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  • 1
    Electronic Resource
    Electronic Resource
    Gradient dependent dilatancy and its implications in shear banding and liquefaction (1989)
    Springer
    Archive of applied mechanics 59 (1989), S. 197-208 
    Details
    ISSN: 1432-0681
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Description / Table of Contents: Übersicht Lokale Inhomogenitäten bei der Verformung granularer Materialien sind hier mit Hilfe einer gradientenabhängigen Dilatanzbeziehung beschrieben. Diese Annahme ist in die Struktur einer klassischen Deformations- und Fließtheorie der Plastizität eingebaut, und die hiermit einhergehenden Konsequenzen werden anhand zweier interessanten Fälle der Musterbildung in Böden, nämlich Scherfugenbildung und Verflüssigung, studiert. Scherfugenbildung ist innerhalb einer modifizierten gradientenabhängigen Deformationstheorie untersucht, wogegen Bodenverflüssigung innerhalb einer modifizierten Fließtheorie analysiert wird. In beiden Fällen bekommt man in der Umgebung des Instabilitätszustandes einen deformationsinduzierten Längenmaßstab, der sich als Scherfugendicke oder als Abstand der verflüssigten Bodenstreifen manifestiert.
    Notes: Summary A gradient dependent dilatancy condition is assumed in order to capture the heterogeneous character of deformation in granular soils. This assumption is incorporated into the structure of classical deformation and flow theories of plasticity and its implications in two interesting examples of patterning instability, that is shear banding and liquefaction, are examined. Shear banding is considered within a modified gradient dependent deformation theory, while liquefaction is studied within a modified gradient dependent flow theory of plasticity. In both cases a deformation induced length scale is obtained near the instability, and this is identified with the thickness of the shear band or the spacing of the liquefying strips.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00532250
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  • 2
    Electronic Resource
    Electronic Resource
    Edge dislocations near phase boundaries in the gradient theory of elasticity (2000)
    Springer
    Physics of the solid state 42 (2000), S. 1659-1667 
    Details
    ISSN: 1063-7834
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A solution of the boundary-value problem in the gradient theory of elasticity concerning a rectilinear edge dislocation parallel to the interface between phases with different elastic moduli and gradient coefficients is obtained. The interaction between the dislocation and the interface is considered on a nanoscopic level. It is shown that the stress field has no singularities on the dislocation line and remains continuous at the interface, unlike the classical solution, which is singular at the dislocation line and allows a discontinuity of two stress components at the interface. The gradient solution also removes the classical singularity of the image force for the dislocation on the interface. An additional elastic image force associated with the difference in the gradient coefficients of contacting phases is also determined. It is found that this force, which has a short range and a maximum at the interface, expels the edge dislocation into the material with a smaller gradient coefficient.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1134/1.1309447
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  • 3
    Electronic Resource
    Electronic Resource
    Dislocations and disclinations in the gradient theory of elasticity (1999)
    Springer
    Physics of the solid state 41 (1999), S. 1980-1988 
    Details
    ISSN: 1063-7834
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The results of application of gradient theory of elasticity to a description of elastic fields and dislocation and disclination energies are considered. The main achievement made in this approach is the removal of the classical singularities at defect lines and the possibility of describing short-range interactions between them on a nanoscopic level. Non-singular solutions for stress and strain fields of straight disclination dipoles in an infinite isotropic medium have been obtained within a version of the gradient theory of elasticity. A description is given of elastic fields near disclination lines and of specific features in the short-range interactions between disclinations, whose study is impossible to make in terms of the classical linear theory of elasticity. The strains and stresses at disclination lines are shown to depend strongly on the dipole arm d. For short-range interaction between disclinations, where d varies from zero to a few atomic spacings, these quantities vary monotonically for wedge disclinations and nonmonotonically in the case of twist disclinations, and tend uniformly to zero as disclinations annihilate. At distances from disclination lines above a few atomic spacings, the gradient and classical solutions coincide. As in the classical theory of elasticity, the gradient solution for the wedge-disclination dipole transforms to the well-known gradient solution for a wedge dislocation at distances d substantially smaller than the interatomic spacing.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1134/1.1131139
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  • 4
    Electronic Resource
    Electronic Resource
    Behavior of screw dislocations near phase boundaries in the gradient theory of elasticity (2000)
    Springer
    Physics of the solid state 42 (2000), S. 1652-1658 
    Details
    ISSN: 1063-7834
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The solution of the boundary-value problem on a rectilinear screw dislocation parallel to the interface between phases with different elastic moduli and gradient coefficients is obtained in one of the versions of the gradient theory of elasticity. The stress field of the dislocation and the force of its interaction with the interface (image force) are presented in integral form. Peculiarities of the short-range interaction between the dislocation and the interface are described, which is impossible in the classical linear theory of elasticity. It is shown that neither component of the stress field has singularities on the dislocation line and remains continuous at the interface in contrast to the classical solution, which has a singularity on the dislocation line and permits a discontinuity of one of the stress components at the interface. This results in the removal of the classical singularity of the image force for the dislocation at the interface. An additional elastic image force associated with the difference in the gradient coefficients of contacting phases is also determined. It is found that this force, which has a short range and a maximum value at the interface, expels a screw dislocation into the material with a larger gradient coefficient. At the same time, new gradient solutions for the stress field and the image force coincide with the classical solutions at distances from the dislocation line and the interface, which exceed several atomic spacings.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1134/1.1309446
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  • 5
    Electronic Resource
    Electronic Resource
    On finite deformation plasticity with directional softening (1993)
    Springer
    Acta mechanica 101 (1993), S. 69-80 
    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
    Notes: Summary It is well-known that twisting of cylindrical specimens has shown that axial stress or strain are induced in constrained or unconstrained torsion respectively. During monotonic loading in torsion, the axial stress or axial strain do not change monotonically, but tensile/compressive or lengthening/shortening phenomena are observed. In this study, a two-component model to account phenomenologically for coexisting different textures of rate-independent and rate-dependent finite deformation plasticity is proposed to predict axial shortening/lengthening and tensile/compressive phenomena in torsion. Such predictions are compared with available experimental data as well as recent simulations based on crystal plasticity models. In most cases, the results are in reasonable agreement with both experiments and simulations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01175598
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  • 6
    Electronic Resource
    Electronic Resource
    On a proposal for a continuum with microstructure (1982)
    Springer
    Acta mechanica 45 (1982), S. 91-121 
    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
    Notes: Summary A recently proposed model for a continuum with microstructure is further substantiated by identifying the microstructure with dislocations. In particular, the continuum is viewed as a superimposed state composed of a perfect lattice state, an immobile dislocation state, and a mobile dislocation state. It is assumed that each state evolves continuously in space-time and transitions from one state to another take place spontaneously according to the balance laws of effective mass and momentum. When the constitutive equations are subjected to the requirements of invariance, familiar statements from dislocation dynamics are deduced. When plastic strain and yield are identified in terms of the parameters characterizing the dislocation states, familiar flow rules and yield surfaces are produced. The capability of the model to predict not only Tresca and Von-Mises plastic behavior but also phenomena such as kinematic hardening, different responses in tension and compression, latent hardening, and the Bauschinger effect, is shown. Finally, the appropriateness of our equations to model creep, cyclic plasticity, and fatigue, is illustrated.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01295573
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  • 7
    Electronic Resource
    Electronic Resource
    Diffusion of a gas in a linear elastic solid (1978)
    Springer
    Acta mechanica 29 (1978), S. 169-184 
    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 Einige neue partielle Differentialgleichungen werden, für die Beschreibung der Diffusion einer verdünnten Lösung in einen linear elastischen Festkörper, unter einer statischen Deformation, entwickelt. Die Analysis basiert ausschließlich auf der Anwendung der Erhaltungssätze für Masse und Impuls, sowie auf der Einführung einer inneren Diffusionskraft zur Bewertung der Diffusionseffekte. Das interessante Ergebnis ist, daß stationäre Zustände unempfindlich gegen mögliches viskoses Verhalten der Diffusionsarten sind. Zusätzlich werden frühere Theorien wieder erhalten und verallgemeinert. Schließlich wird noch die wichtige experimentelle Beobachtung, die zu einer linearen Abhängigkeit des Diffusionskoeffizienten vom hydrostatischen Druck führt, theoretisch nachgewiesen.
    Notes: Summary Some new partial differntial equations are developed to describe the diffusion of a dilute solute in a linear elastic solid supporting a static deformation. The analysis is based exclusively on the use of the conservation laws of mass and momentum, as well as, on the introduction of an internal diffusive force to evaluate the diffusion effects. The interesting result is that steady states are insensitive to possible viscous behavior of the diffusing species. In addition, previous theories dealing with such problems are recovered and generalized. Finally, the important experimental observation that implies a linear dependence of the diffusion coefficient on the hydrostatic pressure is theoretically established.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01176635
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  • 8
    Electronic Resource
    Electronic Resource
    A model for finite-deformation plasticity (1987)
    Springer
    Acta mechanica 69 (1987), S. 97-117 
    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
    Notes: Summary We propose a new large deformation viscoplastic model which includes the effects of static and dynamic recovery in its strain rate response as well as the plastic spin in its rotational response. The model is directly obtained from single slip dislocation considerations with the aid of a maximization procedure and a scale invariance argument. It turns out that the evolution of the back stress and the expression for the plastic spin are coupled within the structure of the theory. The model is used for the prediction of nonstandard effects in torsion, namely the development of axial stress and strain as well as the directional softening of the shear stress. The comparisons between the present continuum model and both experiments and self-consistent polycrystalline calculations are very encouraging.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01175716
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  • 9
    Electronic Resource
    Electronic Resource
    The influence of microstructure-induced gradients on the localization of deformation in viscoplastic materials (1991)
    Springer
    Acta mechanica 89 (1991), S. 217-231 
    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
    Notes: Summary We suggest here a generalization of the conventional constitutive models of viscoplasticity. This is accomplished by the inclusion of spatial gradients of the equivalent stress and strain in the evolution equation for the equivalent plastic strain rate. We restrict attention to plane deformation and elastic effects are neglected for simplicity. The implications of the new terms in the constitutive model are discussed for the case of a general eigenvalue problem of an initially homogeneous and stationary viscous flow. It turns out that the nonclassical material parameters can be chosen in such a way that the governing differential equations are always strongly elliptic irrespective of whether the mateiral is strain softening. As it is well known, the latter typically leads to loss of ellipticity in the conventional theories. Explicit results are presented for the case of a shear band instability. Within the framework of the present theory, and in contrast to conventional models, the shear band kinematics have a well defined geometrical structure.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01171257
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  • 10
    Electronic Resource
    Electronic Resource
    On the gradient-dependent theory of plasticity and shear banding (1992)
    Springer
    Acta mechanica 92 (1992), S. 209-225 
    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
    Notes: Summary After a brief review of a recently developed gradient-dependent theory of plasticity various questions related to the yield function and the loading-unloading condition in the presence of higher order strain gradients and the determination of the corresponding phenomenological coefficients are addressed. For rate-independent materials, we construct as before an analytical solution for the strain profile in the postlocalization regime providing the shear band thickness and strain within it but we now compare these results to recently obtained experimental data by assigning appropriate values to the gradient coefficients. We also address some questions recently raised in the literature regarding our nonlinear shear band analysis. For rate-dependent materials, the resulting spatio-temporal differential equation for the strain is solved numerically using the finite difference method. It is shown that the band width does not depend on the grid size, as long as the the grid size is smaller than a certain characteristic length. Various initial imperfections of different amplitudes and sizes are examined, and the possibility of simultaneous development of two shear bands and their interaction is investigated.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01174177
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