Showing papers in "Acta Mechanica in 1990"
TL;DR: In the theory of saturated porous media and especially in soil mechanics, the concept of effective stresses (total stresses minus pore liquid pressure) plays an important role as mentioned in this paper, and a historical review of the development of this concept and its foundation via the modern mixture theory extended by volume fractions, will reveal some interesting new aspects.
Abstract: In the theory of saturated porous media and especially in soil mechanics, the concept of effective stresses (total stresses minus poreliquid pressure) plays an important role. The historical review of the development of this concept and its foundation via the modern mixture theory extended by the concept of volume fractions, will reveal some interesting new aspects.
158 citations
TL;DR: Eshelby's elastic energy-momentum tensor is shown to satisfy a differential identity which, in the general case of a uniform elastic body with inhomogeneities, is expressible in terms of the torsion of the material connection as discussed by the authors.
Abstract: Eshelby's elastic energy-momentum tensor is shown to satisfy a differential identity which, in the general case of a uniform elastic body with inhomogeneities, is expressible in terms of the torsion of the material connection.
141 citations
TL;DR: In this paper, the authors apply the method of averaging to first order in the small parameter e to the autonomous system and apply it to the problem of approximating limit cycles in the above differential equation.
Abstract: We apply the method of averaging to first order in the small parameter e to the autonomous system
$$x'' + \alpha x + \beta x^3 + \varepsilon g\left( {x, x'} \right) = 0$$
where we do not consider β as small This involves perturbing off of Jacobian elliptic functions, rather than off of trigonometric functions as is usually done The resulting equations involve integrals of elliptic functions which are evaluated using a program written in the computer algebra system MACSYMA The results are applied to the problem of approximating limit cycles in the above differential equation
129 citations
TL;DR: The behavior of incompressible laminar boundary layers in forced flow over a wedge with uniform suction or injection was theoretically investigated in this paper, where boundary layer equations along a wedge were transformed into non-similar partial differential ones, and the ordinary differential equations were obtained by means of the difference-differential method.
Abstract: The behavior of incompressible laminar boundary layers in forced flow over a wedge with uniform suction or injection was theoretically investigated The boundary layer equations along a wedge are transformed into non-similar partial differential ones, and the ordinary differential equations were obtained by means of the difference-differential method The solutions of the resulting equations are expressed in a form of integral equations which are in turn solved by iterative numerical quadratures The numerical results are given for the velocity distribution, temperature distribution and the coefficient of skin friction and heat transfer for various values of suction/injection parameter
127 citations
TL;DR: In this article, the heat transfer from a stretching sheet to a micropolar fluid is analyzed using the theory of Eringen, and the governing equations for momentum, angular momentum and energy have been solved numerically.
Abstract: The heat transfer from a stretching sheet to a micropolar fluid is analyzed using the theory of micropolar fluids formulated by Eringen. The governing equations for momentum, angular momentum and energy have been solved numerically. Numerical data for the friction factor and Nusselt number has been tabulated for a range of Prandtl numbers. Surface mass transfer rate and the power law constant for the wall temperature have considerable influence on the heat transfer mechanism.
100 citations
TL;DR: In this paper, a variational principle of total energy is formulated for finite strain statics of a hyperelastic body whose initial configuration contains a gap, and the equilibrium condition at a gap tip is associated with the well-known Jintegrals by including the reaction of inertia and the flux of kinetic energy.
Abstract: A variational principle of total energy is formulated for finite strain statics of a hyperelastic body whose initial configuration contains a gap From this principle statical equations and boundary conditions for the gapped body are derived The equilibrium condition at a gap tip is associated with the well-knownJ-integrals By including the reaction of inertia and the flux of kinetic energy the principle of total energy is transformed to the variational inequality of evolution for dynamics of a hyperelastic body with a propagating crack A closed system of dynamical equations, boundary conditions and additional conditions on the unknown contact crack surfaces and crack tip is obtained As example the antiplane shear of an infinite gapped body is considered
67 citations
TL;DR: In this article, the authors review the existing exact solutions of the generalized Beltrami flows and present new exact solutions for the Navier-Stokes equations, and present several new solutions.
Abstract: Exact solutions of the Navier-Stokes equations are rare. This paper reviews the existing exact solutions of the generalized Beltrami flows. Several new solutions are presented.
65 citations
TL;DR: In this article, rotationally symmetric flow between two concentric rotating spheres is investigated both theoretically and experimentally, and it is found that a steady state can exist asymmetric with respect to the equator.
Abstract: The rotationally symmetric flow between two concentric rotating spheres is investigated both theoretically and experimentally. The non-uniqueness of the supercritical flow exhibits three different modes with zero, one and two Taylor vortices in each hemisphere. These modes are realized by different accelerations of the inner sphere from the state at rest. A initial value code, based on a finite difference method, is used for the numerical simulation. The existence regions of the different supercritical flows are connected with symmetric and asymmetric transitions. It is found, that a steady state can exist asymmetric with respect to the equator. The flow is analyzed by plotting the size of the Taylor vortices, the depending variables ψ, ζ,V, the velocity distributions and the torque. A comparison between theory and experiments for the observed modes of flow is given.
62 citations
TL;DR: In this article, the authors derived the fundamental solution for the differential system of micropolar elasticity with voids in the steady vibration case by means of an uncoupling representation.
Abstract: By means of an uncoupling representation, we derive the fundamental solution for the differential system of micropolar elasticity with voids in the steady vibration case. Reciprocity properties are also explored.
52 citations
TL;DR: In this paper, a set of microscopic flow relations having a direct counterpart in the macroscopic formulation of plasticity and viscoplasticity is deduced for the simple shear problem, especially in evaluating the development of the axial stress normal to the shear plane.
Abstract: Considering the configuration of a single slip and employing a scale invariance argument, it is possible to deduce a set of “microscopic” plastic flow relations having a direct counterpart in the “macroscopic” formulation of plasticity and viscoplasticity. In particular, a microscopic form of the plastic spin and its macroscopic counterpart for the case of anisotropy induced by kinematic hardening are obtained in terms of elementary physical arguments. Moreover the evolution equation for the back-stress is rigorously derived. Parameters which were assumed to be constant and/or independent from each other in a macroscopic development, are now found to be interrelated and dependent on the accumulated plastic strain. These findings are used for the analysis of the simple shear problem, especially in evaluating the development of the axial stress normal to the shear plane. A preliminary qualitative comparison with available data from fixed-end torsion experiments is discussed.
45 citations
TL;DR: In this article, a finite journal bearing with micropolar fluid was predicted by numerical computation of the generalized Reynolds equation and the equations of shaft motion, and it was shown that some stabilizing effects due to fluids with micro-polar characteristics were observed.
Abstract: Whirl orbits of a shaft in a finite journal bearing lubricated with micropolar fluid is predicted by numerical computation of the generalized Reynolds equation and the equations of shaft motion. Comparing to Newtonian fluids, some stabilizing effects due to fluids with micropolar characteristics is reported.
TL;DR: In this article, a bifurcation analysis of the triaxial compression test on rock specimens is presented, which is modelled by a deformation theory of elasto-plasticity for a pressure sensitive, cohesive-frictional, dilatant material with microstructure.
Abstract: In this paper a bifurcation analysis of the triaxial compression test on rock specimens is presented. Rock behavior is modelled by a deformation theory of elasto-plasticity for a pressure sensitive, cohesive-frictional, dilatant material with microstructure. In particular a Cosserat continuum model for a granular rock is developed. Shape and size effects are discussed on the basis of an analysis of diffuse bifurcation of triaxial tests on a particular sandstone [25].
TL;DR: In this paper, a concentrated heat source is situated at the tip of an otherwise adiabatic rotating cone and the governing equations reduce to set of nonlinear, ordinary differential equations which are then integrated numerically.
Abstract: A concentrated heat source is situated at the tip of an otherwise adiabatic rotating cone. Due to centrifugal forces, velocity and thermal boundary layers spread on the surface. After a similarity transform, the governing equations reduce to set of nonlinear, ordinary differential equations which are then integrated numerically. The related cases of rotating discs and other axisymmetric surfaces are considered.
TL;DR: The linear elastic Delaunay network model developed in a previous paper is used to obtain further results on mechanical properties of graph-representable materials and an increase of effective moduli and a decrease of their scatter are observed.
Abstract: The linear elastic Delaunay network model developed in a previous paper is used to obtain further results on mechanical properties of graph-representable materials. First, we investigate the error involved in the uniform strain approximation — a computationally inexpensive approach widely employed in the determination of effective moduli of granular and fibrous media. Although this approximation gives an upper bound on the macroscopic moduli, it results in very good estimates of their second order statistics. In order to derive a lower bound another window definition has to be introduced. Also, an energy-based derivation of both bounds is given. The final result relates to a modification of a Delaunay network so that its vertices correspond to the centroids of cells of the corresponding Voronoi tessellation; an increase of effective moduli and a decrease of their scatter are observed.
TL;DR: In this paper, Nohguchi et al. used similarity solutions for the two-dimensional flow of a mass of cohesionless granular material down rough, flat and curved beds, where the basal friction force was assumed to be composed of a Mohr-Coulomb type component with a bed friction angle that is position dependent plus a viscous Voellmy-type resistive stress.
Abstract: This paper, though independently written, continues an analysis of similarity solutions for the two-dimensional flow of a mass of cohesionless granular material down rough, flat and curved beds, see Savage and Nohguchi [12], Nohguchi, Hutter and Savage [7]. The basal friction force is assumed to be composed of a Mohr-Coulomb type component with a bed friction angle that is position dependent plus a viscous Voellmy-type resistive stress, that is proportional to the velocity squared. This granular flow model is conjectured to adequately model the motion and dispersion of flow avalanches of snow whose air borne powder component can be ignored. The depth and velocities relative to those of the centre of mass of the moving pile are determined analytically, and it is shown that the pile has a parabolic cap shape and the difference velocity varies linearly with distance from the centre of mass. The length and the position and velocity of the centre mass are calculated numerically. We explicitly show:
TL;DR: In this article, the problem of boundary layer flow on a flat plate with injection and a constant velocity opposite in direction to that of the uniform mainstream is analyzed, and the critical values of λ andC are obtained numerically and their significance in drag reduction is discussed.
Abstract: The problem of boundary layer flow on a flat plate with injection and a constant velocity opposite in direction to that of the uniform mainstream is analyzed. It is shown that the solution of this boundary layer problem not only depends on the ratio of the velocity of the plate to the velocity of the free stream (λ), but also on the injection velocity parameter (C). It is also shown that there exists a range of values of λ andC for which the differential equations associated with the boundary layer problems admit analytic solutions. The critical values of λ andC are obtained numerically and their significance in drag reduction is discussed.
TL;DR: In this paper, the effects of the membrane density, internal head, and upstream head on the frequencies were determined with the use of the finite difference and boundary element methods, where the dam material is assumed to be inextensible.
Abstract: Inflatable dams are used for various purposes in a number of countries. They are cylindrical membrane structures which are attached to a rigid foundation along two of their generators and are inflated with water, air, or a combination of water and air. Some studies of their cross-sectional static profiles have been carried out in the past, both for cases when the dam impounds water and when overflow occurs. Experiments on scale models also have been reported. Vibrations have been observed on actual dams and on the physical models, but a theoretical analysis of the dynamic behavior of inflatable dams has not been published previously. In this paper, two-dimensional linear vibrations are considered. The dam is inflated with water and is used to impound water. Its material is assumed to be inextensible. Vibration modes and frequencies are obtained with the use of the finite difference and boundary element methods. The effects of the membrane density, internal head, and upstream head on the frequencies are determined.
TL;DR: Theoretical study of porous slider bearing with couple stress fluid as lubricant is made and the lubrication qualities of couple stress fluids are examined in this article, where analytical expressions for load capacity, frictional force and the centre of pressure are derived.
Abstract: Theoretical study of porous slider bearing with couple stress fluid as lubricant is made and the lubrication qualities of couple stress fluid are examined. The lower surface is covered by a thin porous material and the upper one, having arbitrary shape, moves in its own plane with constant velocity. Analytical expressions for load capacity, frictional force and the centre of pressure are derived. It yields increase in, load capacity and ensures the decrease in coefficient of friction. The problem is also discussed in the context of various geometries viz, (1) Rayleigh step bearings and (2) inclined slider bearings. Bounds on flow rate, frictional coefficient, centre of pressure and time-height relation are obtained and compared with classical case, Gross [1]. Suitable design parameters are predicted for the efficient lubrication of slider bearings.
TL;DR: In this paper, the authors dealt with natural convection heat transfer from a vertical plate embedded in a fluid saturated porous medium whose ambient temperature is not uniform and solved the problem by integral method of von-Karman type and the closed form solution was obtained.
Abstract: Present investigation deals with natural convection heat transfer from a vertical plate embedded in a fluid saturated porous medium whose ambient temperature is not uniform The problem is solved by integral method of von-Karman type and the closed form solution is obtained The effects of stratification parameter on local and overall heat transfer coefficients, velocity and temperature profiles are analysed
TL;DR: In this paper, the transformation group theoretic approach is applied to present an analysis of the problem of unsteady free convection from the outer surface of a vertical circular cylinder, where the application of two-parameter group reduces the number of independent variables by two.
Abstract: The transformation group theoretic approach is applied to present an analysis of the problem of unsteady free convection from the outer surface of a vertical circular cylinder. The application of two-parameter group reduces the number of independent variables by two, and consequently the system of the governing partial differential equations with the boundary conditions reduces to a system of ordinary differential equations with the appropriate boundary conditions. The ordinary differential equations are solved numerically using a fourth-order Runge-Kutta scheme and the gradient method. Numerical results are obtained for the study of the boundary-layer characteristics. The general analysis developed in this study corresponds to the case of surface temperature that varies exponentially with time and uniform with respect to the axial coordinate, i.e., in the formT
w
=ae
bt
, wherea andb are constants. The effect of Prandtl number,Pr, andb on the boundary layer characteristics and the maximum value of the vertical component of the velocity are studied.
TL;DR: In this paper, the necessary parameters for an invariant description of the elastic behaviour of a transversely isotropic medium in terms of the spectral decomposition of its compliance tensor are the four eigenvalues of it and a dimensionless parameter, appropriately defined, the eigenangle ω.
Abstract: It is shown that the necessary parameters for an invariant description of the elastic behaviour of a transversely isotropic medium in terms of the spectral decomposition of its compliance tensor are the four eigenvalues of it and a dimensionless parameter, appropriately defined, the eigenangle ω. A study of the variational bounds imposed by thermodynamic restrictions on the values of the eigenangle ω is presented. It is further proposed that the eigenangle ω can be successfully used as a single parameter characterizing qualitatively both elasticity and toughness of transversely isotropic media.
TL;DR: In this article, a Boundary Element Method (BEM) is developed for dynamic analysis of thin elastic plates, based on the capability to establish a flexibility matrix (discrete Green's function) with respect to a set of nodal mass points using a BEM solution for the static plate problem.
Abstract: A Boundary element method (BEM) is developed for the dynamic analysis of thin elastic plates. The method is based on the capability to establish a flexibility matrix (discrete Green's function) with respect to a set of nodal mass points using a BEM solution for the static plate problem. A lumped mass matrix is constructed from the tributary mass areas to the nodal mass points. Both free and forced vibrations are considered and numerical examples are presented to illustrate the method and its merits.
TL;DR: In this paper, a constitutive model was proposed to describe the hysteresis loops of stress-strain relations of blood vessels under cyclic loading conditions, where the total strain was expressed as the sum of the elastic part and the inelastic part on the basis of a finite deformation theory.
Abstract: The present paper is concerned with the formulation of a constitutive model describing the hysteresis loops of stress-strain relations of blood vessels under cyclic loading conditions. It is assumed that the hysteresis loop is composed of elastic deformation and viscoplastic deformation. Hence the total strain is expressed as the sum of the elastic part and the inelastic part on the basis of a finite deformation theory. Then the elastic part is established by postulating a strain energy function of an exponential type, while the inelastic part is formulated by modifying the nonlinear kinematic hardening rule in the viscoplastic model proposed by Chaboche et al. A comparison of the numerical result with the literature shows that the present model can describe the hysteresis loop qualitatively.
Abstract: This paper aims at completing and extending the theories as they have been applied to swelling media for the last 50 years, to swelling non-saturated soils. However, having regard to the complicated behaviour of swelling soils, it was thought necessary to keep the state of stress as simple as possible when discussing swelling in cylindrical specimens in which drainage is “completely” prevented. Definitions of the parameters are attemptedbased on equilibrium thermodynamics. Contributions to swelling stress calculation, when expansion is considered in relation to vapor pressure and moisture content, are also given.
TL;DR: In this paper, the effects of inertia forces and the distance from the leading edge of the plate on the velocity and temperature fields as well as on the skin friction and heat transfer coefficients in the boundary layer flow over a semi-infinite flat plate embedded in a saturated porous medium of high porosity are studied.
Abstract: The effects of inertia forces and the distance from the leading edge of the plate on the velocity and temperature fields as well as on the skin friction and heat transfer coefficients in the boundary layer flow over a semi-infinite flat plate embedded in a saturated porous medium of high porosity are studied. It is shown that the inertia forces have a significant influence on the flow characteristics in this problem.
TL;DR: In this article, a cyclic theory of plasticity is formulated for finite deformation in the Eulerian reference system and a new kinematic hardening rule is proposed based on the experimental observations made by Phillips et al.
Abstract: A cyclic theory of plasticity is formulated for finite deformation in the Eulerian reference system. A new kinematic hardening rule is proposed based on the experimental observations made by Phillips et al. [11]–[15]. The Tseng-Lee model [9] is also obtained as a special case of the proposed model.
TL;DR: In this paper, the motion of a simply supported, viscoelastic inextensible beam subjected to large displacements and small strains is analyzed and compared using four methods: the Bubnov-Galerkin method, finite difference method, the finite element method and the method of rigid finite elements.
Abstract: In this paper the motion of a simply supported, viscoelastic inextensible beam subjected to large displacements and small strains is analysed. The results of calculations are obtained and then compared using 4 methods: the Bubnov-Galerkin method, the finite difference method, the finite element method and the method of rigid finite elements.
TL;DR: In this paper, a principal value definition of the basic hypersingular integral in the fundamental integral equation for two-dimensional cracks in three-dimensional isotropic elasticity is proposed.
Abstract: A principal value definition of the basic hypersingular integral in the fundamental integral equation for two-dimensional cracks in three-dimensional isotropic elasticity is proposed. As is the case with the corresponding definitions of Cauchy-type one-dimensional and two-dimensional principal value singular integrals, as well as Mangler-type one-dimensional principal value hypersingular integrals, the present definition is based on the special consideration of an appropriate region around the singular point. The cases of circular, square and equilateral triangular regions are considered in some detail.
TL;DR: In this article, the plane strain thermomechanical deformations of a viscoplastic body containing a rigid non-heat-conducting ellipsoidal inclusion at the center were analyzed.
Abstract: We study the plane strain thermomechanical deformations of a viscoplastic body containing a rigid non-heat-conducting ellipsoidal inclusion at the center. Two different problems, one in which the major axis of the inclusion is parallel to the axis of compression and the other in which it is perpendicular to the loading axis are considered. In each case the deformations are presumed to be symmetric about the two centroidal axes and consequently deformations of a quarter of the block are analyzed. The material of the block is assumed to exhibit strain-rate hardening, but thermal softening. The applied load is such as to cause deformations of the block at an overall strain-rate of 5000 sec−1. The rigid inclusion simulates the presence of second phase particles such as oxides or carbides in a steel and acts as a nucleus for the shear band. It is found that a shear band initiates near the tip of the inclusion and propagates along a line inclined at 45° to the horizontal axis. At a nominal strain of 0.25, the peak temperature rise near the tip of the vertically aligned inclusion equals 75% of that for the horizontally placed inclusion. The precipitous drop in the effective stress near the inclusion tip is followed somewhat later by a rapid rise in the maximum principal logarithmic strain there.
TL;DR: In this article, a solidly rotating finite liquid column consisting of frictionless liquid is subjected to various axial excitation modes and the response of the free liquid surface displacement and velocity distribution has been determined in the elliptic and hyperbolic range.
Abstract: A solidly rotating finite liquid column consisting of frictionless liquid is subjected to various axial excitation modes. The response of the free liquid surface displacement and velocity distribution has been determined in the elliptic (Ω>2Ω0) and hyperbolic range (Ω<2Ω0). Differences of the various cases are presented.