# Showing papers in "Acta Mechanica in 1975"

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TL;DR: In this article, the authors introduced the concept of a bounding surface in the stress space which always encloses the loading surface, and a parameter defined by the relative position of the loading and the bounding surfaces, and the plastic work done during the most recent loading, determine the value of the plastic modulus.

Abstract: A number of observations are made on the macroscopic behavior of materials subjected to uniaxial random cyclic loadings. These observations are then generalized to construct a model describing the material behavior for complex multiaxial loadings, in particular for cyclic loadings. This generalization introduces the concept of a bounding surface in the stress space which always encloses the loading surface. A parameter defined by the relative position of the loading and the bounding surface, and the plastic work done during the most recent loading, determine the value of the plastic modulus.

827 citations

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TL;DR: In this paper, the existence of first integrals for non-convex systems with non-conservative forces is established. But the existence depends on the existence either of solutions of the generalized Noether-Bessel-Hagen equation or of the Killing system of partial differential equations.

Abstract: Noether's theorem and Noether's inverse theorem for mechanical systems with nonconservative forces are established. The existence of first integrals depends on the existence of solutions of the generalized Noether-Bessel-Hagen equation or, which is the same, on the existence of solutions of the Killing system of partial differential equations. The theory is based on the idea that the transformations of time and generalized coordinates together with dissipative forces determine the transformations of generalized velocities, as it is the case with variations in a variational principle of Hamilton's type for purely nonconservative mechanics [17], [18]. Using the theory a few new first integrals for nonconservative problems are obtained.

148 citations

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TL;DR: In this paper, the authors investigated the flow of a conducting liquid past an infinite porous flat plate taking Hall effects into account, the liquid being permeated by a transverse magnetic field.

Abstract: An investigation is made of the flow of a conducting liquid past an infinite porous flat plate taking Hall effects into account, the liquid being permeated by a transverse magnetic field. It is shown that asymptotic solution for the velocity and magnetic field exists both for suction or blowing at the plate. Further when the magnetic Reynolds number is very small, the flow pattern is remarkably similar to that for a non-conducting flow past a flat plate in a rotating frame.

82 citations

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TL;DR: In this paper, the local balance laws and the linear constitutive equations are extracted from the theory of microthermofluids, and the problem of Poiseuille flow between two parallel plates is solved.

Abstract: Microthermopolar fluids are introduced as a subclass of microthermofluids. In this subclass micromotion consists of rigid rotation only. The local balance laws and the linear constitutive equations are extracted from the theory of microthermofluids. Restriction regarding the material coefficients appearing in the constitutive equations are deduced by thermodynamical considerations. The problem of Poiseuille flow between two parallel plates is solved.

57 citations

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Yale University

^{1}TL;DR: In this paper, the equations of motion for condensing flows are given in analogy to those of reacting flows and discontinuities are discussed, and the early history of the discovery of condensation in supersonic wind tunnels is recounted.

Abstract: Diabatic processes dominate compressible flows with phase change where the heat of condensation or vaporization causes changes of enthalpy in the flow. The equations of motion for condensing flows are given in analogy to those of reacting flows and discontinuities are discussed. The nonequilibrium process of condensation by homogeneous nucleation in the supersaturated state is singled out by examples for steady and unsteady nozzle flows, Prandtl-Meyer flow, unsteady expansions and shock waves. A selective guide to the widely dispersed literature is provided and the early history of the discovery of condensation in supersonic wind tunnels is recounted.

56 citations

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TL;DR: In this paper, the history dependence of structural metals is examined and it is shown that prior deformation can change the response of structural metal to the same forcing function permanently but only in degree and not in kind.

Abstract: In slow motions, such as occur in repeated creep, relaxation and low-cycle fatigue loadings, rate and history dependence interact and the conventional metallic material idealizations do not appear to be appropriate. For later use an operational definition of aging, rate and history dependence is given. Constitutive equations capable of reproducing history dependence must not only depend on the forcing function in the present time interval but must also have a not completely fading memory of prior loadings. It is demonstrated that certain forms of integral constitutive equations and defined history dependence. The history dependence of structural metals is examined and it is shown that prior deformation can change the response of structural metals to the same forcing function permanently but only in degree and not in kind; the variable hereditary property of structural metals is limited and is caused by deformation-induced changes of the microstructure. Variant and invariant response properties under prior loading are stated.

45 citations

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TL;DR: In this article, the Couette-Stromung eines aus parallelen Nadeln zusammengesetzten “granularen” Materials (Schneebeli) kinematisch qualitativ zufriedenstellend vorhersagen, auch wenn man die Eigenrotation der “Korner” mit einbezieht and dementsprechend ein plastisches Cosserat-Kontinuum zugrunde legt.

Abstract: Es werden grose ebene, rotationssymmetrische, plastische Formanderungen eines Kontinuums studiert, das dem Coulombschen Flieskriterium und der assoziierten Fliesregel genugt. Damit last sich die Couette-Stromung eines aus parallelen Nadeln zusammengesetzten “granularen” Materials (Schneebeli) kinematisch qualitativ zufriedenstellend vorhersagen, auch wenn man die Eigenrotation der “Korner” mit einbezieht und dementsprechend ein plastisches Cosserat-Kontinuum zugrunde legt. Hingegen sind die auftretenden Momentenspannungen ebenso wie die asymmetrischen Schubspannungsanteile grosenmasig zu vernachlassigen — ein weiterer Hinweis darauf, das verallgemeinerte Kontinua mehr von der Kinematik als von der Statik her Bedeutung besitzen.

44 citations

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ENSCO, Inc.

^{1}TL;DR: In this article, the effect of axial compressive forces on the critical velocity of the track is studied assuming for the base an elastic half space with inertia, and the Winkler model is used.

Abstract: The recent introduction of the welded railroad track raises the possibility that high axial compressive forces may occur in the rails due to constrained thermal expansions. This in turn may reduce the critical velocity of the track to within the operational velocities of present day trains. Recently the effect of axial forces upon the critical velocities of the track was analyzed byA. D. Kerr using the Winkler model for the base response. In this study, the effect of the axial compressive force on the critical velocity of the track is studied assuming for the base an elastic half space with inertia.

37 citations

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TL;DR: In this article, axisymmetric stability and thermal-buckling equations are established for circular plates composed of polarorthotropic layers subjected to mechanical loads depending only onr and thermal fieldsT=T(r, z).

Abstract: Axisymmetric stability and thermal-buckling equations are established for circular plates composed of polarorthotropic layers subjected to mechanical loads depending only onr and thermal fieldsT=T(r, z). Alternative fourth order systems of two coupled differential equations are suggested in terms of the slope β andeither the radial displacementu or a stress function Ψ. The eigenvalue problem is formulated for quasi-heterogeneous composite plates and a closed-type solution is given for certain thermal-buckling problems in the form of Bessel functions of first kind and fractional order. Possibility of an analogy between a thermal and mechanical stability problem is shown and variation of eigenvalues with anisotropy parameters is noted. Numerous examples are presented indicating that suitable lamination of composite circular plates may transcend the buckling loads of individual constituents.

30 citations

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Yale University

^{1}TL;DR: In this paper, the deformation in the totally plastic region can be described in terms of a path independent loading function and incremental response functions according to which the component of the plastic strain increment vector is decomposed into two parts.

Abstract: Experimental data are obtained from thin-walled tubes of annealed polycrystalline aluminum subjected to combined tension-torsion loadings. These data reveal that the plastic deformation in the totally plastic region can be described in terms of a path independent loading function and incremental response functions according to which the component of the plastic strain increment vector is decomposed into two parts: one is due to the expansion of the loading surface and the other is due to the change of the corresponding component of the stress vector and vanishes when the directions of stress and strain vectors coincide.

22 citations

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TL;DR: In this article, a simple model of cyclic loading of a tube and circular plates is presented, which can be applied in treating boundary-value problems for beams, plates and shells.

Abstract: Simple theories of plasticity such as flow rules associated with a single yield surface are sufficiently accurate in predicting plastic behaviour for monotonic loading. However, for alternating or cyclic loads, such theories cannot describe complex plastic behaviour with sufficient accuracy. The concept of multiple loading surfaces or internal state parameters may then be introduced and respective plasticity theories become considerably complicated, requiring step by step integration of incremental relations for both strain and internal parameters. The present paper is aimed at elaborating relatively simple models of cyclic behaviour that could be expressed in terms of generalized stresses and strains and could be applied in treating boundary-value problems for beams, plates and shells. Finite stress-strain relations are derived in several subdomains of the stress space, both for loading, unloading and subsequent loading conditions. It is assumed that a set of discrete points from the past history affects the actual state. Some particular cases of cyclic loading of a tube and circular plates are considered in detail in order to illustrate applicability of proposed description.

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Ghent University

^{1}TL;DR: In this paper, a particular class of stochastic systems is considered, described by linear differential equations with multiplicative colored noise parameters; it is assumed that a certain commutativity condition is true.

Abstract: In this paper a particular class of stochastic systems is considered, described by linear differential equations with multiplicative colored noise parameters; it is assumed that a certain commutativity condition is true. For these systems explicit criteria are derived for the asymptotic stability of the moments of any order and also for almost sure asymptotic stability.

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TL;DR: In this paper, die Stabilitat der zweidimensionalen Stromung einer viskoelastischen Flussigkeit im Raum zwischen zwei ebenen festen Wanden, die einen Winkel miteiander bilden, untersucht.

Abstract: In dieser Arbeit wird die Stabilitat der zweidimensionalen Stromung einer viskoelastischen Flussigkeit im Raum zwischen zwei ebenen festen Wanden, die einen Winkel miteiander bilden, untersucht. Der Winkel zwischen den beiden Ebenen und der Durchflus pro Lange sind zwei charakteristische Parameter der Stromung. Es wird gezeigt, das bei gegebenem Winkel fur bestimmte Bereiche des Durchflusses stationare Storstromungen existieren.

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TL;DR: In this article, the authors use the general framework of multipolar continuum mechanics as developed by Green and Rivlin to predict the existence of second-sound waves which are attenuated in the manner obseved both in the stationary fluid and in the rotating fluid.

Abstract: Using the general framework of multipolar continuum mechanics as developed byGreen andRivlin [1], we discuss a possible alternative to the two-fluid theories of liquid helium II. We show in particular that our theory predicts the existence of second-sound waves which are attenuated in the manner obseved both in the stationary fluid and also in the rotating fluid. Moreover we suggest a possible continuum analogue of the concept of quantised vortex lines.

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TL;DR: In this paper, the authors derived reciprocal relationships for the basic physical problem of a rigid body which translates with constant velocity through a viscous incompressible fluid of infinite extent, and further allowances were made for rotational, magnetic and thermal effects, as well as a restricted type of time dependence.

Abstract: Reciprocal relationships are derived for the basic physical problem of a rigid body which translates with constant velocity through a viscous incompressible fluid of infinite extent. In addition to this basic situation, further allowances are made for rotational, magnetic, and thermal effects, as well as a restricted type of time dependence. The reciprocal relationships involve the net fluid force exerted on the moving body and the net heat flux through its surface. The most interesting result concerns invariance of the drag when the body motion is reversed, independent of any symmetry.

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TL;DR: In this article, it was shown that for thermal radiation conditions at the boundary, pure compressional and flexural modes of motion cannot exist in a traction-free plate, and that the modes become uncoupled only for the special cases of isothermal and adiabatic boundary conditions.

Abstract: It is shown within the framework of the linear theory of thermoelasticity that, for thermal radiation conditions at the boundary, pure compressional and flexural modes of motion cannot exist in a traction-free plate. Rigorously, the modes become uncoupled only for the special cases of isothermal and adiabatic boundary conditions: approximately, however, they are uncoupled even in the general case if the analysis is confined to the lowest-order terms in the small dimensionless frequency associated with such problems. Then the motions represent generalizations of the classical Rayleigh-Lamb waves. The effect of thermal conductivity is to reduce the phase velocity and introduce disipation, and is noticeable primarily for long waves.

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TL;DR: In this article, the effect of biaxial cyclic loading in the first and second quadrant of the principal stress plane on the shape of the yield surfaces of M-63 brass was investigated.

Abstract: Experimental results for thirtysix thin walled tubular specimens of M-63 brass are presented in a study of the effect of biaxial cyclic loading in the first and second quadrant of the principal stress plane on the shape of the yield surfaces. These results show that tested material strained cyclically beyond the initial yield locus works under a fully elastic regime after a few cycles of the initial transitory period.

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TL;DR: In this paper, a system of equations describing wave propagation in fluid-filled elastic tubes is examined with a view to achieving its reduction to a canonical form associated with the conventional wave equation.

Abstract: A system of equations descriptive of wave propagation in fluid-filled elastic tubes is examined with a view to achieving its reduction to a canonical form associated with the conventional wave equation. Two specific solutions are displayed and these are then used to consider a specific boundary value problem.

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Yale University

^{1}TL;DR: In this paper, a theoretical and experimental study of heat diffusion in a half-space, initially at constant temperature, when one-half of the bounding surface is suddently subjected to a different temperature while the other half remains insulated is presented.

Abstract: The paper presents a theoretical and experimental study of heat diffusion in a half-space, initially at constant temperature, when one-half of the bounding surface is suddently subjected to a different temperature while the other half remains insulated. An analytic solution is given in both series form and integral form. The isotherms as well as the far-field behavior are discussed in detail. The results are illustrated experimentally, using liquid crystals to visualize the isotherms.

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TL;DR: In this article, a review of the governing equations of classical thermoelasticity, several commonly used methods of solutions are discussed, and a survey is made of thermo-elastic boundary value problems which appear in the literature.

Abstract: Following a brief review of the governing equations of classical thermoelasticity, several commonly used methods of solutions are discussed, and a survey is made of thermoelastic boundary value problems which appear in the literature. References are also given to investigations concerned with the prediction of effective thermo-elastic coefficients for composites, and to studies of the average and local thermal stresses in reinforced structures. Finally, a few recently developed continuum theories which take into account the microstructure of composite materials are cited.

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TL;DR: In this paper, an analytical analysis of the large deflection behavior of clamped, elliptical, orthotropic plates under uniform lateral pressure is made, and a solution of the vonKarman-type large deflections equations for the problem under consideration is obtained by the method of perturbation.

Abstract: An analytical investigation of the large deflection behaviour of clamped, elliptical, orthotropic plates under uniform lateral pressure is made. A solution of the vonKarman-type large deflection equations for the problem under consideration is obtained by the method of perturbation. Stresses and deflections for three types of high modulus fibre-reinforced plates are graphically presented and discussed. In the case of isotropic plates, the present solution is in good agreement with the other available solutions.

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TL;DR: In this article, the Spitzenkatastrophe is described in a spezielle form, in which a Polynom bestimmt and erlaubt eine anschaulich geometrische interpretation.

Abstract: Mittels der Katastrophentheorie wird das Durchschlagen einfacher Strukturen anhand von funf Beispielen untersucht. Es zeigt sich, das unter bestimmten Voraussetzungen der Durchschlagsprozes durch eine einzige spezielle Form, namlich die Spitzenkatastrophe beschrieben wird. Diese ist durch ein Polynom bestimmt und erlaubt eine anschaulich geometrische Interpretation, wenn man sie durch eine Flache in einem von Parametern und Variablen aufgespannten Raum darstellt.

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TL;DR: In this article, the method of initial functions, in which the elasticity equations are solved by assuming Maclaurin series expansions for stresses and displacements, is extended to axisymmetric cylindrical shells.

Abstract: The method of initial functions, in which the elasticity equations are solved by assuming Maclaurin series expansions for stresses and displacements, is extended to axisymmetric cylindrical shells Numerical results have been obtained for the problem of a circular cylindrical shell subjected to periodically spaced band loads using theories of different orders and are compared with those of the elasticity solution given by Klosner and Levine

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TL;DR: In this article, the finite spherically symmetric dynamic expansion of a spherical cavity in an unbounded isotropic compressible hyperelastic solid is analyzed by the method of characteristics.

Abstract: The finite spherically symmetric dynamic expansion of a spherical cavity in an unbounded isotropic compressible hyperelastic solid is analysed by the method of characteristics. A spatially uniform step function application of pressure at the cavity wall is considered and a numerical procedure is given for the determination of the field of characteristics and the shock front path. Results are presented for a particular strain energy function.

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TL;DR: In this paper, the wave propagation in an inhomogeneous hyperbolic-viscoelastic bar of variable cross section, when the various parameters of the solid depend on one space coordinate only, is considered, and a transform technique is used to obtain conditions on these parameters which give solutions to the governing equation in terms of confluent hypergeometric functions.

Abstract: Wave propagation in an inhomogeneous hyperbolic-viscoelastic bar of variable cross section, when the various parameters of the solid depend on one space coordinate only, is considered. A transform technique, based on Eason's [1], is used to obtain conditions on these parameters which give solutions to the governing equation in terms of confluent hypergeometric functions and some particular problems are discussed. The formal Karal-Keller asymptotic technique is then introduced and shown to give results which are in agreement with those obtained by the transform technique.