Formulation and optimization of the energy-based blended quasicontinuum method

M. Luskin; C. Ortner; B. Van Koten

doi:10.1016/j.cma.2012.09.007

Formulation and optimization of the energy-based blended quasicontinuum method

M. Luskin
, C. Ortner
, B. Van Koten

School of Mathematics

Research output: Contribution to journal › Article › peer-review

36 Scopus citations

Abstract

We formulate an energy-based atomistic-to-continuum coupling method based on blending the quasicontinuum method for the simulation of crystal defects. We utilize theoretical results from Van Koten and Luskin [32] and Ortner and Van Koten [24] to derive optimal choices of approximation parameters (blending function and finite element grid) for microcrack and di-vacancy test problems and confirm our analytical predictions in numerical tests.

Original language	English (US)
Pages (from-to)	160-168
Number of pages	9
Journal	Computer Methods in Applied Mechanics and Engineering
Volume	253
DOIs	https://doi.org/10.1016/j.cma.2012.09.007
State	Published - Jan 1 2013

Bibliographical note

Funding Information:
ML and BVK were supported in part by the NSF PIRE Grant OISE-0967140 , DOE Award DE-SC0002085, AFOSR Award FA9550-12-1-0187, and the University of Minnesota Supercomputing Institute. CO was supported by EPSRC grant EP/H003096 “Analysis of atomistic-to-continuum coupling methods”.

Keywords

Atomistic models
Atomistic-to-continuum coupling
Coarse graining
Quasicontinuum method

Publisher link

10.1016/j.cma.2012.09.007

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title = "Formulation and optimization of the energy-based blended quasicontinuum method",

abstract = "We formulate an energy-based atomistic-to-continuum coupling method based on blending the quasicontinuum method for the simulation of crystal defects. We utilize theoretical results from Van Koten and Luskin [32] and Ortner and Van Koten [24] to derive optimal choices of approximation parameters (blending function and finite element grid) for microcrack and di-vacancy test problems and confirm our analytical predictions in numerical tests.",

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AU - Luskin, M.

AU - Ortner, C.

AU - Van Koten, B.

N1 - Funding Information: ML and BVK were supported in part by the NSF PIRE Grant OISE-0967140 , DOE Award DE-SC0002085, AFOSR Award FA9550-12-1-0187, and the University of Minnesota Supercomputing Institute. CO was supported by EPSRC grant EP/H003096 “Analysis of atomistic-to-continuum coupling methods”.

PY - 2013/1/1

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N2 - We formulate an energy-based atomistic-to-continuum coupling method based on blending the quasicontinuum method for the simulation of crystal defects. We utilize theoretical results from Van Koten and Luskin [32] and Ortner and Van Koten [24] to derive optimal choices of approximation parameters (blending function and finite element grid) for microcrack and di-vacancy test problems and confirm our analytical predictions in numerical tests.

AB - We formulate an energy-based atomistic-to-continuum coupling method based on blending the quasicontinuum method for the simulation of crystal defects. We utilize theoretical results from Van Koten and Luskin [32] and Ortner and Van Koten [24] to derive optimal choices of approximation parameters (blending function and finite element grid) for microcrack and di-vacancy test problems and confirm our analytical predictions in numerical tests.

KW - Atomistic models

KW - Atomistic-to-continuum coupling

KW - Coarse graining

KW - Quasicontinuum method

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DO - 10.1016/j.cma.2012.09.007

M3 - Article

AN - SCOPUS:84868651996

SN - 0045-7825

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SP - 160

EP - 168

JO - Computer Methods in Applied Mechanics and Engineering

JF - Computer Methods in Applied Mechanics and Engineering

ER -

Formulation and optimization of the energy-based blended quasicontinuum method

Abstract

Bibliographical note

Keywords

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