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John W. Hutchinson - One of the best experts on this subject based on the ideXlab platform.

  • 2012, “Generalizing J2 Flow Theory: Fundamental issues in strain gradient plasticity
    2016
    Co-Authors: John W. Hutchinson
    Abstract:

    Abstract It has not been a simple matter to obtain a sound extension of the classical J2 Flow Theory of plasticity that in-corporates a dependence on plastic strain gradients and that is capable of capturing size-dependent behaviour of metals at the micron scale. Two classes of basic extensions of clas-sical J2 Theory have been proposed: one with increments in higher order stresses related to increments of strain gradi-ents and the other characterized by the higher order stresses themselves expressed in terms of increments of strain gra-dients. The theories proposed by Muhlhaus and Aifantis in 1991 and Fleck and Hutchinson in 2001 are in the first class, and, as formulated, these do not always satisfy ther-modynamic requirements on plastic dissipation. On the other hand, theories of the second class proposed by Gudmundson in 2004 and Gurtin and Anand in 2009 have the physical deficiency that the higher order stress quantities can change discontinuously for bodies subject to arbitrarily small load changes. The present paper lays out this background to the quest for a sound phenomenological extension of the rate-independent J2 Flow Theory of plasticity to include a de-pendence on gradients of plastic strain. A modification of the Fleck–Hutchinson formulation that ensures its thermo-dynamic integrity is presented and contrasted with a compa-rable formulation of the second class where in the higher or-der stresses are expressed in terms of the plastic strain rate. Both versions are constructed to reduce to the classical J2 Flow Theory of plasticity when the gradients can be neglected and to coincide with the simpler and more readily formulated J2 deformation Theory of gradient plasticity for deformation histories characterized by proportional straining

  • Generalizing J2 Flow Theory: Fundamental issues in strain gradient plasticity
    Acta Mechanica Sinica, 2012
    Co-Authors: John W. Hutchinson
    Abstract:

    It has not been a simple matter to obtain a sound extension of the classical J2 Flow Theory of plasticity that in- corporates a dependence on plastic strain gradients and that is capable of capturing size-dependent behaviour of metals at the micron scale. Two classes of basic extensions of clas- sical J2 Theory have been proposed: one with increments in higher order stresses related to increments of strain gradi- ents and the other characterized by the higher order stresses themselves expressed in terms of increments of strain gra- dients. The theories proposed by Muhlhaus and Aifantis in 1991 and Fleck and Hutchinson in 2001 are in the first class, and, as formulated, these do not always satisfy ther- modynamic requirements on plastic dissipation. On the other hand, theories of the second class proposed by Gudmundson in 2004 and Gurtin and Anand in 2009 have the physical deficiency that the higher order stress quantities can change discontinuously for bodies subject to arbitrarily small load changes. The present paper lays out this background to the quest for a sound phenomenological extension of the rate- independent J2 Flow Theory of plasticity to include a de- pendence on gradients of plastic strain. A modification of the Fleck-Hutchinson formulation that ensures its thermo- dynamic integrity is presented and contrasted with a compa- rable formulation of the second class where in the higher or- der stresses are expressed in terms of the plastic strain rate. Both versions are constructed to reduce to the classical J2 Flow Theory of plasticity when the gradients can be neglected and to coincide with the simpler and more readily formulated J2 deformation Theory of gradient plasticity for deformation histories characterized by proportional straining.

  • Generalizing J _2 Flow Theory: Fundamental issues in strain gradient plasticity
    Acta Mechanica Sinica, 2012
    Co-Authors: John W. Hutchinson
    Abstract:

    It has not been a simple matter to obtain a sound extension of the classical J _2 Flow Theory of plasticity that incorporates a dependence on plastic strain gradients and that is capable of capturing size-dependent behaviour of metals at the micron scale. Two classes of basic extensions of classical J _2 Theory have been proposed: one with increments in higher order stresses related to increments of strain gradients and the other characterized by the higher order stresses themselves expressed in terms of increments of strain gradients. The theories proposed by Muhlhaus and Aifantis in 1991 and Fleck and Hutchinson in 2001 are in the first class, and, as formulated, these do not always satisfy thermodynamic requirements on plastic dissipation. On the other hand, theories of the second class proposed by Gudmundson in 2004 and Gurtin and Anand in 2009 have the physical deficiency that the higher order stress quantities can change discontinuously for bodies subject to arbitrarily small load changes. The present paper lays out this background to the quest for a sound phenomenological extension of the rateindependent J _2 Flow Theory of plasticity to include a dependence on gradients of plastic strain. A modification of the Fleck-Hutchinson formulation that ensures its thermodynamic integrity is presented and contrasted with a comparable formulation of the second class where in the higher order stresses are expressed in terms of the plastic strain rate. Both versions are constructed to reduce to the classical J _2 Flow Theory of plasticity when the gradients can be neglected and to coincide with the simpler and more readily formulated J _2 deformation Theory of gradient plasticity for deformation histories characterized by proportional straining.

  • a phenomenological Theory for strain gradient effects in plasticity
    Journal of The Mechanics and Physics of Solids, 1993
    Co-Authors: N A Fleck, John W. Hutchinson
    Abstract:

    Abstract A Strain Gradient Theory of plasticity is introduced, based on the notion of statistically stored and geometrically necessary dislocations. The strain gradient Theory fits within the general framework of couple stress Theory and involves a single material length scale l. Minimum principles are developed for both deformation and Flow Theory versions of the Theory which in the limit of vanishing l, reduce to their conventional counterparts: J2 deformation and J2 Flow Theory. The strain gradient Theory is used to calculate the size effect associated with macroscopic strengthening due to a dilute concentration of bonded rigid particles; similarly, predictions are given for the effect of void size upon the macroscopibic softening due to a dilute concentration of voids. Constitutive potentials are derived for this purpose.

Michael Hoyler - One of the best experts on this subject based on the ideXlab platform.

  • external urban relational process introducing central Flow Theory to complement central place Theory
    Urban Studies, 2010
    Co-Authors: Peter J Taylor, Michael Hoyler
    Abstract:

    Central place hierarchies have been the traditional basis for understanding external urban relations. However, in contemporary studies of these relations, a new emphasis on urban networks has emerged. Rather than either abandoning or extending central place thinking, it is here treated as representing one of two generic processes of external urban relations. Town-ness is the making of ‘local’ urban—hinterland relations and ‘city-ness’ is the making of ‘non-local’ interurban relations. Central place Theory describes the former through an interlocking hierarchical model; this paper proposes a central Flow Theory to describe the latter through an interlocking network model. The key difference is the level of complexity in the two processes.

V Novak - One of the best experts on this subject based on the ideXlab platform.

  • preferential transport of water and 131 iodide in a clay loam assessed with tdr techniques and boundary layer Flow Theory
    Hydrology and Earth System Sciences, 1997
    Co-Authors: Mdaghri A Alaoui, Peter F Germann, Lubomir Lichner, V Novak
    Abstract:

    Abstract. Rapid soil moisture variations were measured with TDR equipment at five depths ranging from 0.1 to 0.9 m during five consecutive infiltration experiments under ponding. Each time, 27 mm of water were applied. The water of the second experiment was spiked with 200 mbq of K 131 I-tracer. Its activity was recorded as functions of depth and time with Geiger-Muller probes in 12 vertically installed access tubes. The soil moisture variations were classified as showing (i) no reaction, (ii) monotonous increase, and (iii) rapid increase followed by a gradual decrease. Reaction type (iii) was investigated further according to the boundary-layer Flow Theory and diagnosed as preferential Flow. Rapid variations of 131 I-activities occurred at all depths showing soil moisture reaction type (iii). However, some of the reaction types (i) and (ii) also included rapid variations of the activities. The approach based on boundary-laver Flow Theory allows fluxes to be estimated from soil moisture variations. Seven estimated total volumes of rapid Flow ranged from 0.15 to 1.1 of the applied volume of water, and in only one case was the total volume badly overestimated by a factor of almost 3. The approach is worth further exploration.

Alexander Düster - One of the best experts on this subject based on the ideXlab platform.

  • the finite cell method for the j2 Flow Theory of plasticity
    Finite Elements in Analysis and Design, 2013
    Co-Authors: A Abedian, Alexander Düster, J Parvizian, E Rank
    Abstract:

    The finite cell method (FCM) is an extension of a high-order finite element approximation space with the aim of simple meshing. In this paper, the FCM is implemented for J"2 Flow Theory with nonlinear isotropic hardening for small displacements and small strains. The Newton-Raphson iteration scheme, combined with a radial return algorithm, is applied to find approximate solutions for the underlying physically nonlinear problem. A modified quadtree integration scheme is presented for the first time to capture the geometry accurately and overcome the high calculation cost of the standard quadtree integration scheme. Numerical examples in two and three dimensions demonstrate the efficiency of the FCM and the proposed integration scheme at solving materially nonlinear problems.

  • a p version finite element approach for two and three dimensional problems of the j2 Flow Theory with non linear isotropic hardening
    International Journal for Numerical Methods in Engineering, 2002
    Co-Authors: Alexander Düster
    Abstract:

    In this paper an implementation of a two- and three-dimensional p-version approach to the J 2 Flow Theory with non-linear isotropic hardening for small displacements and small strains is presented. Based on higher-order quadrilateral and hexahedral element formulations, a Newton-Raphson iteration scheme combined with a radial return algorithm is applied to find approximate solutions for the underlying physically non-linear model problem. Curved boundaries are taken care of with the blending function method, allowing an accurate representation of geometry with only a few p-elements. Numerical examples demonstrate, that the p-version supplies efficient and accurate approximations to this class of physically non-linear problems.

Shigeru Takata - One of the best experts on this subject based on the ideXlab platform.