fluid bounded by two parallel infinite insulated horizontal plates and the heat transfe through it are studied.
Abstract: In the present paper, the steady flow of an electrically conducting, viscous, incompressible fluid bounded by two parallel infinite insulated horizontal plates and the heat transfe through it are studied. The upper plate is given a constant velocity while the lower plate is kept stationary. The viscosity of the fluid is assumed to vary with temperature. The effect of an external uniform magnetic field as well as the action of an inflow perpendicular to the plates together with the influence of the pressure gradient on the flow and temperature distributions are reported. A numerical solution for the governing non-linear ordinary differential equations is developed.
189 citations
TL;DR: In this paper, a closed form solution is obtained under some restrictions on the linear mass flux for viscous incompressible flow over a stretching sheet, where the velocity of the sheet is a quadratic polynomial of the distance from the slit.
Abstract: This study deals with the viscous incompressible flow over a stretching sheet. The velocity of the sheet is a quadratic polynomial of the distance from the slit and the sheet is subjected to a linear mass flux. A closed form solution is obtained under some restrictions on the linear mass flux. Stream line patterns are plotted and the effect of mass flux on the flow is also studied.
122 citations
TL;DR: In this paper, a linear analysis of the temporal instability of an annular viscous liquid jet moving in an inviscid gas medium was carried out, which includes three limiting cases of a round liquid jet, a gas jet and a plane liquid sheet.
Abstract: A linear analysis has been carried out for the temporal instability of an annular viscous liquid jet moving in an inviscid gas medium, which includes three limiting cases of a round liquid jet, a gas jet and a plane liquid sheet. It is found that there exist two independent unstable modes, which become the well-known sinuous and varicose modes for plane liquid sheets as annular jet radii approach to infinity. Hence, they are named as para-sinuous and para-varicose. It is shown that an ambient gas medium always enhances the annular jet instability. The curvature effects in general increase the disturbance growth rate, and may not be neglected for the breakup process of an annular or conical liquid sheet. An annular jet with a sufficiently small thickness tends to break up much faster than the corresponding plane liquid sheet, in accordance with existing experimental observations. Liquid viscosity has complicated dual effects on the instability. It is also found that there exists a critical Weber number below which surface tension is the source of instability. Whereas above it, instability is suppressed by surface tension effect and it promoted by aerodynamic interaction between the liquid and gas phase. For the practical importance of large Weber numbers such as related to liquid atomization, the para-sinuous mode is always predominant.
106 citations
TL;DR: In this article, the steady flow of a power-law fluid past a stationary circular cylinder was considered and the governing nonlinear equations, expressed in terms of a stream function and vorticity, were solved by finite differences for Reynolds numbers (based on the radius of the cylinder)R=5,20, 40 for various power law indices,n.
Abstract: Considered in this paper is the two-dimensional steady flow of a power-law fluid past a stationary circular cylinder. The governing nonlinear equations, expressed in terms of a stream function and vorticity, were solved by finite differences for Reynolds numbers (based on the radius of the cylinder)R=5,20, 40 for various power-law indices,n. Parameters such as the drag coefficient, separation angle, wake length and critical Reynolds number are presented and contrasted with those of a Newtonian fluid (n=1) to illustrate the non-Newtonian effects. For a given-Reynolds number a consistent behaviour withn was observed in the parameters for the ranges considered. The results obtained for the Newtonian case agree well with documented results.
99 citations
TL;DR: In this article, the authors developed agradient theory of internal variables using a variational principle in conjunction with the dissipation inequality and showed that the internal variables obey field equations instead of evolution equations and are subject to boundary conditions that are dictated by the applied tractions and displacements as well as the physical structure of the material domain.
Abstract: In this paper we develop agradient theory of internal variables using a variational principle in conjunction with the dissipation inequality. The basic findings are (i), that the internal variables are, non-local in that they obey field equations instead of evolution equations and (ii) they are subject to boundary conditions that are dictated by the applied tractions and displacements as well as the physical structure of the material domain. As a consequence, spatiallyinhomogeneous strain fields exist in the presence ofuniform boundary tractions and/or displacements. This phenomenon is illustrated in the simple case of one dimension.
84 citations
TL;DR: In this article, a thermodynamically admissible formulation of anelasticity viewed as a G-structure evolution is proposed, and the material Eshelby tensor is shown to be the driving force behind this evolution.
Abstract: G-structures are the geometric backbone of the theory of material uniformity in continuum mechanics. Within this geometric framework, anelasticity is seen as a result of evolving distributions of inhomogeneity reflected as material nonintegrability. Constitutive principles governing thetime evolution of the G-structure underlying the finite-strain theory of anelasticity (e.g., plasticity) are proposed. The material Eshelby stress tensor is shown to be thedriving force behind this evolution. This should allow for a thermodynamically admissible formulation of anelasticity viewed as a G-structure evolution.
81 citations
TL;DR: In this paper, the authors address the phenomena of mechanical creep and deformation in rock formations, coupled with the hydraulic effects of fluid flow through the correspondence principle, based on Biot's poroelasticity.
Abstract: This paper addresses the phenomena of mechanical creep and deformation in rock formations, coupled with the hydraulic effects of fluid flow. The theory is based on Biot's poroelasticity, generalized to encompass viscoelastic effects through the correspondence principle. Based on the resultant poroviscoelastic theory, stress and deformation analyses are performed. The interactions between the fluid pore pressure diffusion and the elastic/viscoelastic rock matrix deformation are illustrated via two important examples. First, the problem of a borehole subject to a non-hydrostatic stress state, but deforming under plane strain condition, is examined. Second, a cylinder under generalized plane strain conditions is solved. Three rocks, Berea Sandstone, Danian Chalk, and a deep water Gulf of Mexico Shale, covering a wide range of permeabilities, are considered. The significance of poro-and viscoelastic time-dependent effects is discussed.
80 citations
TL;DR: In this article, the revised Enskog theory was employed to analyze granular flows of binary-sized mixtures, and the governing equations and constitutive relations were used to investigate granular thermal diffusion, a diffusion process resulting from the granular temperature gradient.
Abstract: The revised Enskog theory was employed to analyze granular flows of binary-sized mixtures. The governing equations and constitutive relations were used to investigate granular thermal diffusion —a diffusion process resulting from the granular temperature gradient. The granular thermal diffusion causes the smaller or the lighter particles to concentrate in the region of the flow with higher granular temperature, and causes the larger or the heavier particles to concentrate in a region of lower granular temperature. A granular flow of binary mixtures in an oscillatory no-flow system and in a sheared system was examined, and indicated a complete segregation when the granular thermal diffusion was sufficiently large.
69 citations
TL;DR: In this paper, the authors used nonlinear stress-strain behavior in both shear and peel for adhesive to formulate two coupled nonlinear governing equations for an adhesive-adherend sandwich of single-lap type.
Abstract: Arbitrarily nonlinear stress-strain behaviour in both shear and peel for adhesive are utilised to formulate two coupled nonlinear governing equations for an adhesive-adherend sandwich of single-lap type. For a balanced adhesive-adherend sandwich, the two equations can be integrated, and simple formulas for bond strength are developed for characterising pure shear, peel and mixed failure in adhesive. These formulas define the bond strength in terms of the maximum strain energy density in the adhesive. It is shown that the product of the adhesive strain energy density and the adhesive thickness is equal to the energy release rateJ of mode I, mode II and mixed fracture.
62 citations
TL;DR: In this paper, the macro-scale constitutive law for a granular material is derived from the micro-scale of two interacting particles, and the effects of inter-particle stiffness on the macro scale constitutive constants are discussed.
Abstract: The granular material perceived as a collection of particles is modelled as a Cosserat or multipolar continuum taking into account the effect of material microstructure. The macro-scale constitutive law for a granular material is derived from the micro-scale of two interacting particles. We adopt an approach based on a static hypothesis and establish two relationships: i) macro-to-micro static relationship, and ii) micro-to-macro kinematic relationship. We derive macro-scale constitutive constants for granular materials with idealized isotropic packing structure. The effects of inter-particle stiffness on the macro-scale constitutive constants are discussed. In addition, Green's function for concentrated force and couple is derived to be expressed in terms of inter-particle stiffness. Using the expressions of Green's function, the physical meaning and the effect of the internal characteristic length for granular materials are discussed.
60 citations
TL;DR: In this paper, the oblique flow of a viscous fluid impinging on a flat wall with suction or blowing is studied and it is found that when suction is applied the fluid penetrates the wall while blowing causes the shifting of the stagnation point.
Abstract: The oblique flow of a viscous fluid impinging on a flat wall with suction or blowing is studied. It is found that when suction is applied the fluid penetrates the wall while blowing causes the shifting of the stagnation point. It is also found that this shifting depends upon the magnitude of the blowing.
TL;DR: In this paper, an approach based on the multiparticle effective field method is introduced for determining the overall elastoplastic behavior of the material under monotonic loading, and linearized problems are solved at each step of an iterative procedure.
Abstract: A multiphase material is considered, which consists of a homogeneous elastoplastic matrix containing a homogenous statistically uniform random set of ellipsoidal elastic inclusions. An approach based on the multiparticle effective field method is introduced for determining the overall elastoplastic behavior of the material under monotonic loading. A secant modulus concept is employed, and linearized problems are solved at each step of an iterative procedure. Physically consistent assumptions are used for linearizing nonlinear functions which depend on the phase averages of the second invariant of stress and on the stress deviator. Exact expressions for the second moments of the microstresses are employed.
TL;DR: In this article, the authors considered the scattering of normally incident longitudinal waves by a finite crack in an infinite isotropic dielectric body under a uniform electric field and reduced the problem to that of solving two simultaneous dual integral equations.
Abstract: We consider the scattering of normally incident longitudinal waves by a finite crack in an infinite isotropic dielectric body under a uniform electric field. By the use of Fourier transforms, we reduce the problem to that of solving two simultaneous dual integral equations. The solution of the dual integral equations is then expressed in terms of a Fredholm integral equation of the second kind having the kernel that is a finite integral. The dynamic stress intensity factor versus frequency is computed, and the influence of the electric field on the normalized values is displayed graphically.
TL;DR: In this paper, the state space approach for one-dimensional problems of viscoelastic magnetohydrodynamic unsteady free convection flow through a porous medium past an infinite vertical plate is formulated.
Abstract: In this work we formulate the state space approach for one-dimensional problems of viscoelastic magnetohydrodynamic unsteady free convection flow through a porous medium past an infinite vertical plate. Laplace transform techniques are used. The resulting formulation is applied to a thermal shock problem and to a problem for the flow between two parallel fixed plates both without heat sources. Also a problem with a distribution of heat sources is considered. A numerical method is employed for the inversion of the Laplace transforms. Numerical results are given and illustrated graphically for the problem considered.
TL;DR: In this paper, the free vibration of thin doubly-curved shallow shells of rectangular planform has been investigated under wide combinations of free, simply supported and clamped boundary conditions.
Abstract: This paper presents the free vibration of thin doubly-curved shallow shells of rectangular planform. The study covers wide combinations of free, simply supported and clamped boundary conditions. Both positive and negative Gaussian curvatures (spherical and hyperbolic paraboloidal shells resepectively) are considered. The pb-2 Ritz energy based approach, along with the in-plane and transverse deflections assumed in the form of a product of mathematically complete two-dimensional orthogonal polynomials and a basic function, is employed to model the vibratory characteristic of these shells. Numerical results have been established through convergence study and comparison with published data from the open literature. Extensive sets of new results for various ranges of aspect ratio, curvature ratio and x- and y- shallowness ratios have been presented for future reference.
TL;DR: A two-layered mathematical model of blood flow through an artery provided with a cosine-shaped constriction of a peripheral plasma layer free from red cells and a core region represented by a Casson fluid is investigated.
Abstract: The present investigation deals with a two-layered mathematical model of blood flow through an artery provided with a cosine-shaped constriction. The model consists of a peripheral plasma layer free from red cells and a core region represented by a Casson fluid. The geometry of the interface between the plasma layer and the core region has been determined and compared with that of the constriction along the length of the tube. The theoretical results obtained in this analysis are the expressions for wall shear stress and pressure drop for variable plasma layer thickness. The effect of the variable plasma layer thickness on the flow characteristics has been shown graphically for different parameter values to enable a better understanding of the biomechanical problem.
TL;DR: In this article, the three-dimensional Poisson-Voronoi model was used to study the stress distribution within a simulated polycrystalline aggregate having 200 grains, and different micro-stresses such as the maximum principal stress, maximum shear stress, first invariant of stress, and Von-Mises stress were found to vary systematically with the anisotropy of single crystal.
Abstract: The three-dimensional Poisson-Voronoi model, which is topologically equivalent to the microstructure of real ceramics and metals, has been used to study the stress distribution within a simulated polycrystalline aggregate having 200 grains. Micro-stresses such as the maximum principal stress, maximum shear stress, first invariant of stress, and Von-Mises stress are found to vary systematically with the anisotropy of single crystal.
TL;DR: In this paper, the authors investigated the applicability of incremental plasticity theories for cyclic loading and obtained first order stress-strain results for proportional loadings when either category of hardening rules is chosen.
Abstract: Incremental plasticity theories are being incorporated into many engineering numerical analyses. There are two basic categories of incremental plasticity algorithms, (i) multiple surface such as proposed by Mroz and Garud, and (ii) the Armstrong-Frederick type as modified by Chaboche et al. Engineering bounds on the general applicability of these models for cyclic loading have not been the subject of a detailed investigation. Similar first order stress-strain results are obtained for proportional loadings when either category of hardening rules is chosen.
TL;DR: In this article, the elastic buckling of symmetric cross-ply laminated rectangular plates with two parallel edges simply supported, one edge free and the remaining edge clamped was analyzed.
Abstract: This paper considers the elastic buckling of symmetric cross-ply laminated rectangular plates with two parallel edges simply supported, one edge free and the remaining edge free, simply supported or clamped. The first-order shear deformation plate theory is used in the analysis. An error apparently made by previous researchers for boundary conditions at free edges subjected to in-plane loads is corrected. Closed-form buckling factors are obtained using a generalised Levy-type solution method to solve the differential equations which govern the buckling behaviour of the laminates. Comparisons are made with previously published results, and the differences between buckling factors obtained with the appropriate and inappropriate free edge conditions are examined. The variation of buckling factors with plate aspect ratio, thickness ratio and the number of layers is investigated. Sets of first-known buckling solutions for cross-ply laminates are reported in design charts and tables.
TL;DR: In this article, the problem of heat transfer in the unsteady free convection flow over a continuous moving vertical sheet in an ambient fluid has been investigated and it is found that a better cooling performance could be achieved by using a liquid as a cooling medium rather than a gas.
Abstract: The problem of heat transfer in the unsteady free convection flow over a continuous moving vertical sheet in an ambient fluid has been investigated. Both constant surface temperature and constant surface heat flux conditions have been considered. The nonlinear coupled partial differential equations governing the flow have been solved numerically using the Keller box method and the Nakamura method which both give closely similar solutions. The results indicate that the cooling rate of the sheet can be enhanced by increasing the buoancy parameter or the velocity of the sheet. It is found that a better cooling performance could be achieved by using a liquid as a cooling medium rather than a gas. The overshoot in the velocity occurs near the surface when the buoyancy parameter exceeds a certain critical value.
TL;DR: In this article, a boundary layer analysis is presented to study the effects of magnetic field with vectored surface mass transfer and induced buoyancy streamwise pressure gradients on heat transfer to a horizontal plate placed in a micropolar fluid.
Abstract: A boundary layer analysis is presented to study the effects of magnetic field with vectored surface mass transfer and induced buoyancy streamwise pressure gradients on heat transfer to a horizontal plate placed in a micropolar fluid. Numerical solution are obtained for different values of the magnetic-, mass transfer-, buoyancy-, and material-parameters. A discussion is provided for the effects of the transverse magnetic field, vectored surface mass transfer and the buoyancy force on the friction factor and heat transfer rate.
TL;DR: In this paper, the nonlinear stability of electrically conductive liquid condensation film that flows down a vertical flat plate is investigated analytically, and the generalized kinematic equations for the film thickness with phase change at the interface are modified to take into account the effect of an uniform magnetic field applied transversely to the plate.
Abstract: In the present paper, the nonlinear stability of electrically conductive liquid condensation film that flows down a vertical flat plate is investigated analytically. The generalized kinematic equations for the film thickness with phase change at the interface is modified to take into account the effect of an uniform magnetic field applied transversely to the plate. The results show that both the supercritical stability and the subcritical instability still can be found in the magnetic fluid film flow system. The effect of the magnetic field (which was revealed as a Hartmann number,m) is to stabilize the film flow. Therefore, the instability could be counteracted by controlling the applied magnetic field. Moreover, this paper presents more accurate assessment for the instability of electrically conductive liquid film flow in a magnetic field.
TL;DR: In this paper, the free convection boundary layer flow induced by a heated vertical cylinder which is embedded in a fluid-saturated porous medium was considered and the fully numerical and asymptotic calculations were in stisfactory agreement, especially for exponentsn close to zero.
Abstract: We consider the free convection boundary layer flow induced by a heated vertical cylinder which is embedded in a fluid-saturated porous medium. The surface of the cylinder is maintained at a temperature whose value above the ambient temperature of the surrounding fluid varies as thenth power of the distance from the leading edge. Asymptotic analyses and numerical calculations are presented for the governing nonsimilar boundary layer equations and it is shown that, whenn 1, only a simple single layer is present far downstream, but a multiple layer structure exists close to the cylinder leading edge. We have shown that the fully numerical and asymptotic calculations are in stisfactory agreement, especially for exponentsn close to zero. Comparisons of the present numerical solutions obtained using the Keller-box method with previous numerical solutions using local methods are also given.
TL;DR: In this article, the scattering of antiplane shear waves in a metal matrix composite reinforced by fibers with interfacial layers was studied and the effect of interface properties on scattering cross section, phase velocity, attenuation of coherent plane wave, and effective elastic constant was shown graphically.
Abstract: This paper deals with the scattering of antiplane shear waves in a metal matrix composite reinforced by fibers with interfacial layers. We assume same-size cylindrical inclusions and same-thickness interface layers with nonhomogeneous elastic properties. The effective complex wave numbers follow from the coherent wave equation which depends only upon the scattering amplitude of the single scattering problem. Effective elastic constants can be obtained from phase velocities of coherent waves. Numerical calculations for an SiC-fiber-reinforced Al composite are carried out, and the effect of interface properties on scattering cross section, phase velocity, attenuation of coherent plane wave, and effective elastic constant is shown graphically.
TL;DR: In this article, the axisymmetric vibration of a piezoelectric laminated hollow circular cylinder has been studied for an imperfect interface model and the frequency equation is derived for traction free inner and outer surfaces of the hollow cylinder with continuity conditions at the bonding interfaces.
Abstract: The axisymmetric vibration of a piezoelectric laminated hollow circular cylinder has been studied for an imperfect interface model. The frequency equation is derived for traction free inner and outer surfaces of the hollow cylinder with continuity conditions at the bonding interfaces. The composite cylinder is composed of two different piezoelectric materials belonging to 6 mm class and a hypothetical Linear Elastic Material with Voids (LEMV) as bonding layer. Numerical solutions of the frequency equation are obtained for the composite cylinder ceramic(1)/LEMV/ceramic(2). Computational results are presented as dispersion curves as well as in tables to characterize the attenuation of axial waves for three layered cylinders with and without voids in the thin LEMV layer.
TL;DR: In this article, the authors established clear criteria for the well-posedness of the initial, boundary/initial and boundary value problems when the plasticity theory is associative as well as non-associative.
Abstract: Associative plasticity theories do not predict correctly the volumetric plastic strain, in the course of plastic deformation, in the case of materials where the position and conformation of the yield surface are functions of the prevailing hydrostatic stress. Non-associative theories have been proposed and used to correct this deficiency. Such theories, however, lead to other serious difficulties. In this paper we establish clear criteria for the well-posedness of the initial, boundary/initial and boundary value problems when the plasticity theory is associative as well as non-associative. We further show cases where non-associativity leads to ill-posedness of these problems even when the material is not at failure. Specifically we demonstrate that the initial/boundary and boundary value problems either have no solution, or if they do, the solution is not unique. We also show by specific examples that the banding condition, i.e., the vanishing of the determinant of the acoustic tensor, is tantamount (a) to loss of hyperbolicity of the equation of motion and (b) lack of existence or loss of uniqueness of the solution of the boundary value problem, in certain situations. Finally, we show the existence of a fundamental criterion that governs the stability of infinitesimal as well as finite elastoplastic domains.
TL;DR: In this article, the underlying structure of the theory of continuous distributions of defects in second-grade elastic bodies is presented in terms of second-order G-structures, where the structure of defects can be expressed as follows:
Abstract: The underlying structure of the theory of continuous distributions of defects, such as dislocations and disclinations, in second-grade elastic bodies is presented in terms of second-orderG-structures.
TL;DR: In this article, the athermohyperelastic constitutive model for near-incompressible elastomers is formulated in terms of the Helmholtz free energy density ϕ.
Abstract: Elastomers are often used in hot and confining environments in which thermomechanical properties are important. It appears that published constitutive models for elastomers are mostly limited to isothermal conditions. In this study, athermohyperelastic constitutive model for near-incompressible elastomers is formulated in terms of the Helmholtz free energy density ϕ. Shear and volume aspects of the deformation are decoupled. Thermomechanical coupling occurs mostly as thermal expansion. Criteria for thermodynamic stability are derived in compact form. As illustration, a particular expression for ϕ is presented which represents the thermomechanical counterpart of the conventional two-term incompressible Mooney-Rivlin model. It is used to analyze several adiabatic problems in a rubber rod.
TL;DR: In this article, a thin longitudinal isothermal circular cylinder moving in a flowing stream is considered, and the results show that the velocity and temperature distributions as well as the coefficients of skin friction and the local Nusselt number are appreciably affected by the relative velocity parameter.
Abstract: Summary. Steady laminar boundary layer flow and heat transfer over a thin longitudinal isothermal circular cylinder moving in a flowing stream has been studied in this paper. The cases in which the cylinder is moving in the same (parallel) or in the opposite (reverse) direction to the free stream are considered. The transformed nonsimilar boundary layer equations are solved numerically using the Keller-box method for some values of the curvature parameter, the Prandtl number and relative velocity parameter. The results show that the velocity and temperature distributions as well as the coefficients of skin friction and the local Nusselt number are appreciably affected by the relative velocity parameter.
TL;DR: In this article, the response to axial synchronous, counter-and one-sided excitation for anchored contact lines at the disc-rim is determined for a rotating viscous cylindrical liquid column of finite length.
Abstract: For a solidly rotating viscous cylindrical liquid column of finite length the response to axial synchronous, counter- and one-sided excitation is determined for anchored contact lines at the disc-rim. For a rotating column additional responses of inertial waves (hyperbolic range) appear forΩ < 2Ω
0, while in the elliptic rangeΩ < 2Ω
0 the sloshing response occurs. The various responses for the free surface displacement have been numerically evaluated. Only in the one-sided exitation case all resonance peaks appear, while for synchronous excitation only the odd resonances and for counter-excitation only the even resonance peaks occur.