Concurrent coupling of atomistic and continuum models at finite temperature

Mathew, Nithin; Picu, Catalin R.; Bloomfield, Max O.

doi:10.1016/j.cma.2010.09.018

Cited by 19 publications

(12 citation statements)

References 21 publications

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“…However, as other authors have suggested [3,4], an approximate separation may be obtained by splitting the frequency spectrum into low and high frequency phonons using a cut-off frequency. This is achieved by monitoring the mechanical component of the relative motion of pairs of atoms.…”

Section: Methodsmentioning

confidence: 99%

Demand‐based coupling of the scales in the finite temperature CADD method

Wurm

Ulz

2019

Proc Appl Math and Mech

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Concurrent finite temperature atomistic-to-continuum models commonly use a fixed time interval coupling of the atomistic and continuum scale. With special focus on the continuum, this means, that its solution fields are updated in fixed intervals of time. However, in times, when the change in the continuum boundary conditions is negligible, these computations are unnecessary. We present the novel idea of a demand-based coupling in this work, in which the continuum solution fields are only updated if needed, to save computational effort. To demonstrate the approach, we apply the coupling to a prototypical representative of the mentioned models, namely the coupled atomistic and discrete dislocation (CADD) model. We test the basic functionality of the approach in a 1-dimensional pulse propagation problem.

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Section: Methodsmentioning

confidence: 99%

Demand‐based coupling of the scales in the finite temperature CADD method

Wurm

Ulz

2019

Proc Appl Math and Mech

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“…Note that the equation of motion given in Equation does not include thermal fluctuation of the atoms. To account for the temperature effect, one can employ the Langevin equation of motion in which a dissipative friction force and a random force due to thermal fluctuation are added to Equation . For a system with a large number of atoms, direct time integration of Equation becomes very expensive.…”

Section: Theorymentioning

confidence: 99%

A multiscale component mode synthesis approach for dynamic analysis of nanostructures

Lan

2012

Numerical Meth Engineering

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SUMMARY A component mode synthesis‐based multiscale approach is developed for dynamic analysis of nanostructures. The multiscale approach decomposes a nanostructure into atomistic and continuum regions and employs vibrational modes to connect the regions of different scales, enabling a reflectionless atomistic‐to‐continuum coupling. Dynamic response of the coupled atomistic and continuum regions is computed concurrently using a common time scale. Numerical results indicate that the multiscale approach has significant condensation and scaling advantages, and it is well suited for modeling and simulation of large and complex systems. Copyright © 2012 John Wiley & Sons, Ltd.

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“…For instance, Karpov et al [80] have developed a concurrent atomistic continuum model by using analytical expressions for Θ and including a random force term to allow the passage of thermal energy between the atomistic and continuum regions. Mathew et al [81] have used a time dependent friction force and a weighted random force to treat thermal fluxes across the atomistic-continuum interface. The common feature in all these methods is the time history kernel function, which is built using different techniques.…”

Section: State Of the Art Of Multiscale Methodsmentioning

confidence: 99%

MD/FE Multiscale Modeling of Contact

Ramisetti

Anciaux

Molinari

2014

Fundamentals of Friction and Wear on the Nanoscale

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Limitations of single scale approaches to study the complex physics involved in friction have motivated the development of multiscale models. We review the state-of-the-art multiscale models that have been developed up to date. These have been successfully applied to a variety of physical problems, but that were limited, in most cases, to zero Kelvin studies. We illustrate some of the technical challenges involved with simulating a frictional sliding problem, which by nature generates a large amount of heat. These challenges can be overcome by a proper usage of spatial filters, which we combine to a direct finite-temperature multiscale approach coupling molecular dynamics with finite elements. The basic building block relies on the proper definition of a scale transfer operator using the least square minimization and spatial filtering. Then, the restitution force from the generalized Langevin equation is modified to perform a two-way thermal coupling between the two models. Numerical examples are shown to illustrate the proposed coupling formulation.

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Concurrent coupling of atomistic and continuum models at finite temperature

Cited by 19 publications

References 21 publications

Demand‐based coupling of the scales in the finite temperature CADD method

Demand‐based coupling of the scales in the finite temperature CADD method

A multiscale component mode synthesis approach for dynamic analysis of nanostructures

MD/FE Multiscale Modeling of Contact

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