Spanning the continuum to quantum length scales in a dynamic simulation of brittle fracture

Abraham, Farid F.; Broughton, Jeremy Q.; Bernstein, Noam; Kaxiras, Efthimios

doi:10.1209/epl/i1998-00536-9

Cited by 292 publications

(197 citation statements)

References 12 publications

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“…In contrast to all of the previous theoretical studies of the XYB 14 crystal family, which have used the bulk modulus as an indicator of the bond strength, the approach used here allows for the local bond strength to be investigated on a plane-by-plane basis. Unlike the more sophisticated, multi-scale modeling approaches, which have been deployed to study fracture in polycrystalline diamond, Si, and other metallic systems, [35][36][37][38] the method used here is relatively simple. We believe that our approach can be used to screen prospective structures prior to their being investigated using a more elaborate theoretical technique.…”

mentioning

confidence: 99%

Fracture Strength ofAlLiB14

Wan

Beckman

2012

Phys. Rev. Lett.

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mentioning

confidence: 99%

Fracture Strength ofAlLiB14

Wan

Beckman

2012

Phys. Rev. Lett.

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“…Uniform flows for model (1) are constant equilibrium distributions f = E [ρ]. Because of the function h, f is approximated in the micro-Macro model (19)(20) by non-uniform distributions E[ρ] + g K .…”

Section: Preservation Of Uniform Flowsmentioning

confidence: 99%

Diffusion approximation

Gass¹,

Harris²

2001

Encyclopedia of Operations Research and Management Science

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Abstract.This paper presents a general methodology to design macroscopic fluid models that take into account localized kinetic upscaling effects. The fluid models are solved in the whole domain together with a localized kinetic upscaling that corrects the fluid model wherever it is necessary. This upscaling is obtained by solving a kinetic equation on the non-equilibrium part of the distribution function. This equation is solved only locally and is related to the fluid equation through a downscaling effect. The method does not need to find an interface condition as do usual domain decomposition methods to match fluid and kinetic representations. We show our approach applies to problems that have a hydrodynamic time scale as well as to problems with diffusion time scale. Simple numerical schemes are proposed to discretized our models, and several numerical examples are used to validate the method.

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“…Over the past decade, various methods have been developed to address different problems involving atomistically large material domains [1][2][3][4][5][6][7][8][9][10][11][12]. The most challenging problem in developing these coupled methods is the formulation of a seamless computational connection along an interface between different material representations.…”

Section: Introductionmentioning

confidence: 99%

“…A common feature of many of these approaches [1][2][3][4][5][6][7][8][9][10][11][12] for coupling atomistic and continuum representations is the refinement of the finite element (FE) mesh to atomic length scales to link the kinematics of the FE nodes to that of the discrete atoms along an interface. In this paper, approaches that relate atoms and FE nodes in a one-to-one manner, or through a form of interpolation, will be referred to as direct coupling (DC) approaches.…”

Section: Introductionmentioning

confidence: 99%

An embedded statistical method for coupling molecular dynamics and finite element analyses

Saether

Yamakov

Glaessgen

2009

Numerical Meth Engineering

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SUMMARYThe coupling of molecular dynamics (MD) simulations with finite element methods (FEM) yields computationally efficient models that link fundamental material processes at the atomistic level with continuum field responses at higher length scales. The theoretical challenge involves developing a seamless connection along an interface between two inherently different simulation frameworks. Various specialized methods have been developed to solve particular classes of problems. Many of these methods link the kinematics of individual MD atoms with FEM nodes at their common interface, necessarily requiring that the finite element mesh be refined to atomic resolution. Some of these coupling approaches also require simulations to be carried out at 0 K and restrict modeling to two-dimensional material domains due to difficulties in simulating full threedimensional material processes. In the present work, a new approach to MD-FEM coupling is developed based on a restatement of the standard boundary value problem used to define a coupled domain. The method replaces a direct linkage of individual MD atoms and finite element (FE) nodes with a statistical averaging of atomistic displacements in local atomic volumes associated with each FE node in an interface region. The FEM and MD computational systems are effectively independent and communicate only through an iterative update of their boundary conditions. With the use of statistical averages of the atomistic quantities to couple the two computational schemes, the developed approach is referred to as an embedded statistical coupling method (ESCM). ESCM provides an enhanced coupling methodology that is inherently applicable to three-dimensional domains, avoids discretization of the continuum model to atomic scale resolution, and permits finite temperature states to be applied.

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Spanning the continuum to quantum length scales in a dynamic simulation of brittle fracture

Cited by 292 publications

References 12 publications

Fracture Strength ofAlLiB14

Fracture Strength ofAlLiB14

Diffusion approximation

An embedded statistical method for coupling molecular dynamics and finite element analyses

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