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Vikram Deshpande - One of the best experts on this subject based on the ideXlab platform.

  • climb enabled discrete dislocation plasticity of superalloys
    Key Engineering Materials, 2015
    Co-Authors: C Ayas, Vikram Deshpande
    Abstract:

    Ni-based superalloys comprising of elastic particles embedded in a single crystal elastic-plastic matrix are usually subject to loading at elevated service temperatures. In order to enhance the understanding of high temperature deformation mechanisms a two dimensional discrete dislocation plasticity framework wherein the dislocations movement that incorporates both glide and climb is formulated. The climbing dislocations are modelled as point sources/sinks of vacancies and the vacancy diffusion boundary value problem is solved by superposition of the vacancy concentration fields of the point sources/sinks in an infinite medium and a complementary non-Singular Solution that enforces the relevant boundary conditions. The vacancy concentration field along with the Peach-Kohler force provides the climb rate of the dislocations.

  • climb enabled discrete dislocation plasticity
    Journal of The Mechanics and Physics of Solids, 2014
    Co-Authors: C Ayas, Vikram Deshpande, Van Jaw Hans Dommelen
    Abstract:

    A small strain two-dimensional discrete dislocation plasticity framework coupled to vacancy diffusion is developed wherein the motion of edge dislocations is by a combination of glide and climb. The dislocations are modelled as line defects in a linear elastic medium and the mechanical boundary value problem is solved by the superposition of the infinite medium elastic fields of the dislocations and a complimentary non-Singular Solution that enforces the boundary conditions. Similarly, the climbing dislocations are modelled as line sources/sinks of vacancies and the vacancy diffusion boundary value problem is also solved by a superposition of the fields of the line sources/sinks in an infinite medium and a complementary non-Singular Solution that enforces the boundary conditions. The vacancy concentration field along with the stress field provides the climb rate of the dislocations. Other short-range interactions of the dislocations are incorporated via a set of constitutive rules. We first employ this formulation to investigate the climb of a single edge dislocation in an infinite medium and illustrate the existence of diffusion-limited and sink-limited climb regimes. Next, results are presented for the pure bending and uniaxial tension of single crystals oriented for single slip. These calculations show that plasticity size effects are reduced when dislocation climb is permitted. Finally, we contrast predictions of this coupled framework with an ad hoc model in which dislocation climb is modelled by a drag-type relation based on a quasi steady-state Solution.

Hou, Thomas Y. - One of the best experts on this subject based on the ideXlab platform.

  • Finite Time Blowup of 2D Boussinesq and 3D Euler Equations with C^(1,α) Velocity and Boundary
    'Springer Science and Business Media LLC', 2021
    Co-Authors: Chen Jiajie, Hou, Thomas Y.
    Abstract:

    Inspired by the numerical evidence of a potential 3D Euler Singularity by Luo-Hou [30, 31] and the recent breakthrough by Elgindi [11] on the Singularity formation of the 3D Euler equation without swirl with C^(1,α) initial data for the velocity, we prove the finite time Singularity for the 2D Boussinesq and the 3D axisymmetric Euler equations in the presence of boundary with C^(1,α) initial data for the velocity (and density in the case of Boussinesq equations). Our finite time blowup Solution for the 3D Euler equations and the Singular Solution considered in [30, 31] share many essential features, including the symmetry properties of the Solution, the flow structure, and the sign of the Solution in each quadrant, except that we use C^(1,α) initial data for the velocity field. We use a dynamic rescaling formulation and follow the general framework of analysis developed by Elgindi in [11]. We also use some strategy proposed in our recent joint work with Huang in [7] and adopt several methods of analysis in [11] to establish the linear and nonlinear stability of an approximate self-similar profile. The nonlinear stability enables us to prove that the Solution of the 3D Euler equations or the 2D Boussinesq equations with C^(1,α) initial data will develop a finite time Singularity. Moreover, the velocity field has finite energy before the Singularity time

  • Finite time blowup of 2D Boussinesq and 3D Euler equations with $C^{1,\alpha}$ velocity and boundary
    2021
    Co-Authors: Chen Jiajie, Hou, Thomas Y.
    Abstract:

    Inspired by the numerical evidence of a potential 3D Euler Singularity by Luo-Hou \cite{luo2013potentially-1,luo2013potentially-2} and the recent breakthrough by Elgindi \cite{elgindi2019finite} on the Singularity formation of the 3D Euler equation without swirl with $C^{1,\alpha}$ initial data for the velocity, we prove the finite time Singularity for the 2D Boussinesq and the 3D axisymmetric Euler equations in the presence of boundary with $C^{1,\alpha}$ initial data for the velocity (and density in the case of Boussinesq equations). Our finite time blowup Solution for the 3D Euler equations and the Singular Solution considered in \cite{luo2013potentially-1,luo2013potentially-2} share many essential features, including the symmetry properties of the Solution, the flow structure, and the sign of the Solution in each quadrant, except that we use $C^{1,\alpha}$ initial data for the velocity field. We use a dynamic rescaling formulation and follow the general framework of analysis developed by Elgindi in \cite{elgindi2019finite}. We also use some strategy proposed in our recent joint work with Huang in \cite{chen2019finite} and adopt several methods of analysis in \cite{elgindi2019finite} to establish the linear and nonlinear stability of an approximate self-similar profile. The nonlinear stability enables us to prove that the Solution of the 3D Euler equations or the 2D Boussinesq equations with $C^{1,\alpha}$ initial data will develop a finite time Singularity. Moreover, the velocity field has finite energy before the Singularity time.Comment: Revised introduction. Added motivations and discussions in Sections 5, 9. 82 Page

  • Finite time blowup of 2D Boussinesq and 3D Euler equations with $C^{1,\alpha}$ velocity and boundary
    2019
    Co-Authors: Chen Jiajie, Hou, Thomas Y.
    Abstract:

    Inspired by the recent numerical evidence of a potential 3D Euler Singularity \cite{luo2013potentially-1,luo2013potentially-2}, we prove the finite time Singularity for the 2D Boussinesq and the 3D axisymmetric Euler equations in the presence of boundary with $C^{1,\alpha}$ initial data for the velocity (and density in the case of Boussinesq equations). Our finite time blowup Solution for the 3D Euler equations and the Singular Solution considered in \cite{luo2013potentially-1,luo2013potentially-2} share many essential features, including the symmetry properties of the Solution, the flow structure, and the sign of the Solution in each quadrant, except that we use $C^{1,\alpha}$ initial data for the velocity field. We use the method of analysis proposed in our recent joint work with Huang in \cite{chen2019finite} and the simplification of the Biot-Savart law derived by Elgindi in \cite{elgindi2019finite} for $C^{1,\alpha}$ velocity to establish the nonlinear stability of an approximate self-similar profile. The nonlinear stability enables us to prove that the Solution of the 3D Euler equations or the 2D Boussinesq equations with $C^{1,\alpha}$ initial data will develop a finite time Singularity. Moreover, the velocity field has finite energy before the Singularity time

  • Finite time blowup of 2D Boussinesq and 3D Euler equations with C^(1,α) velocity and boundary
    2019
    Co-Authors: Chen Jiajie, Hou, Thomas Y.
    Abstract:

    Inspired by the recent numerical evidence of a potential 3D Euler Singularity [28, 29], we prove the finite time Singularity for the 2D Boussinesq and the 3D axisymmetric Euler equations in the presence of boundary with C^(1,α) initial data for the velocity (and density in the case of Boussinesq equations). Our finite time blowup Solution for the 3D Euler equations and the Singular Solution considered in [28,29] share many essential features, including the symmetry properties of the Solution, the flow structure, and the sign of the Solution in each quadrant, except that we use C^(1,α) initial data for the velocity field. We use the method of analysis proposed in our recent joint work with Huang in [5] and the simplification of the Biot-Savart law derived by Elgindi in [11] for C^(1,α) velocity to establish the nonlinear stability of an approximate self-similar profile. The nonlinear stability enables us to prove that the Solution of the 3D Euler equations or the 2D Boussinesq equations with C^(1,α) initial data will develop a finite time Singularity. Moreover, the velocity field has finite energy before the Singularity time

J Rodriguezquintero - One of the best experts on this subject based on the ideXlab platform.

  • ir finiteness of the ghost dressing function from numerical reSolution of the ghost sd equation
    Journal of High Energy Physics, 2008
    Co-Authors: Ph Boucaud, J P Leroy, Le A Yaouanc, J Micheli, O Pene, J Rodriguezquintero
    Abstract:

    We solve numerically the Schwinger-Dyson ghost equation in the Landau gauge for a given, finite at k = 0 gluon propagator (i.e. the infrared exponent of its dressing function, αgluon, is 1) and under the usual assumption of constancy of the ghost-gluon vertex ; we show that there exist two possible types of ghost dressing function Solutions, as we have previously inferred from analytical considerations: one which is Singular at zero momentum (the infrared exponent of its dressing function, αghost, (We shall use αG and αF as shorthands for αgluonand αghost respectively; let us recall that we denote the gluon by a G and the ghost by a F, for ``fantome''.) is <0), satisfies the familiar relation αgluon+2αghost = 0 and has therefore αghost = −1/2, and another one which is finite at the origin with αghost = 0 and violates the relation. It is most important that the type of Solution which is realized depends on the value of the coupling constant. There are regular ones — αF = 0 — for any coupling below some value, while there is only one Singular Solution — αF <0 —, obtained for a single critical value of the coupling. For all momenta k <.5 GeV where they can be trusted, our lattice data exclude neatly the Singular one, and agree very well with the regular Solution we obtain at a coupling constant compatible with the bare lattice value.

  • ir finiteness of the ghost dressing function from numerical reSolution of the ghost sd equation
    arXiv: High Energy Physics - Phenomenology, 2008
    Co-Authors: Ph Boucaud, J P Leroy, Le A Yaouanc, J Micheli, O Pene, J Rodriguezquintero
    Abstract:

    We solve numerically the Schwinger-Dyson (SD hereafter) ghost equation in the Landau gauge for a given gluon propagator finite at k=0 (alpha_gluon=1) and with the usual assumption of constancy of the ghost-gluon vertex ; we show that there exist two possible types of ghost dressing function Solutions, as we have previously inferred from analytical considerations : one Singular at zero momentum, satisfying the familiar relation alpha_gluon+2 alpha_ghost=0 between the infrared exponents of the gluon and ghost dressing functions(in short, respectively alpha_G and alpha_F) and having therefore alpha_ghost=-1/2, and another which is finite at the origin (alpha_ghost=0), which violates the relation. It is most important that the type of Solution which is realized depends on the value of the coupling constant. There are regular ones for any coupling below some value, while there is only one Singular Solution, obtained only at a critical value of the coupling. For all momenta k<1.5 GeV where they can be trusted, our lattice data exclude neatly the Singular one, and agree very well with the regular Solution we obtain at a coupling constant compatible with the bare lattice value.

D. Dini - One of the best experts on this subject based on the ideXlab platform.

  • Sharp Notch Roots; The length scale implicit in the Solution
    2011
    Co-Authors: D.a. Hills, D. Dini
    Abstract:

    Reentrant notches whose internal angle exceeds about 257 o induce two Singular eigenSolutions, from the classical Williams procedure, where the symmetric term is always more strongly Singular than the antisymmetric term. This implies the presence of a length scale within the Singular Solution, and it means that notch root process zones are not self-similar but vary in character according to their size; small ones will be mode-I like, larger ones mode-II like, larger ones still not existing under small scale yielding conditions. Here we explore explicitly within the framework of the Singular Solution (i.e. a semi-infinite notch) the conditions under which mode I type behaviour exists, or mode II behaviour, or the Solution is mixed in character. These general results are then applied to example finite problems, and used to show the range of loads under which pure mode I, small scale yielding Singular behaviour is to be expected. This is of practical relevance because it means that, even if both eigenmodes are excited in a particular example problem, the process zone may practically be considered to be mode I in nature. It is shown that, in each of the example problems examined so far, there is a wide range of conditions where this is so, and this property may be used to simplify the way we treat the effects of sharp corners, whether at notches or at the edges of complete contacts, as characterizers of the local process zone.

  • Characteristics of the process zone at sharp notch roots
    International Journal of Solids and Structures, 2011
    Co-Authors: D.a. Hills, D. Dini
    Abstract:

    AbstractThe classical Williams Solution for the state of stress at the tip of a semi-infinite notch is re-visited and the two-term Singular Solution re-written in a form making the mode mixity and load magnitude explicit. This is used to show that, for a 270° solid angle, the majority of notch problems exhibit a process zone which is entirely or substantially mode I in character, which in turn means that the notch strength may practically be governed by a single elastic parameter. A method for finding the practical limit on the load and stress intensity ratio where this holds is described

Chen Jiajie - One of the best experts on this subject based on the ideXlab platform.

  • Finite Time Blowup of 2D Boussinesq and 3D Euler Equations with C^(1,α) Velocity and Boundary
    'Springer Science and Business Media LLC', 2021
    Co-Authors: Chen Jiajie, Hou, Thomas Y.
    Abstract:

    Inspired by the numerical evidence of a potential 3D Euler Singularity by Luo-Hou [30, 31] and the recent breakthrough by Elgindi [11] on the Singularity formation of the 3D Euler equation without swirl with C^(1,α) initial data for the velocity, we prove the finite time Singularity for the 2D Boussinesq and the 3D axisymmetric Euler equations in the presence of boundary with C^(1,α) initial data for the velocity (and density in the case of Boussinesq equations). Our finite time blowup Solution for the 3D Euler equations and the Singular Solution considered in [30, 31] share many essential features, including the symmetry properties of the Solution, the flow structure, and the sign of the Solution in each quadrant, except that we use C^(1,α) initial data for the velocity field. We use a dynamic rescaling formulation and follow the general framework of analysis developed by Elgindi in [11]. We also use some strategy proposed in our recent joint work with Huang in [7] and adopt several methods of analysis in [11] to establish the linear and nonlinear stability of an approximate self-similar profile. The nonlinear stability enables us to prove that the Solution of the 3D Euler equations or the 2D Boussinesq equations with C^(1,α) initial data will develop a finite time Singularity. Moreover, the velocity field has finite energy before the Singularity time

  • Finite time blowup of 2D Boussinesq and 3D Euler equations with $C^{1,\alpha}$ velocity and boundary
    2021
    Co-Authors: Chen Jiajie, Hou, Thomas Y.
    Abstract:

    Inspired by the numerical evidence of a potential 3D Euler Singularity by Luo-Hou \cite{luo2013potentially-1,luo2013potentially-2} and the recent breakthrough by Elgindi \cite{elgindi2019finite} on the Singularity formation of the 3D Euler equation without swirl with $C^{1,\alpha}$ initial data for the velocity, we prove the finite time Singularity for the 2D Boussinesq and the 3D axisymmetric Euler equations in the presence of boundary with $C^{1,\alpha}$ initial data for the velocity (and density in the case of Boussinesq equations). Our finite time blowup Solution for the 3D Euler equations and the Singular Solution considered in \cite{luo2013potentially-1,luo2013potentially-2} share many essential features, including the symmetry properties of the Solution, the flow structure, and the sign of the Solution in each quadrant, except that we use $C^{1,\alpha}$ initial data for the velocity field. We use a dynamic rescaling formulation and follow the general framework of analysis developed by Elgindi in \cite{elgindi2019finite}. We also use some strategy proposed in our recent joint work with Huang in \cite{chen2019finite} and adopt several methods of analysis in \cite{elgindi2019finite} to establish the linear and nonlinear stability of an approximate self-similar profile. The nonlinear stability enables us to prove that the Solution of the 3D Euler equations or the 2D Boussinesq equations with $C^{1,\alpha}$ initial data will develop a finite time Singularity. Moreover, the velocity field has finite energy before the Singularity time.Comment: Revised introduction. Added motivations and discussions in Sections 5, 9. 82 Page

  • Finite time blowup of 2D Boussinesq and 3D Euler equations with $C^{1,\alpha}$ velocity and boundary
    2019
    Co-Authors: Chen Jiajie, Hou, Thomas Y.
    Abstract:

    Inspired by the recent numerical evidence of a potential 3D Euler Singularity \cite{luo2013potentially-1,luo2013potentially-2}, we prove the finite time Singularity for the 2D Boussinesq and the 3D axisymmetric Euler equations in the presence of boundary with $C^{1,\alpha}$ initial data for the velocity (and density in the case of Boussinesq equations). Our finite time blowup Solution for the 3D Euler equations and the Singular Solution considered in \cite{luo2013potentially-1,luo2013potentially-2} share many essential features, including the symmetry properties of the Solution, the flow structure, and the sign of the Solution in each quadrant, except that we use $C^{1,\alpha}$ initial data for the velocity field. We use the method of analysis proposed in our recent joint work with Huang in \cite{chen2019finite} and the simplification of the Biot-Savart law derived by Elgindi in \cite{elgindi2019finite} for $C^{1,\alpha}$ velocity to establish the nonlinear stability of an approximate self-similar profile. The nonlinear stability enables us to prove that the Solution of the 3D Euler equations or the 2D Boussinesq equations with $C^{1,\alpha}$ initial data will develop a finite time Singularity. Moreover, the velocity field has finite energy before the Singularity time

  • Finite time blowup of 2D Boussinesq and 3D Euler equations with C^(1,α) velocity and boundary
    2019
    Co-Authors: Chen Jiajie, Hou, Thomas Y.
    Abstract:

    Inspired by the recent numerical evidence of a potential 3D Euler Singularity [28, 29], we prove the finite time Singularity for the 2D Boussinesq and the 3D axisymmetric Euler equations in the presence of boundary with C^(1,α) initial data for the velocity (and density in the case of Boussinesq equations). Our finite time blowup Solution for the 3D Euler equations and the Singular Solution considered in [28,29] share many essential features, including the symmetry properties of the Solution, the flow structure, and the sign of the Solution in each quadrant, except that we use C^(1,α) initial data for the velocity field. We use the method of analysis proposed in our recent joint work with Huang in [5] and the simplification of the Biot-Savart law derived by Elgindi in [11] for C^(1,α) velocity to establish the nonlinear stability of an approximate self-similar profile. The nonlinear stability enables us to prove that the Solution of the 3D Euler equations or the 2D Boussinesq equations with C^(1,α) initial data will develop a finite time Singularity. Moreover, the velocity field has finite energy before the Singularity time