Multipole representation of the elastic field of dislocation ensembles

Wang, Zhiqiang; Ghoniem, N.M.; LeSar, Richard

doi:10.1103/physrevb.69.174102

Cited by 27 publications

(29 citation statements)

References 15 publications

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“…The issue of spatial averaging has been recently dealt with by LeSar and Rickman (2002) and Wang et al (2003b). Starting from the work of Kossevich (1979) on the interaction energy of systems of dislocations, an energy expression in terms of the dislocation density tensor ) is derived.…”

Section: N M Ghoniem Et Almentioning

confidence: 99%

“…Numerical implementation of the multipole expansion for the Peach-Kohler force on a test dislocation separated from a volume containing a dense dislocation aggregate revealed that such a technique is highly accurate and can result in significant coarse graining in current DD simulations. The relative error in the multipole expansion, expressed as j multipole À accurate j= accurate has been tested by Wang et al (2003b). These numerical tests are performed for different sizes (1 mm, 5 mm and 10 mm), different orders of the expansion and different R=h ratios (R being the distance from the centre of the volume to the test dislocation and h being the volume size).…”

Section: N M Ghoniem Et Almentioning

confidence: 99%

“…Starting from the work of Kossevich (1979) on the interaction energy of systems of dislocations, an energy expression in terms of the dislocation density tensor ) is derived. The basic idea in this approach is to divide space into small averaging volumes to calculate the local multipole moments of the dislocation microstructure and then to write the energy (LeSar and Rickman 2002) or the force (Wang et al 2003b) as an expansion over the multipoles. Numerical implementation of the multipole expansion for the Peach-Kohler force on a test dislocation separated from a volume containing a dense dislocation aggregate revealed that such a technique is highly accurate and can result in significant coarse graining in current DD simulations.…”

Section: N M Ghoniem Et Almentioning

confidence: 99%

See 2 more Smart Citations

Multiscale modelling of nanomechanics and micromechanics: an overview

Ghoniem

Busso

Kioussis

et al. 2003

Philosophical Magazine

139

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Recent advances in analytical and computational modelling frameworks to describe the mechanics of materials on scales ranging from the atomistic, through the microstructure or transitional, and up to the continuum are reviewed. It is shown that multiscale modelling of materials approaches relies on a systematic reduction in the degrees of freedom on the natural length scales that can be identified in the material. Connections between such scales are currently achieved either by a parametrization or by a 'zoom-out' or 'coarse-graining' procedure. Issues related to the links between the atomistic scale, nanoscale, microscale and macroscale are discussed, and the parameters required for the information to be transferred between one scale and an upper scale are identified. It is also shown that seamless coupling between length scales has not yet been achieved as a result of two main challenges: firstly, the computational complexity of seamlessly coupled simulations via the coarse-graining approach and, secondly, the inherent difficulty in dealing with system evolution stemming from time scaling, which does not permit coarse graining over temporal events. Starting from the Born-Oppenheimer adiabatic approximation, the problem of solving quantum mechanics equations of motion is first reviewed, with successful applications in the mechanics of nanosystems. Atomic simulation methods (e.g. molecular dynamics, Langevin dynamics and the kinetic Monte Carlo method) and their applications at the nanoscale are then discussed. The role played by dislocation dynamics and statistical mechanics methods in understanding microstructure self-organization, heterogeneous plastic deformation, material instabilities and failure phenomena is also discussed.

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Section: N M Ghoniem Et Almentioning

confidence: 99%

Section: N M Ghoniem Et Almentioning

confidence: 99%

Section: N M Ghoniem Et Almentioning

confidence: 99%

See 1 more Smart Citation

Multiscale modelling of nanomechanics and micromechanics: an overview

Ghoniem

Busso

Kioussis

et al. 2003

Philosophical Magazine

139

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“…Replacing remote segments by a small number of equivalent superdislocations is another [7]. Development of a multipole expansion method is plausible in that it may provide O(N) computations [14]. Despite all these efforts, a maximum plastic strain currently reached is lower than 0.1%.…”

Section: Introductionmentioning

confidence: 98%

Numerical methods to improve the computing efficiency of discrete dislocation dynamics simulations

Shin

Fivel²,

Verdier³

et al. 2006

Journal of Computational Physics

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“…The higher-order derivatives of the radial function r can be calculated by following the recursion formula Based on Equation (12), the higher-order derivatives can be deduced as [41] …”

mentioning

confidence: 99%

Taylor series multipole boundary element‐mathematical programming method for 3D multi‐bodies elastic contact problems

Xiao

Xia

2009

Numerical Meth Engineering

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SUMMARYUtilizing the mathematical programming technique of contact problems and Fast Multipole Boundary Element Method (FM-BEM) theory, Taylor Series Multipole BEM (TSMBEM) for solving 3D multibodies elastic frictional contact problems is presented based on the 'node-to-surface' contact model. The numerical method is able to analyze the large-scale contact problems using non-conforming or conforming boundary meshes. For multi-bodies contact problems, the computational costs of contact identification can be effectively reduced by the contact table. The mathematical programming method for TSMBEM is presented based on the interpolation approach of contact elements. The linear system arising from multipole BEM is solved by using Generalized Minimal RESidual algorithm GMRES(m) in conjunction with near-field preconditioning technique. The numerical experiments of flat punch and HC roll system are carried out by the newly developed multipole BEM. The numerical results are compared with the Hertz theoretical solutions, which illustrate the effectiveness and the validity of the numerical method for 3D multi-bodies elastic frictional contact analysis.

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Multipole representation of the elastic field of dislocation ensembles

Cited by 27 publications

References 15 publications

Multiscale modelling of nanomechanics and micromechanics: an overview

Multiscale modelling of nanomechanics and micromechanics: an overview

Numerical methods to improve the computing efficiency of discrete dislocation dynamics simulations

Taylor series multipole boundary element‐mathematical programming method for 3D multi‐bodies elastic contact problems

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