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  • 1
    Electronic Resource
    Electronic Resource
    Steady flow past a sluice gate (1986)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 29 (1986), S. 3962-3970 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The problem of steady two-dimensional flow, under the action of gravity, of an incompressible inviscid fluid sheet past a sluice gate is reexamined with particular reference to the theoretical prediction of the contraction ratio, i.e., the ratio of the far downstream height to the sluice opening. The problem is formulated here by a direct approach with the use of the theory of a directed fluid sheet, which includes appropriate jump conditions arising in a natural way within the scope of the basic theory. The determination of the contraction ratio is effected by a novel procedure in the utilization of the jump conditions at the gate. Detailed numerical calculations are made for two different sluice openings and these provide very good agreement with the experimental results of Benjamin [J. Fluid Mech. 1, 227 (1956)].
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.865736
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  • 2
    Electronic Resource
    Electronic Resource
    The flow of fluid through an elastic solid (1970)
    Springer
    Acta mechanica 9 (1970), S. 329-340 
    Details
    ISSN: 1619-6937
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Description / Table of Contents: Zusammenfassung Etliche Autoren haben Materialgleichungen in ähnlichen Untersuchungen über die Wechselwirkung von Kontinuen auf der Grundlage der Theorie vonGreen undNaghdi [1] diskutiert und angewendet. Es wird gezeigt, daß die Ergebnisse für viele Zwecke zufriedenstellend sind, auch wenn die Ausdrücke für die Partialspannungen unvollständig sind. In dieser Arbeit werden vollständige Materialgleichungen angegeben. Ein Eindeutigkeitssatz für die langsame Strömung einer linear viskosen Flüssigkeit durch einen anisotropen linear elastischen Festkörper wird aufgestellt.
    Notes: Summary The discussions of constitutive equations and their use in related studies by a number of writers for interacting continua, which is based on the form of theory given byGreen andNaghdi [1], is shown to be satisfactory for many purposes even though the expressions given for the partial stresses are incomplete. Complete constitutive equations are given in this paper, and a uniqueness theorem is stated, for the slow flow of a linear viscous fluid through an anisotropic linear elastic solid.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01179830
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  • 3
    Electronic Resource
    Electronic Resource
    Some general results in the theory of crystallographic slip (1994)
    Springer
    Zeitschrift für angewandte Mathematik und Physik 45 (1994), S. 687-732 
    Details
    ISSN: 1420-9039
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract Crystallographic slip of a Bravais lattice is analyzed utilizing the main results of a recently constructed theory of structured solids, where explicit account is taken of the influence of dislocation density identified in terms of Curl of plastic deformationG p . In the present paper, the scope of the subject is enlarged to also include defects (other than dislocations) such as substitutional impurities and vacancies and it is shown that these point defects may also be characterized in terms of the plastic deformation fieldG p . Several general results pertaining to the kinematics and kinetics of Crystallographic slip are proved within the scope of an appropriate constraint theory suitable for Crystallographic slip; the latter is motivated by the well-known basic mechanism of Crystallographic slip that constrains the admissible modes of plastic deformation. The constraint responses (or forces) that are necessary to maintain the active slip systems, as well as the conditions for the transitions between the slip systems, are determined. In spite of the nature of the assumption pertaining to the mechanism of Crystallographic slip on distinct slip systems, it is shown that the yield surface does not necessarily exhibit sharp corners. Instead, the shape of the yield surface is in the form of hyperplanes joined by round corners. In fact, the presence of sharp corners is mainly a result of the use of a special set of constitutive assumptions. The predictive capability of the theoretical results is further illustrated by using a two-dimensional crystal subjected to simple shear. The effect of the initial dislocation density on the response of the sheared-crystal is studied by carrying out detailed calculations for two substantially different initial dislocation densities. The calculations show that while the response of the crystal is sensitive to the initial dislocation density in the early stages of deformation, its influence diminishes with progressively larger deformations. Furthermore, the crystal exhibits a well-defined shear band which evolves naturally due to the presence of initial dislocation distribution and is easily visible at large deformations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00942749
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  • 4
    Electronic Resource
    Electronic Resource
    Consequences of the second law for a turbulent fluid flow (1991)
    Springer
    Continuum mechanics and thermodynamics 3 (1991), S. 65-77 
    Details
    ISSN: 1432-0959
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Second Law statements in thermomechanics applicable to turbulent fluid flow, in which the internal energy in a macroscopic field theory includes contributions both from molecular vibrations and from turbulent fluctuations, are discussed. In the absence of turbulence, these statements naturally reduce to the known and accepted Second Law statements for a nonturbulent medium. The usual version of the Second Law statements — which deny the existence of perpetual motion and place restrictions on the constitutive equations —is extended here in the presence of turbulence; and an additional statement is introduced associated with the tendency of turbulent fluctuations to decay in the absence of external work or the addition of thermal heat. The mathematical representations of various Second Law statements are then used to derive several restrictions on the response variables of the macroscopic turbulence theory. Examples of such variables include the rates of production and dissipation of turbulent fluctuations, the rate of thermal entropy production, internal energy (involving constitutive coefficients which may be taken to be the thermal and turbulent specific heats), turbulent viscosity coefficients and other response functions which control the degree of flow “anisotropy” in the medium. These Second Law restrictions are then applied to a recent theory of macroscopic turbulent flow by the present authors in which fairly general constitutive equations are presented for the dependent variables of the theory. It is found that not only is the range of values of several constitutive coefficients limited by these Second Law restrictions, but the presence of a number of terms in the constitutive equations is entirely denied.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01128966
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  • 5
    Electronic Resource
    Electronic Resource
    A demonstration of consistency of an entropy balance with balance of energy (1991)
    Springer
    Zeitschrift für angewandte Mathematik und Physik 42 (1991), S. 159-168 
    Details
    ISSN: 1420-9039
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract It is shown in this note that a general balance of entropy postulated previously with only a limited motivation (based on the form of the energy equation for an inviscid fluid) is consistent with, and can be derived from, a general balance of energy. In this derivation, an early form of entropy balance does not make use of invariance conditions under superposed rigid body motions. However, with the help of the latter invariance conditions, additional results are also derived which provide some insight on the structure of the basic equations in thermomechanics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00945790
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  • 6
    Electronic Resource
    Electronic Resource
    A critical review of the state of finite plasticity (1990)
    Springer
    Zeitschrift für angewandte Mathematik und Physik 41 (1990), S. 315-394 
    Details
    ISSN: 1420-9039
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract The object of this paper is to provide a critical review of the current state of plasticity in the presence of finite deformation. In view of the controversy regarding a number of fundamental issues between several existing schools of plasticity, the areas of agreement are described separately from those of disagreement. Attention is mainly focussed on the purely mechanical, rate-independent, theory of elastic-plastic materials, although closely related topics such as rate-dependent behavior, thermal effects, experimental and computational aspects, microstructural effects and crystal plasticity are also discussed and potentially fruitful directions are identified. A substantial portion of this review is devoted to the area of disagreement that covers a detailed presentation of argument(s), bothpro andcon, for all of the basic constitutive ingredients of the rate-independent theory such as the primitive notion or definition of plastic strain, the structure of the constitutive equation for the stress response, the yield function, the loading criteria and the flow and the hardening rules. The majority of current research in finite plasticity theory, as with its infinitesimal counterpart, still utilizes a (classical) stress-based approach which inherently possesses some shortcomings for the characterization of elastic-plastic materials. These and other anomalous behavior of a stress-based formulation are contrasted with the more recent strain-based formulation of finite plasticity. A number of important features and theoretical advantages of the latter formulation, along with its computational potential and experimental interpretation, are discussed separately.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00959986
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  • 7
    Electronic Resource
    Electronic Resource
    Wave reflection and transmission by steps and rectangular obstacles in channels of finite depth (1990)
    Springer
    Theoretical and computational fluid dynamics 1 (1990), S. 287-301 
    Details
    ISSN: 1432-2250
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract Relatively simple analytical solutions are obtained for the reflection and transmission of surface waves by steps and by surface obstacles of rectangular cross-section in channels of finite depth. The analysis employs the linearized version of a recent approximate nonlinear theory of wave propagation in waters of finite depth (Green and Naghdi, 1986, 1987), which incorporates the possibility of one or more discontinuities (say, in waveheight). Whenever possible, the predictions of the theory are compared extensively with previous experimental, analytical, and numerical results. In addition, the results of a new experimental investigation (conducted at Berkeley) of wave reflection from rectangular surface obstacles of various widths and depths are reported and are compared with the theoretical predictions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00271583
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  • 8
    Electronic Resource
    Electronic Resource
    On thermal effects in a special class of viscoelastic fluids (1973)
    Springer
    Rheologica acta 12 (1973), S. 321-329 
    Details
    ISSN: 1435-1528
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Summary A brief account of a non-isothermal theory of a restricted class of viscoelastic fluids with fading memory followed by its application to some special viscometric flows.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01635123
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  • 9
    Electronic Resource
    Electronic Resource
    On the Lagrangian description of vorticity (1991)
    Springer
    Archive for rational mechanics and analysis 115 (1991), S. 1-14 
    Details
    ISSN: 1432-0673
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract This paper exploits a Lagrangian form of the vorticity field that is based on a formula of Beltrami, the merits of which do not seem to have been fully appreciated. A number of new results are readily derived by using the Lagrangian description, and the classical vorticity theorems are also included. The results, being purely kinematical, apply to all deformable media (including viscous fluids) and may also be of value in computations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01881677
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  • 10
    Electronic Resource
    Electronic Resource
    On the relationship between the Eulerian and Lagrangian descriptions of finite rigid plasticity (1988)
    Springer
    Archive for rational mechanics and analysis 102 (1988), S. 351-375 
    Details
    ISSN: 1432-0673
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract The motivation for the present paper is to clarify certain unresolved issues pertaining to the relation between the Lagrangian (or referential) and Eulerian (or spatial) strain-space formulations of finite plasticity. For conceptual simplicity, attention is confined to rigid-plastic materials. It is shown first that for constitutive equations in which the hardening parameter is a scalar, the Lagrangian and Eulerian descriptions are equivalent; and that, additionally, the choice of objective stress rate is immaterial. In the light of these developments, the role of objective rates is further explored in connection with more general (“anisotropic”) hardening laws which contain a shift tensor. A form of the constitutive equation for the rate of the shift tensor is motivated in which the choice of objective rate is arbitrary. It is then demonstrated that the structure of the constitutive equations of the theory — in both the Eulerian and Lagrangian descriptions — is form-invariant under arbitrary transformations of objective rate. The approach taken here contrasts with that adopted in a number of recent papers in which preference is given to one particular objective rate or another.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00251535
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